scholarly journals Fitting Wind Speed to a 3-Parameter Distribution Using Maximum Likelihood Technique

2021 ◽  
Author(s):  
Benedict Troon
Keyword(s):  
Maximum Likelihood ◽  
Wind Speed ◽  
Gamma Distribution ◽  
Model Comparison ◽  
Information Criterion ◽  
Parameter Distribution ◽  
Wind Speed Data ◽  
Distribution Parameters ◽  
Total Capacity ◽  
Maximum Likelihood Technique

Kenya is one of the countries in the world with a good quantity of wind. This makes the country to work ontechnologies that can help in harnessing the wind with a vision of achieving a total capacity of 2GW of wind energy by 2030.The objective of this research is to find the best three-parameter wind speed distribution for examining wind speed using the maximum likelihood fitting technique. To achieve the objective, the study used hourly wind speed data collected for a period of three years (2016 – 2018) from five sites within Narok County. The study examines the best distributions that the data fits and then conducted a suitability test of the distributions using the Kolmogorov-Smirnov test. The distribution parameters were fitted using maximum likelihood technique and model comparison test conducted using Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC) values with the decision rule that the best distribution relies on the distribution with the smaller AIC and BIC values. The research showed that the best distribution is the gamma distribution with the shape parameter of 2.071773, scale parameter of 1.120855, and threshold parameter of 0.1174. A conclusion that gamma distribution is the best three-parameter distribution for examining the Narok country wind speed data

scholarly journals The Weibull-Gamma Distribution: Properties and Applications

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 438 ◽  
Author(s):  
Hadeel S. Klakattawi
Keyword(s):  
Maximum Likelihood ◽  
Gamma Distribution ◽  
Maximum Likelihood Method ◽  
Data Distribution ◽  
Likelihood Method ◽  
Parameter Distribution ◽  
Great Flexibility ◽  
Special Cases ◽  
New Distribution ◽  
Family Of Distributions

A new member of the Weibull-generated (Weibull-G) family of distributions—namely the Weibull-gamma distribution—is proposed. This four-parameter distribution can provide great flexibility in modeling different data distribution shapes. Some special cases of the Weibull-gamma distribution are considered. Several properties of the new distribution are studied. The maximum likelihood method is applied to obtain an estimation of the parameters of the Weibull-gamma distribution. The usefulness of the proposed distribution is examined by means of five applications to real datasets.

A python program to model and analyze wind speed data

2021 ◽  
Vol 9 (6) ◽  
pp. 769-784
Keyword(s):  
Maximum Likelihood ◽  
Wind Speed ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Weibull Function ◽  
Method Of Moment ◽  
Wind Speed Data ◽  
Statistical Errors ◽  
Wind Potential ◽  
Wind Distribution

A python program has been developed to analyze wind distributions using the Weibull density function. A two-parameter Weibull function is frequently used to model and assess wind potential and wind distribution. This python program finds first Weibull parameters from the recorded wind data by five different methods, namely, Empirical Method(EPM), Method of Moment (MoM), Energy Pattern Factor Method (EPFM), Maximum Likelihood Method (MLM), Modified Maximum Likelihood Method (MMLM), the parameters are then used to find theoretically fitted pdfs. The program is implemented on wind distribution of two cities of Pakistan (Chakri and Sadiq Abad). The program-generated pdfs were plotted with the histogram of recorded data, the fitting was excellent. To check the validity of the fitted pdfs, statistical errors Root Mean Square (RMSE), MeanAbsolute Percent Error (MAPE), Mean Absolute Error (MABE), and Chi-square statistic are calculated. In all cases,these statistical errors are well below the acceptance range. Both pictorial results and numerical values of statistical errors indicate the performance of the python program to analyze wind speed data

Application of differential evolution for wind speed distribution parameters estimation

2021 ◽  
pp. 0309524X2199996
Author(s):  
Rajesh Kumar ◽  
Arun Kumar
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Wind Speed ◽  
Weibull Distribution ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Speed Distribution ◽  
De Algorithm ◽  
Wind Speed Distribution ◽  
Distribution Parameters

Weibull distribution is an extensively used statistical distribution for analyzing wind speed and determining energy potential studies. Estimation of the wind speed distribution parameter is essential as it significantly affects the success of Weibull distribution application to wind energy. Various estimation methods viz. graphical method, moment method (MM), maximum likelihood method (ML), modified maximum likelihood method, and energy pattern factor method or power density method have been presented in various reported research studies for accurate estimation of distribution parameters. ML is the most preferred approach to study the parameter estimation. ML works on the principle of forming a likelihood function and maximizing the function for parameter estimation. ML generally uses the numerical based iterative method, such as Newton–Raphson. However, the iterative methods proposed in the literature are generally computationally intensive. In this paper, an efficient technique utilizing differential evolution (DE) algorithm to enhance the estimation accuracy of maximum likelihood estimation has been presented. The [Formula: see text] of GA-Weibull, SA-Weibull, and DE-Weibull is 0.958, 0.953, and 0.973 respectively, and value of RMSE of DE-Weibull 0.0083, GA-Weibull (0.0104), and SA-Weibull (0.0110), for the yearly wind speed data are obtained. The lowest root mean square error and larger regression value for both monthly and yearly wind speed data indicate that the DE-Weibull distribution has the best goodness of fit and advocate the DE algorithm for the parameter estimation.

The Poisson Gamma distribution for wind speed data

2016 ◽  
Author(s):  
Selen Çakmakyapan ◽  
Gamze Özel
Keyword(s):  
Wind Speed ◽  
Gamma Distribution ◽  
Wind Speed Data

scholarly journals Modelling the Botswana Pula/Us Dollar exchange rate using the Skewed generalized t (SGT) distributions

2021 ◽  
Vol 9 (12) ◽  
pp. 10-16
Author(s):  
Wilson Moseki Thupeng
Keyword(s):  
Exchange Rate ◽  
Maximum Likelihood ◽  
Model Comparison ◽  
Information Criterion ◽  
Error Distribution ◽  
Dollar Exchange Rate ◽  
The Us ◽  
Generalized Error Distribution ◽  
Us Dollar ◽  
T Distribution

The economy of Botswana heavily relies on mineral exports (mainly diamond exports), which are largely dependent on the exchange rate. And, the US Dollar is one of the most important currencies in the basket of currencies to which the Botswana Pula is pegged. Therefore, this paper seeks to empirically establish the baseline characteristics of the Botswana Pula (BWP) and the US Dollar (USD) exchange rate and to identify the most plausible probability distribution from the skewed generalized t (SGT) family that can be used to model the log-returns of the daily BWP/USD exchange rates for the period January 2001 to December 2020. The SGT family is a highly versatile class of models that can capture the skewness and kleptokurticity that are inherent in financial time series. Four probability distributions are considered in this study: skewed t, skewed generalized error, generalized t and skewed generalized t. The maximum likelihood approach is used to estimate the parameters of each model. Model comparison and selection are based on the Akaike information criterion (AIC) and Bayesian information criterion (BIC). The results of the study show that the daily BWP/USD exchange rate series is nonnormal, negatively skewed heavy-tailed. It is also found that, based on the values of both the AIC and BIC, the model that gives the best fit to the data is the skewed t, which is closely followed by the skewed generalized error distribution, while the generalized t gives the worst fit. Keywords: Pula/US Dollar exchange rate, log returns, Generalized t distribution, Skewed generalized error distribution, Skewed generalized t distribution, Skewed t distribution, skewness, kurtosis, maximum likelihood

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