Int. Journal of Renewable Energy Development 7 (2) 2018: 139-150
P a g e | 139

Contents list available at IJRED website

Int. Journal of Renewable Energy Development (IJRED)
Journal homepage: http://ejournal.undip.ac.id/index.php/ijred
Research Article

The Use of Odd and Even Class Wind Speed Time Series of
Distribution Histogram to Estimate Weibull Parameters
Adekunlé Akim Salami a,*, Ayité Sénah Akoda Ajavon a, Mawugno Koffi Kodjo a,
Seydou Ouedraogo b and Koffi-Sa Bédja a
a

Equipe de Recherche en Sciences de l’Ingénieur (ERSI), Department of Electrical Engineering, Ecole Nationale Supérieure d’Ingénieurs
(ENSI), University of Lomé, BP 1515, Lomé, Togo
b

Polytechnic University of bobo-Dioulasso, Burkina-Faso

ABSTRACT. In this article, we introduced a new approach based on graphical method (GPM), maximum likelihood method (MLM),
energy pattern factor method (EPFM), empirical method of Justus (EMJ), empirical method of Lysen (EML) and moment method
(MOM) using the even or odd classes of wind speed series distribution histogram with 1 m/s as bin size to estimate the Weibull
parameters. This new approach is compared on the basis of the resulting mean wind speed and its standard deviation using seven
reliable statistical indicators (RPE, RMSE, MAPE, MABE, R2, RRMSE and IA). The results indicate that this new approach is adequate
to estimate Weibull parameters and can outperform GPM, MLM, EPF, EMJ, EML and MOM which uses all wind speed time series data
collected for one period. The study has also found a linear relationship between the Weibull parameters K and C estimated by MLM,
EPFM, EMJ, EML and MOM using odd or even class wind speed time series and those obtained by applying these methods to all class
(both even and odd bins) wind speed time series. Another interesting feature of this approach is the data size reduction which
eventually leads to a reduced processing time.
Keywords: Odd bin wind speed time series, Even bin wind speed time series, Weibull parameters, Statistical analysis, Comparative evaluation.
Article History: Received February 16th 2018; Received in revised form May 5th 2018; Accepted May 27th 2018; Available online
How to Cite This Article: Salami, A.A., Ajavon, A.S.A., Kodjo, M.K. , Ouedraogo, S. and Bédja, K. (2018) The Use of Odd and Even Class Wind
Speed Time Series of Distribution Histogram to Estimate Weibull Parameters. Int. Journal of Renewable Energy Development 7(2), 139-150.
https://doi.org/10.14710/ijred.7.2.139-150

1.

Introduction

In the last century, several climate changes have
been observed in regions all over the world. The main
cause of these climatic changes is the rise in fossil fuel
use, which is due to the important demographic and
industrial developments. These negative effects have
forced scientists to draw attention to renewable energy
sources such as solar, wind and hydraulic energy, which
are the most suitable solution in the future (Dahmouni et
al. 2011). Recently, interest in wind energy has been
growing and many researchers have attempted to
develop and to perform reliable wind energy conversion
systems.
Wind energy conversion systems design required
considerable efforts in recognizing a suitable statistical
model for wind speed frequency distribution. The widely
used function to model wind speed data is the Weibull
distribution function(Celik, 2004). Recently it has become
a reference distribution function in commercially used
wind energy software i-e the Wind Atlas Analysis and
Application Program (Sahin, 2004). We characterized the
Weibull distribution by two parameters, a scale and a
shape parameter (C and K) (Salami et al., 2016).

*

To estimate Weibull parameters several methods
have been suggested in the literature, such as the
graphical method (GPM), the maximum likelihood
method (MLM), the moment method (MOM), the
empirical method of Justus (EMJ), the empirical method
of Lysen (EML), the method of the modified maximum
likelihood (MMLM), the equivalent energy method
(EQM)(Rocha et al., 2012) and the energy pattern factor
method (EPFM) (Kasra et al., 2016).
To estimate Weibull parameters for a site using the
methods frequently used and cited above, the wind speed
time series data collected in an interval of one (1) hour in
a given period are used (Garcia et al., 1998). The recent
works of (Yuan et al., 2015) aims to compare the
performance of the MLM and the MOM. The results
show that for an extreme small data size, the MLM
slightly outperforms the MOM and generally, the MLM
has an advantage over medium and large data sizes. In
conclusion, for life data analysis, it is suggested to use
MLM for the two-parameter Weibull distribution. Given
that, wind speed distribution is used in estimating
Weilbull parameters; we argue that it is possible to
reduce the length of the input series through filtering. A
reduced data size will lead to higher computational
efficiency in estimating Weibull parameters and key

Corresponding author: akim_salami@yahoo.fr

© IJRED – ISSN: 2252-4940, July 15th 2018, All rights reserved

Citation: Salami, A.A., Ajavon, A.S.A., Kodjo, M.K., Ouedraogo, S. and Bédja, K. (2018), The Use of Odd and Even Class Wind Speed Time Series of Distribution
Histogram to Estimate Weibull Parameters. Int. Journal of Renewable Energy Development, 7(2), 139-150, doi.org/10.14710/ijred.7.2.139-150

P a g e | 140
wind site characteristics such us mean wind speed and
wind speed standard deviation. The main question to
address is what filtering to perform in order to achieve
this much-desired computational efficiency while
maintaining acceptable estimation accuracy? To the best
of our knowledge, no existing work proposed a filtering
method that allies accuracy and efficiency for Weibull
parameter estimation in wind energy applications. This
paper proposes the following contributions.
In order to reduce data size and therefore parameter
estimation time, while maintaining a high accuracy of
mean wind speed and standard deviation, a new
approach is proposed. Indeed, the series of wind speed is
grouped in classes (or bins), each class being represented
by a bin in the distribution histogram. The set of classes
is divided into two subsets: even and odd order speed
classes. In this paper, we aim to adequately determine
the overall Weibull parameters (K and C) using those
estimated for the subsets of odd and even speed classes.
For each subset, the Weibull parameters are estimated
using six well known methods namely graphical method
(GPM), empirical method of Justus (EMJ), empirical
method of Lysen (EML), energy pattern factor method
(EPFM), maximum likelihood method (MLM) and
moment method (MOM). So in this article eighteen
methods are used to estimate Weibull parameters for a
given period at a geographic locality, these are:
•
GPM, EMJ, EML, EPFM, MLM, MOM using all
bins wind speed time series;
•
GPM, EMJ, EML, EPFM, MLM, MOM using
Odd Bins wind speed time series (GPOBM,
EMJOB,
EMLOB,
EPFOBM,
MLOBM,
MOOBM);
•
GPM, EMJ, EML, EPFM, MLM, MOM using
Even Bins wind speed time series (GPEBM,
EMJEB,
EMLEB,
EPFEBM,
MLEBM,
MOEBM).
Consequently, in this study the capability of eighteen
parameter estimation methods is evaluated to calculate
the K and C parameters for adjusting the Weibull
distribution of wind speeds. The main goal is identifying
the most appropriate method for computing the mean
and standard deviation at two sites (Lomé in Togo and
Ouagadougou in Burkina Faso). To achieve this, a
comprehensive statistical analysis based upon several
statistical parameters and approaches is conducted using
the eighteen parameter estimation methods.
The rest of this paper is structured as follows. Section
2 describes numerical methods for determining the
Weibull parameters. Section 3 presents in detail the
proposed approaches to estimate Weibull parameters. In
Section 4, statistical indicators for performance
evaluation are illustrated. The results and discussions
along with the underlying case study data are presented
in Section 5. Finally, conclusions are drawn in Section 6.
2. Numerical Methods for determining the Weibull
parameters
Wind speed is a random variable, and to determine
the wind potential of a region it is necessary to use
statistical analysis (Salami et al., 2013). This requires
the existence of time series records of wind speed.
Such records are the wind data. Based on the wind
speed data collected, the Weibull distribution can be
described as a probability density function f(V) and a

cumulative distribution function F(V) are respectively
determined by Eqs. (1) and (2) (Ahmed, 2013):
æ K öæV ö
÷ç ÷
è C øè C ø

f (V ) = ç

æ

K-1

é æ V öK ù
÷ ú
êë è C ø úû

(1)

exp ê- ç

é æ V öK ù ö
÷ ú÷
C ø ú÷
ëê è
ûø

(2)

F (V ) = ç1- exp ê- ç

ç
è

The mean and standard deviation of the wind speed
series are given by Eq. (3). and Eq. (4).

V=

1 n
æ 1ö
å Vi = CΓ ç1+ ÷
n i=1
è Kø
1

(3)

1

é æ 2 ö 2 æ 1 öù 2
é 1 n
ù 2
å Vi - V ú = C ê Γ ç1+ ÷ - Γ ç1+ ÷ ú
ë n - 1 i=1
û
è K øû
ë è Kø

σ=ê

(

)

(4)

where: C and K are respectively scale and shape
parameters of the Weibull distribution function and G
represents the gamma function defined by the Euler
integral of the second kind.
Wind power density is an important indicator for
determining the potential of wind resources and to
describe the amount of wind energy at various wind
speeds at a particular location. Knowledge of wind power
density is also useful to evaluate the performance of wind
turbines and select the optimum wind turbines. Wind
power density resembles the level of accessible energy at
the site which can be converted to electricity by wind
turbines. Indeed, the mean kinetic energy, available at a
site per unit of time and per unit area is expressed by Eq.
(5) (Seguro et al., 2000):

1 +∞
1
1
æ 3ö
P = r ò V 3 f(V)dV = rV 3 = rC 3 Γ ç1+ ÷
2 0
2
2
è Kø
where:
•
•
•

(5)

r is air density (kg m-3),
V is wind speed
f(V) is the Weibull probability distribution
function (pdf) (Eq. 1),

•
V 3 is the cubic mean wind speed.
There are some methods introduced in the literature
(Dinler et al., 2009) to calculate the K and C parameters
of the Weibull distribution function. In this study, six
methods: graphical method (GPM), empirical method of
Justus (EMJ), empirical method of Lysen (EML), energy
pattern factor method (EPFM), maximum likelihood
method (MLM) and moment method (MOM) frequently
used to compute the K and C parameters are selected for
comparative evaluation. The descriptions of these six
methods are provided briefly in what follows.

2.1. Graphical method (GPM)
The graphical method is achieved through the
cumulative distribution function. In this distribution
method, wind speed data are interpolated by a straight
line, using the concept of least squares. The equation for

© IJRED – ISSN: 2252-4940, July 15th 2018, All rights reserved

Int. Journal of Renewable Energy Development 7 (2) 2018: 139-150
P a g e | 141
this method can be represented by a double logarithmic
transformation (Rocha et al., 2012) as follows,

{

}

ln -ln [1- F(V)] = Kln(V) - Kln(C)

(6)

-1
éé n
ù é n
ùù
K
ê ê å Vi ln(Vi ) ú ê å ln(Vi ) ú ú
K = ê ê i=1 n
ú - ê i=1
úú
n
êê
K
ú ê
úú
Vi
å
ê ëê
ú
ê
i=1
û
ë
ûú úû
ë

(12)

1

2.2. Empirical method of Justus (EMJ)
Based on the empirical method introduced by Justus, the
K and C parameters are computed, respectively by Eq.
(7) and Eq. (8)(Kasra et al., 2016):

K
é n
K ù
V
å
i ú
ê
C = ê i=1
ú
ê n ú
ëê
ûú

(13)

-1.086

æσ ö
K =ç ÷
èV ø
C=

V

2.6. Moment method (MOM)

(8)

The moment method can be used as an alternative to the
maximum likelihood method and, in this case, the
parameters K and C are respectively determined by Eq.
(14) and Eq. (15) (Mostafaeipour et al. 2011).

1 ö
æ
Γ ç 1+
÷
K
è
ø

where:
•
•
•

(7)

V is the mean wind speed,

s is the standard deviation of the observed
data,
Γ(x) is the gamma function.

1 ö
æ
V = CΓ ç 1+
÷
K
è
ø

(14)

1

2
1 öù 2
é
æ
σ = C ê Γ(1+
) - Γ 2 ç 1+
÷
K
K øú
è
ë
û

(15)

2.3. Empirical method of Lysen (EML)
In the empirical method suggested by Lysen, K is
calculated by Eq. (7) same as the Justus method. In fact,
the only difference is the equation of C. In the empirical
method of Lysen, C is obtained by Eq. (9) (Kasra et al.,
2016):
-1

0.433 ö K
æ
C = V ç 0.568 +
÷
K ø
è

(9)

3. Proposed approaches to Weibull parameter
estimation
The information contained in the wind measurements at
a given site can be represented as a histogram. Given
( V1 , V2 , V3 , , Vr ), r wind speeds measured at a site, this
sequence can be grouped into m ( m £ r ) classes
( Bin 0 , Bin1 , Bin 2 , , Bin m-1 ); let f j, be the relative
frequency of class Bin j , the graph (Bin j ´ f j, ) represents

2.4. Energy pattern factor method (EPFM)
The energy pattern factor method is related to the
averaged data of wind speed and is defined by the
following equations (Kasra et al., 2016):

æV3 ö
E pf = ç 3 ÷
çV ÷
è
ø

(10)

æ
ö
3.69 ÷
K = ç 1+
ç
E pf 2 ÷
è
ø

(11)

the histogram of the distribution of relative frequencies
of wind speed at this site.
Thus, for all n samples of wind measurements
( V1 , V2 , V3 , ,Vn ) obtained during a period of time at a
given site, the application of the 6 selected methods
(GPM, MLM, EPFM, EMJ, EML and MOM) gives the
shape K and scale C parameters of the Weibull.
In order to reduce the number of data to be processed
while maintaining accurate standard deviation and mean
wind speed, all samples of n wind measurements
( V1 , V2 , V3 , ,Vn ) obtained during a period of time at a
given site are grouped into classes and represented as a
histogram (the graph (Bin j ´ f j, ) ). The obtained wind
speed classes can be divided into two groups: the group of
even speed classes ( Bin 2k ) and the group of odd classes

and parameter C is also computed similarly as in the
empirical method of Justus by Equation (8).

( Bin 2k +1 ).

2.5. Maximum likelihood method (MLM)

( X1 , X2 , X3 ,

The maximum likelihood estimation method is difficult to
solve, since numerical iterations are needed to determine
the parameters of the Weibull distribution (Kidmo et al.
2015). In this method, the parameters K and C are
determined according to the equations below:

Samples

of

p

wind

speed

measurements

, Xp ) of the group of even classes group

( Bin 2k ), subsets of ( V1 , V2 , V3 , ,Vn ), are used to estimate
the shape parameter K and scale parameter C using 6
selected methods. So this new approach is referred to as:
•
graphical with Even Bin time series method
(GPEBM) when GPM is used;

© IJRED – ISSN: 2252-4940, July 15th 2018, All rights reserved

Citation: Salami, A.A., Ajavon, A.S.A., Kodjo, M.K., Ouedraogo, S. and Bédja, K. (2018), The Use of Odd and Even Class Wind Speed Time Series of Distribution
Histogram to Estimate Weibull Parameters. Int. Journal of Renewable Energy Development, 7(2), 139-150, doi.org/10.14710/ijred.7.2.139-150

P a g e | 142
•
•
•
•
•

maximum likelihood with Even Bin time series
method (MLEBM) when MLM is used;
energy pattern factor with Even Bin time series
method (EPFEBM) when EPFM is used;
empirical method of Justus with Even Bin time
series (EMJEB) when EMJ is used;
empirical method of Lysen with Even Bin time
series (EMLEB) when EML is used;
moment with Even Bin time series method
(MOEBM) when MOM is used.

Likewise,
( Y1 , Y2 , Y3 ,

samples

of

q

wind

measurements

,Yq ) of the group of odd classes ( Bin 2k +1 ),

subsets of ( V1 , V2 , V3 , ,Vn ), are used to estimate K and C
(shape and scale parameters) using 6 selected methods.
So this new approach is referred to as:
•
graphical with Odd Bin time series method
(GPOBM) when GPM is used;
•
maximum likelihood with Odd Bin time series
method (MLOBM) when MLM is used;
•
energy pattern factor with Odd Bin time series
method (EPFOBM) when EPFM is used;
•
empirical method of Justus Odd Bin time series
(EMJOB) when EMJ is used;
•
empirical method of Lysen Odd Bin time series
(EMLOB) when EML is used;
•
moment with Odd Bin time series method
(MOOBM) when MOM is used.
Thus, this study aims to verify if, from each speed
class group (even or odd) taken individually; it is possible
to estimate the parameters (K and C) suitable for an
accurate estimation of the mean wind speed and
standard deviation at the Lomé and Ouagadougou sites.
4. Statistical indicators used for performance
evaluation
To assess the performance of the eighteen parameter
estimation methods of the Weibull distribution for
estimating mean wind speed and standard deviation,
different statistical approaches including seven reliable
statistical indicators (Legates et al., 1999) have been
used in this study. Several statistical parameters
including relative percentage error (RPE), mean absolute
percentage error (MAPE), mean absolute bias error
(MABE), root mean square error (RMSE), relative root
mean square error (RRMSE), correlation coefficient (R2)
and index of agreement (IA) (Kasra et al., 2016) along
with some other statistical tools have been utilized to
offer an appropriate comparative assessment. In the
following, a brief description of the considered statistical
parameters is offered
4.1. Relative percentage error (RPE)
The RPE shows the percentage deviation between the
calculated wind speed and standard deviation from the
Weibull function xi and those obtained by measured
values yi and its values ranging between -10% and +10%
which are usually considered acceptable. RPE is defined
as:

æ y -x ö
RPE(%) =100 × ç i i ÷
ç y
÷
i ø
è

(16)

where:
•
N is the number of observations,
•
yi is the measured values,
•

x i is the predicted values.

4.2. Mean absolute percentage error (MAPE)
The MAPE shows the mean absolute percentage
difference between the computed mean wind speed and
standard deviation using the Weibull function and those
attained by measured values. The MAPE is calculated by
Eq. (17):

MAPE =

1 N yi - x i
×100
å
N i=1 y i

(17)

4.3. Mean absolute bias error (MABE)
The MABE represents the average quantity of total
absolute bias errors between the calculated mean wind
speed and standard deviation by Weibull function and
those obtained by measured values. The MABE is defined
by Eq. (18):

MABE =

1 N
å y -x
N i=1 i i

(18)

4.4. Root mean square error (RMSE)
The RMSE identifies model accuracy by comparing the
deviation between the values achieved by the Weibull
function and those of measured data. The RMSE has
always a positive value and it is calculated using Eq.
(19):

RMSE =

2
1 N
å ( yi - x i )
N i=1

(19)

4.5. Relative root means square error (RRMSE)
The RRMSE is obtained by dividing the RMSE by the
average of mean wind speed and standard deviation
obtained by measured values as follows:

RRMSE(%) =

2
1 N
å ( yi - x i )
N i=1
×100
1 N
å y
N i=1 i

(20)

Different ranges of RRMSE can be defined to
represent the precision of the model as (Legates et al.,
1999):
•
Excellent for RRMSE < 10%;
•
Good for 10% < RRMSE < 20%;
•
Fair for 20% < RRMSE < 30%;
•
Poor for RRMSE > 30%.
4.6. Correlation coefficient (R2)
The R2 which indicates the strength of the linear
relationship between the calculated mean wind speed

© IJRED – ISSN: 2252-4940, July 15th 2018, All rights reserved

Int. Journal of Renewable Energy Development 7 (2) 2018: 139-150
P a g e | 143
and standard deviation by the Weibull function and those
computed using measured values is calculated by Eq.
(21):

å ( x i - x i )( y i - y i )
N

R2 =

(21)

i=1

å ( x i - x i ) å ( yi - yi )
N

2 N

i=1

i=1

2

4.7 Index of agreement (IA)
The IA generally shows the degree of precision of the
predicted values compared to the measured values. The
IA which varies from 0 to 1 is calculated by Eq. (22):

IA =

(

N
å y - xi
i=1 i

N
å x - x i + yi - yi
i=1 i

(22)

)

5. Results and discussion
5.1 Case study and wind speed data
The data for the two sites, Lomé in Togo and
Ouagadougou in Burkina Faso were chosen for this study
because several wind energy projects have become a
necessity in both countries.
The demand for electricity in Togo continues to
increase at an average rate of 8% per year and could
double in the next 10 years. The country's electricity
supply is heavily dependent on oil and its derivative
products (including natural gas), which are subject to
international price volatility (Kimatu et al., 2011) . Togo
is ranked among the quiet areas although transient
spikes wind speed can reach high values up to 4m/s in
some areas especially in the northern part of the country
during the harmattan period. Only the coastal area of the
country has favorable evidence with wind speeds of 3 m/s
on average. The development of wind power can be
considered as a viable alternative. A project of two wind
farms of 12 MW each located near Lomé is undergoing by
a private company named Eco Delta Development (EDD)
and its subsidiary Delta Wind Togo.
In Burkina Faso, renewable energy concerns mainly
the use of the wood fuel. Indeed, at household level in
peri-urban and rural areas, biomass is the primary
energy source for cooking. Due to accelerating
urbanization in recent decades, services in peri-urban
areas are collapsing under the strain of rapid
development, resulting in uncontrolled sanitation
problems and household energy insecurity. However, the
further development of renewable energy technologies is
only marginally supported by the government, despite its
significant potential (Al-Mulali et al., 2012). Due to the
western location of Burkina Faso, the potential for wind
power is very limited. The average wind speed ranges
between 1 and 3 m/s, with the maximum only obtained in

the North. However, small-scale generators at suitable
sites for selective purposes (e.g. water pumping,
desalination systems etc.) might be feasible(Bugaje,
2006). Hourly mean wind speed data used for Lomé and
Ouagadougou were obtained from the meteorological
database at
http://weather.uwyo.edu/area/meteorogram/’.
The coordinates of the two sites in our case study are
given in Table 1. The data is recorded every day at one
hour intervals (this is the mean over the 10 minutes
before the hour) at a height of 10 m above the ground.
Table 1
Coordinates of the case study sites
Sites
Lomé
Ouagadougou

Coordinates
6.17N, 1.25E, 25 meters
12.35N, 1.52 °W, 306 meters

Data collected cover the period, from January 2004 to
December 2015 for the Lomé site (record length of
approximately twelve (12) years) and from January 2009
to December 2015 for the Ouagadougou site (record
length of approximately seven (7) years).
Using the methodology described earlier, we processed
the 10-minute averaged hourly wind speed data collected
at the Lomé and Ouagadougou sites. In order to assess
the performance of our proposed approach, it is
important to apply it over several periods. Given the
importance of the analysis of monthly variations of wind
characteristics at a given site, our case study covers each
month (the entire dataset is grouped monthly into 12
study periods: January, February, March, April, May,
June, July, August, September, October, November,
December), each month of each year and the aggregate
for the whole year. As the data collected at the Lomé site
covers a period from January 2004 to December 2015, the
total number of periods of the study is 157 for the Lomé
site. Total study periods considered for the Ouagadougou
site is 97, since the data collected on this site covers a
period from January 2009 to December 2015. For each
given period and each of the two sites considered, we
classified wind speeds in bins of size 1 m/s each according
to Table 2.
For each period and each site, the results are
presented and analyzed. Table 3 and 4 present some
descriptive statistics including maximum, mean,
standard deviation, skewness and kurtosis of the used
wind speed data at the two sites for even, odd and all
classes of wind speed data subset.
Table 2
Wind speed classes adopted for the two sites.
Wind speed (m/s)
Bins
]0, 1[
Bin0
[1, 2[
Bin1
[2, 3[
Bin2
…
…
…
…
]21, 22[
Bin21

© IJRED – ISSN: 2252-4940, July 15th 2018, All rights reserved

Type
Even bin
Odd bin
Even bin
…
…
Odd bin

Citation: Salami, A.A., Ajavon, A.S.A., Kodjo, M.K., Ouedraogo, S. and Bédja, K. (2018), The Use of Odd and Even Class Wind Speed Time Series of Distribution
Histogram to Estimate Weibull Parameters. Int. Journal of Renewable Energy Development, 7(2), 139-150, doi.org/10.14710/ijred.7.2.139-150

P a g e | 144
Table 3
Descriptive statistics of the used wind speed data according to wind speed classes for the Lomé site 2004-2015.
Wind speed
classes (Bins)
All
Odd
Even

Rel. Freq.
(%)
100
51.46085
48.53915

Max.
(m/s)
16
13
16

Mean
(m/s)
3.52870
3.52034
3.53756

Std. Dev.
(m/s)
2.02964
2.03017
2.02906

Kurt.
2.33358
2.19198
2.48615

Skew.
0.26247
0.32246
0.19880

Table 4
Descriptive statistics of the used wind speed data according to wind speed classes for the Ouagadougou site 2009-2015
Wind speed
classes (Bins)
All
Odd
Even

Max.
(m/s)
22
15
22

Rel. Freq. (%)
100
49.59290
50.40710

Mean
(m/s)
2.99562
3.06272
2.92961

The mean wind speed and standard deviation are
similar for all three data classes considered for each site.
This is a preliminary indication that the Weibull
parameters estimated from either even or odd class speed
data subset might yield similar mean wind speed and
standard deviation as the entire dataset (all class data).
As noticed, Lomé has the highest mean wind speed of
3.5287 m/s and Ouagadougou has the lowest wind speed
of 2.99562 m/s. Moreover, for the Ouagadougou site, the
coefficient of Kurtosis is significantly higher than the
Lomé site.
Hitogram of wind speed

(Lome site)

0.35
All Bins
Odd Bins
Even Bins

0.3

Frequency

0.25

0.2

0.15

0.1

0.05

0
-2

0

2

4

6
8
10
Wind speed (m/s)

12

14

16

18

Fig. 1. Histograms of wind speed data according to the wind
speed classes at the Lomé site.
Hitogram of wind speed

Std. Dev.
(m/s)
1.66267
1.63272
1.68904

(Ouagadougou site)

Mean wind speed (Lome site)

Frequency

0.5

0.4

0.3

0.2

0.1

0

5

10
Wind speed (m/s)

15

20

25

Fig. 2
Histograms of wind speed data according to the wind
speed classes at the Ouagadougou site.

Calculated by odd or Even Bins measured data (m/s)

5.5
All Bins
Odd Bins
Even Bins

0.6

Skew.
0.78947
0.79136
0.79843

Fig. 1 and Fig. 2 show the probability densities of the
utilized wind speed data according to the wind speed
classes for two selected sites, respectively.
Also in order to show that the Weibull parameters
can be estimated from even or odd class wind speed data
for the periods considered at a site, we checked if there is
a linear correlation between all class wind speed data
characteristics (means and standard deviations of wind
speed time series for chosen periods) calculated, and even
or odd class wind speed data characteristics (means and
standard deviations of wind speed time series for chosen
periods) calculated.
The results in Fig. 3 and Fig. 4, show that there is:
• a strong linear correlation (R2 = 0.95735) between the
means of wind speed time series calculated
considering all class data and the means of wind
speed time series calculated considering the even
class data first, against a linear correlation (R2 =
0.80231) considering odd class data when the data
collected at the Lomé site are used;
• a strong linear correlation (R2 = 0.98234) between the
means of wind speed time series calculated
considering all class data and the means of wind
speed time series calculated considering the even
class data first, against a linear correlation ( R2 =
0.9705) considering odd class data when the data
collected at the Ouagadougou site are used.

0.7

0
-5

Kurt.
4.59290
4.40914
4.76355

Y=X
All Bins vs. Odd Bins : R× = 0.80231
All Bins vs. Even Bins : R× = 0.95735

5
4.5
4
3.5
3
2.5
2
1.5

2

2.5

3
3.5
4
4.5
Calculated by all measured data (m/s)

5

5.5

Fig. 3
Scatter plots of computed mean wind speed values
using all bin time series versus those computed using even bin
or odd bin wind speed time series for Lomé.

© IJRED – ISSN: 2252-4940, July 15th 2018, All rights reserved

Int. Journal of Renewable Energy Development 7 (2) 2018: 139-150
P a g e | 145
Standard deviation (Ouagadougou site)

Mean wind speed (Ouagadougou site)

2.5

Y=X
All Bins vs. Odd Bins : R× = 0.9705
All Bins vs. Even Bins : R× = 0.98234

3.8

Calculated by odd or Even Bins measured data (m/s)

Calculated by odd or Even Bins measured data (m/s)

4

3.6
3.4
3.2
3
2.8
2.6
2.4
2.2
2

2

2.2

2.4

2.6
2.8
3
3.2
3.4
3.6
Calculated by all measured data (m/s)

3.8

Y=X
All Bins vs. Odd Bins : R×= 0.93225
All Bins vs. Even Bins : R×= 0.96961

2

1.5

4

Fig. 4
Scatter plots of computed mean wind speed values
using all bin time series versus those computed using even bin
or odd bin wind speed time series for Ouagadougou.

From the results of Fig. 5 and Fig. 6, we note that
there is:
• a strong linear correlation (R2 = 0.95469) between the
standard deviations of wind speed time series
calculated considering all class data and standard
deviations of wind speed time series calculated
considering the even class data first, against low
linear correlation (R2 = 0.23878) considering odd
class data when the data collected at the Lomé site
are used;
• a strong linear correlation (R2 = 0.96961) between the
standard deviations of wind speed time series
calculated considering all class data and standard
deviations of wind speed time series calculated
considering the even class data first, against a linear
correlation (R2 = 0.93225) considering odd class data
when the data collected at the Ouagadougou site are
used.

1

1.3

1.4

1.5
1.6
1.7
1.8
1.9
Calculated by all measured data (m/s)

2

2.1

Fig. 6
Scatter plots of computed wind speed standard
deviation values using all bin time series versus those computed
using even bin or odd bin wind speed time series for
Ouagadougou.

5.2 Fitting histogram to Weibull functions
Our goal in this article is to identify the most appropriate
method for fitting wind speed probability distribution
histograms for wind energy applications at two sites:
Lomé (Togo) and Ouagadougou (Burkina Faso). From
Fig. 7 and Fig. 8 it is possible to verify how the curves
representing the Weibull probability density function, for
each of the eighteen numerical methods considered in the
analysis, match the histograms, giving an idea of which
method yields the best fit to the data of wind speed
collected.
Hitogram of wind speed

(Lome site)

0.35
All Bins
GPM
GPOBM
GPEBM
MLM
MLOBM
MLEBM
EPFM
EPFOBM
EPFEBM
EMJ
EMJOB
EMJEB
EML
EMLOB
EMLEB
MOM
MOOBM
MOEBM

0.3

Standard deviation (Lome site)

2.6

0.25

Probability

Calculated by odd or Even Bins measured data (m/s)

2.8
Y=X
All Bins vs. Odd Bins : R×= 0.23878
All Bins vs. Even Bins : R×= 0.95469

2.4

0.15

0.05

2

0
-2

1.8

0

2

4

6
8
10
Wind speed (m/s)

12

14

16

18

Fig. 7
Weibull distribution functions for the Lomé site (years
2004-2015).

1.6

1.4
1.4

0.2

0.1

2.2

2.2

1.6

1.8
2
2.2
2.4
Calculated by all measured data (m/s)

2.6

2.8

Fig. 5
Scatter plots of computed wind speed standard
deviation values using all bin time series versus those computed
using even bin or odd bin wind speed time series for Lomé.

From the results of Figs. 3, 4, 5 and 6, we can hope
that we can estimate the Weibull parameters at two (02)
study Sites by using only odd or even bin wind speed
time series. This is true when we use the moment
method which consists in solving equations of the mean
(Eq. 14) and standard deviation (Eq. 5).

Graphically, it is observed that, all methods present a
better curve fit with the histogram of wind speed at the
two sites, excepted GPM, GPOBM and GPEBM.
To choose an adequate method that better adjusts the
wind speed histogram at each site, we calculated the
RMSE and R2. The results in Tables 5 and 6 show that:
• at the Lomé site, only five methods (MLOBM,
EMLEB, EMJEB, EML and EMJ) have RMSE lower
and equal to 0.0200 and R2 which is above 0.9665; the
adequate method is MLOBM;
• on Ouagadougou site, only five methods (MLM,
EMJOB, EMLOB, MLOBM, and EPFOBM) have

© IJRED – ISSN: 2252-4940, July 15th 2018, All rights reserved

Citation: Salami, A.A., Ajavon, A.S.A., Kodjo, M.K., Ouedraogo, S. and Bédja, K. (2018), The Use of Odd and Even Class Wind Speed Time Series of Distribution
Histogram to Estimate Weibull Parameters. Int. Journal of Renewable Energy Development, 7(2), 139-150, doi.org/10.14710/ijred.7.2.139-150

P a g e | 146
Hitogram of wind speed

All Bins
GPM
GPOBM
GPEBM
MLM
MLOBM
MLEBM
EPFM
EPFOBM
EPFEBM
EMJ
EMJOB
EMJEB
EML
EMLOB
EMLEB
MOM
MOOBM
MOEBM

0.3

0.25

0.2

0.15

0.1

0.05

0
-5

0

5

R2
0.90607
0.80298
0.88165
0.96206
0.96612
0.92621
0.96515
0.96518
0.96503
0.96619
0.96590
0.96647
0.96628
0.96600
0.96656
0.96510
0.96514
0.96497

Table 6
Statistical analysis of Weibull parameters estimated for the Ouagadougou site (years 2009-2015).
K
1.56205
1.37146
1.43075
2.10118
1.97528
2.24057
1.87026
1.94847
1.79813
1.89527
1.98012
1.81861
1.89527
1.98012
1.81861
1.87126
1.95747
1.80013

C
2.91854
2.33153
2.42168
3.53456
3.46123
3.61116
3.37404
3.45396
3.29417
3.37560
3.45524
3.29592
3.37781
3.45727
3.29826
3.37404
3.45431
3.29426

10
Wind speed (m/s)

15

20

25

Fig. 8
Weibull distribution functions for the Ouagadougou
site (years 2009-2015).

Table 5
Statistical analysis of Weibull parameters estimated for the Lomé site (years 2004-2016).
Methods
K
C
RMSE
GPM
1.89612
3.24713
0.04074
GPOBM
1.56804
2.58127
0.05951
GPEBM
1.99766
3.11241
0.04805
MLM
2.03100
4.17884
0.02134
MLOBM
1.79134
3.96250
0.01967
MLEBM
2.38769
4.41967
0.03054
EPFM
1.88456
3.97553
0.02075
EPFOBM
1.86990
3.96502
0.02067
EPFEBM
1.90034
3.98662
0.02085
EMJ
1.82327
3.97037
0.01989
EMJOB
1.81807
3.96046
0.02000
EMJEB
1.82882
3.98088
0.01979
EML
1.82327
3.97318
0.01985
EMLOB
1.81807
3.96328
0.01995
EMLEB
1.82882
3.98368
0.01974
MOM
1.88656
3.97561
0.02078
MOOBM
1.87190
3.96509
0.02071
MOEBM
1.90234
3.98669
0.02089

Methods
GPM
GPOBM
GPEBM
MLM
MLOBM
MLEBM
EPFM
EPFOBM
EPFEBM
EMJ
EMJOB
EMJEB
EML
EMLOB
EMLEB
MOM
MOOBM
MOEBM

(Ouagadougou site)

0.35

Probability

RMSE lower and equal to 0.01477 and R2 which is
above 0.9840; and the adequate method is MLM.
The results show that:
• there is a strong linear correlation between the shapes
parameters (K) estimated using all bin speed time
series and the estimate using even bin or odd bin wind
speed time series; unless the GPM method is used;
• there is a strong linear correlation between the scale
parameters (C) estimated using all bin speed time
series and the estimate using even bin or odd bin wind
speed time series.
Thus we can conclude that the Weibull parameters can
be estimated at the two sites using anyone of five
methods (EMJ, EML, EPFM, MLM, MOM) with even or
odd bin wind speed time series and then we used a linear
function to estimate the Weibull parameters when the
entire series of wind speed data is used

RMSE
0.03393
0.05464
0.05131
0.01409
0.01433
0.01681
0.01670
0.01477
0.01949
0.01605
0.01423
0.01885
0.01604
0.01424
0.01883
0.01668
0.01461
0.01943

R2
0.91999
0.81172
0.83444
0.98608
0.98538
0.98075
0.98008
0.98442
0.97289
0.98168
0.98562
0.97471
0.98170
0.98560
0.97478
0.98015
0.98479
0.97307

© IJRED – ISSN: 2252-4940, July 15th 2018, All rights reserved

Int. Journal of Renewable Energy Development 7 (2) 2018: 139-150
P a g e | 147
5.3 Comparison between the mean wind speed predicted
by the methods and the observed data
The statistical indicators introduced in Section 4 are
utilized to evaluate the performances of the eighteen
parameter estimation methods. Tables 7 and 8 provide
the results of the performance evaluation of the eighteen
methods in terms of MAPE, MABE, RMSE, RRMSE
RPE, R2 and IA, respectively for the Lomé and
Ouagadougou sites. It is significant to note that each
statistical parameter offers different useful way of
comparing the methods. Thus, the combination of all of
these statistical indicators provides a possibility to
compare the differences between the calculated mean
wind speed from measured data and those from the
Weibull
distribution
function
within
different
perspectives with much higher reliability.
The results show that the accuracy of computed mean
wind speed values changes when the parameter

estimation method changes. It is clear that for the Lomé
site when eight methods EPF, EMJ, EML, MOM,
EPFEBM, EMJEB, EMLEB and MOEBM, and for the
Ouagadougou site when fifteen methods of EPF, EMJ,
EML, MOM, EPFEBM, EMJEB, EMLEB, MOEBM,
MOOBM, EPFOBM, EMLOB, EMJOB, MLOBM, MLM
and MLEBM are used to compute the Weibull
parameters, the calculated mean wind speed values by
the Weibull distribution function are in good agreement
with the mean wind speed values computed from
measured data. This conclusion is drawn because of the
low values of MAPE, MABE, RMSE, RRMSE, RPE (RPE
whose histograms are shown in Figs 9 and 10) and the
high values of R2 and IA. On the other hand, it is found
that the lowest agreements are attained when the
GPOBM, GPEBM and GPM methods are applied for K
and C parameter calculations

Table 7
Performance evaluation of mean wind speed calculated by all 18 methods using different statistical indicators for the Lomé site.

Methods
GPM
GPOBM
GPEBM
MLM
MLOBM
MLEBM
EPFM
EPFOBM
EPFEBM
EMJ
EMJOB
EMJEB
EML
EMLOB
EMLEB
MOM
MOOBM
MOEBM

MAPE
(%)
16.555
25.454
24.655
8.726
7.077
11.830
0.0000
7.101
5.197
0.000
7.101
5.197
0.053
7.108
5.211
0.002
7.101
5.200

MABE
0.605
0.945
0.893
0.271
0.219
0.377
0.000
0.220
0.165
0.000
0.220
0.165
0.001
0.220
0.165
0.000
0.220
0.165

RMSE
0.623
1.021
0.910
0.463
0.429
0.534
0.000
0.431
0.289
0.000
0.431
0.289
0.001
0.432
0.290
0.000
0.431
0.289

RRMSE
(%)
17.017
27.889
24.855
12.659
11.733
14.588
0.000
11.791
7.897
0.000
11.791
7.897
0.053
11.802
7.930
0.003
11.791
7.903

R2
0.978
0.788
0.968
0.812
0.803
0.806
1.000
0.802
0.957
1.000
0.802
0.957
1.000
0.802
0.956
1.000
0.802
0.957

IA
0.574
0.509
0.519
0.734
0.786
0.637
1.000
0.787
0.875
1.000
0.787
0.875
0.998
0.787
0.875
0.999
0.787
0.875

Table 8
Performance evaluation of mean wind speed calculated by all 18 methods using different statistical indicators for the Ouagadougou site

Methods
GPM
GPOBM
GPEBM
MLM
MLOBM
MLEBM
EPFM
EPFOBM
EPFEBM
EMJ
EMJOB
EMJEB
EML
EMLOB
EMLEB
MOM
MOOBM
MOEBM

MAPE
(%)
16.555
25.454
24.655
8.726
7.077
11.834
0.000
7.101
5.197
0.000
7.101
5.197
0.053
7.108
5.211
0.002
7.101
5.200

MABE
0.605
0.945
0.893
0.271
0.219
0.377
0.000
0.220
0.165
0.000
0.220
0.165
0.001
0.220
0.165
0.000
0.220
0.165

RMSE
0.623
1.021
0.910
0.463
0.429
0.534
0.000
0.431
0.289
0.000
0.431
0.289
0.001
0.432
0.290
0.000
0.431
0.289

RRMSE
(%)
17.017
27.889
24.855
12.659
11.733
14.588
0.000
11.791
7.897
0.000
11.791
7.897
0.053
11.802
7.930
0.003
11.791
7.903

R2
0.978
0.788
0.968
0.812
0.803
0.806
1.000
0.802
0.957
1.000
0.802
0.957
1.000
0.802
0.956
1.000
0.802
0.957

© IJRED – ISSN: 2252-4940, July 15th 2018, All rights reserved

IA
0.574
0.509
0.519
0.734
0.786
0.637
1.000
0.787
0.875
1.000
0.787
0.875
0.998
0.787
0.875
0.999
0.787
0.875

Citation: Salami, A.A., Ajavon, A.S.A., Kodjo, M.K., Ouedraogo, S. and Bédja, K. (2018), The Use of Odd and Even Class Wind Speed Time Series of Distribution
Histogram to Estimate Weibull Parameters. Int. Journal of Renewable Energy Development, 7(2), 139-150, doi.org/10.14710/ijred.7.2.139-150

P a g e | 148
5.4. Comparison between wind speed standard deviation
predicted by the methods and measured data
The same statistical analyses to compare the mean wind
speed predicted by the methods to that calculated from
collected data are made here.
Mean wind speed (Lome site)
160
GPM
GPOBM
GPEBM
MLM
MLOBM
MLEBM
EPFM
EPFOBM
EPFEBM
EMJ
EMJOB
EMJEB
EML
EMLOB
EMLEB
MOM
MOOBM
MOEBM

140

120

Frequency

100

80

60

40

namely EML, EMJ, MOM, EPF, EMJEB, EMLEB and
MOEBM are used to compute the Weibull parameters,
the calculated wind speed standard deviation by the
Weibull distribution function are in good agreement with
the wind speed standard deviation values computed from
measured data. This conclusion is drawn because of the
low values of MAPE, MABE, RMSE, RRMSE, RPE (RPE
whose histograms are shown in Figs 11 and 12). On the
other hand, it is found that the lowest agreements are
obtained when the GPOBM, GPEBM and GPM methods
are applied for K and C parameter calculation.

Mean wind speed (Ouagadougou site)
100

80
70
60

-50

-40

-30

-20

-10
0
10
Class of RPE (%)

20

30

40

50

Frequency

20

0

GPM
GPOBM
GPEBM
MLM
MLOBM
MLEBM
EPFM
EPFOBM
EPFEBM
EMJ
EMJOB
EMJEB
EML
EMLOB
EMLEB
MOM
MOOBM
MOEBM

90

Fig. 9
Histograms of RPE (%) of mean wind speed predicted
with 18 methods for Lomé.

50
40
30
20

Tables 9 and 10 provide the results of the
performance evaluation for the eighteen methods in
terms of MAPE, MABE, RMSE, RRMSE, R2 and IA,
respectively for the Lomé and Ouagadougou sites. The
results show that the accuracy of computed wind speed
standard deviation values changes when the parameter
estimation method changes. It is clear that for the Lomé
site when four methods namely EML, EMJ, EMLEB and
EMJEB, and for the Ouagadougou site when six methods

10
0

-50

-40

-30

-20

-10
0
10
Class of RPE (%)

20

30

40

50

Fig. 10 Histograms of RPE (%) of mean wind speed predicted
with 18 methods for Ouagadougou.

Table 9
Performance evaluation of the standard deviation of wind speed calculated by all 18 methods using different statistical indicators for
the Lomé site
Methods
GPM
GPOBM
GPEBM
MLM
MLOBM
MLEBM
EPFM
EPFOBM
EPFEBM
EMJ
EMJOB
EMJEB
EML
EMLOB
EMLEB
MOM
MOOBM
MOEBM

MAPE(%)
19.407
19.059
26.328
8.175
6.601
13.863
4.260
6.632
6.256
0.994
6.177
3.606
0.942
6.189
3.564
4.154
6.661
6.225

MABE
0.397
0.387
0.535
0.176
0.143
0.287
0.089
0.145
0.129
0.020
0.134
0.071
0.019
0.134
0.070
0.087
0.145
0.128

RMSE
0.490
0.514
0.628
0.272
0.237
0.358
0.111
0.242
0.172
0.021
0.234
0.084
0.020
0.234
0.083
0.112
0.244
0.173

RRMSE(%)
24.424
25.637
31.309
13.601
11.839
17.889
5.552
12.099
8.605
1.059
11.707
4.204
1.002
11.701
4.173
5.591
12.169
8.666

© IJRED – ISSN: 2252-4940, July 15th 2018, All rights reserved

R2
0.238
0.234
0.186
0.309
0.234
0.327
0.944
0.284
0.760
0.999
0.257
0.957
0.999
0.256
0.957
0.956
0.306
0.771

IA
0.500
0.516
0.498
0.534
0.500
0.495
0.666
0.515
0.576
0.932
0.518
0.810
0.935
0.517
0.812
0.683
0.531
0.588

Int. Journal of Renewable Energy Development 7 (2) 2018: 139-150
P a g e | 149
Table 10
Performance evaluation of the standard deviation of wind speed calculated by all 18 methods using different statistical indicators for
the Ouagadougou site.
Methods
GPM
GPOBM
GPEBM
MLM
MLOBM
MLEBM
EPFM
EPFOBM
EPFEBM
EMJ
EMJOB
EMJEB
EML
EMLOB
EMLEB
MOM
MOOBM
MOEBM

MAPE (%)
12.385
15.291
18.570
5.679
3.481
10.464
1.929
4.743
3.111
1.010
3.670
3.028
0.955
3.658
3.027
0.769
3.588
2.928

MABE
0.203
0.247
0.299
0.093
0.058
0.167
0.030
0.075
0.048
0.016
0.061
0.048
0.015
0.061
0.048
0.013
0.059
0.046

RMSE
0.281
0.319
0.370
0.110
0.077
0.189
0.036
0.099
0.063
0.017
0.079
0.060
0.016
0.078
0.060
0.025
0.078
0.060

RRMSE (%)
17.765
20.144
23.350
6.987
4.916
11.986
2.334
6.281
3.983
1.090
5.004
3.832
1.029
4.980
3.832
1.577
4.967
3.825

R2
0.326
0.469
0.421
0.959
0.935
0.881
0.985
0.855
0.951
0.999
0.933
0.969
0.999
0.933
0.969
0.995
0.927
0.960

IA
0.513
0.539
0.530
0.673
0.770
0.590
0.887
0.684
0.848
0.945
0.763
0.864
0.948
0.764
0.864
0.952
0.765
0.860

Standard deviation (Lome site)
160
GPM
GPOBM
GPEBM
MLM
MLOBM
MLEBM
EPFM
EPFOBM
EPFEBM
EMJ
EMJOB
EMJEB
EML
EMLOB
EMLEB
MOM
MOOBM
MOEBM

140

120

Frequency

100

80

60

40

20

0

Fig. 11

-50

-40

-30

-20

-10
0
10
Class of RPE (%)

20

30

40

50

Histograms of RPE (%) for wind speed standard deviations predicted with 18 methods for Lomé.

Standard deviation (Ouagadougou site)
100
GPM
GPOBM
GPEBM
MLM
MLOBM
MLEBM
EPFM
EPFOBM
EPFEBM
EMJ
EMJOB
EMJEB
EML
EMLOB
EMLEB
MOM
MOOBM
MOEBM

90
80
70

Frequency

60
50
40
30
20
10
0

-50

-40

-30

-20

-10
0
10
Class of RPE (%)

20

30

40

50

Fig. 12 Histograms of RPE (%) for wind speed standard
deviations predicted with 18 methods for Ouagadougou.

6.
Conclusion
The following conclusions can be drawn from the
preceding analysis:
• the approaches based on odd or even class wind speed
time series with 1 m/s as bin size using Maximum
Likelihood Method (MLM), the Energy Pattern Factor
Method (EPFM), the Empirical Method of Justus
(EMJ), the Empirical Method of Lysen (EML) and the
Moment method (MOM) are efficient methods for
determining the K and C parameters to fit Weibull
distribution curves to wind speed data collected in
Lomé, Togo and Ouagadougou, Burkina Faso
analyzed using statistical tests;
• the maximum likelihood with the odd bin time series
method (MLOBM) is an adequate method that gave
lower RMSE value of Weibull parameters K = 1.79134
and C = 3.96250 m/s at the Lomé site using the whole
data collected;

© IJRED – ISSN: 2252-4940, July 15th 2018, All rights reserved

Citation: Salami, A.A., Ajavon, A.S.A., Kodjo, M.K., Ouedraogo, S. and Bédja, K. (2018), The Use of Odd and Even Class Wind Speed Time Series of Distribution
Histogram to Estimate Weibull Parameters. Int. Journal of Renewable Energy Development, 7(2), 139-150, doi.org/10.14710/ijred.7.2.139-150

P a g e | 150
•

•

•

•

the MLM is an adequate method that yields lower
RMSE value of the Weibull parameters K = 2.10118
and C = 3.53456 m/s at the Ouagadougou site using
the whole data collected;
the accuracy of computed mean and standard
deviation of wind speed values changes when the
parameter estimation method changes at the Lomé
and Ouagadougou sites;
in the evaluation of the mean and standard deviation,
the GPM, the Graphical with Even Bin time series
Method (GPEBM) and the Graphical with Odd Bin
time series Method (GPOBM) are the least effective
methods for fitting Weibull distribution curves to the
wind speed using the data analyzed for the Lomé and
Ouagadougou sites;
there is a linear relationship between the Weibull
parameters K and C estimated by MLM, EPFM, EMJ,
EML and MOM using odd or even class wind speed
time series and all class wind speed time series; this
result empowers one to compress wind data by
removing either even or odd bins (depending on the
site) prior to any available energy assessment while
still expecting the same outcome as when the entire
data is used.

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© IJRED – ISSN: 2252-4940, July 15th 2018, All rights reserved