DEVELOPMENT OF EXPONENTIATED GENERALIZED EXPONENTIATED EXPONENTIAL DISTRIBUTION
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Date
2019-12
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UNIVERSITY OF ILORIN
Abstract
Probability distributions have been used in describing and predicting real life phenomena. The inability of existing distributions to fit diverse nature of the data sets has necessitated the development of more flexible distributions for real life data set. Recent studies on developing new families of distributions from existing ones have helped in describing data better. The inability of exponential distributions to properly fit skewed data has been a serious concern. This study therefore aimed at developing a new tractable distribution that will fit data that are positively or negatively skewed. The objectives of the study were to: (i) derive a new distribution and its statistical properties. (ii) examine the effect of the shape and scale parameters on the distribution; and (iii) compare the performance of the proposed distribution with the existing ones using simulated and real-life data sets.
The generator employed in developing the proposed probability distribution function is the Exponentiated Generalized Family of distribution using the Exponentiated Exponential as the baseline distribution. The properties of the distribution such as mean, median and their deviations, quantile, Renyon entropy, skweness and kurtosis were obtained using analytical and simulation method. Simulated and real life data were used to assess and compare the performances of the proposed distribution with the existing ones using Akaike information criterion (AIC), Bayesian information criterion (BIC), log-likelihood function and likelihood ratio test.
The findings of the study were that:
(i) the probability density function (pdf) and cumulative distribution functions(cdf) of the Exponentiated Generalized Exponentiated Exponential (EGEE) were derived together with their properties such as moments, quantiles, skewness, kurtosis, etc.;
(ii) Exponential (E), Exponentiated Exponential (EE) and Exponentiated Generalized Exponential (EGE) distributions were obtain by setting the shape parameters value to one;
(iii) the mean, standard deviation and median are increasing functions of the scale and shape parameters of the proposed distribution while the skewness and kurtosis were unaffected by scale parameter but only by the shape parameters; and
(iv) the proposed EGEE competed very well with other existing distributions for small sample sizes and even performed better as the sample size increases.
The study therefore concluded that EGEE distribution can serve a better alternative distribution to the existing distributions (E, EE and EGE) in fitting skewed data. Therefore, the proposed EGEE distribution is preferred and recommended for fitting a skewed data.
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Keywords
EXPONENTIATED, GENERALIZED, EXPONENTIAL DISTRIBUTION