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Keywords:
Bathtub shaped hazard rate function; convex-concave shaped; ExpIntegralE function; regularized incomplete gamma function; reverse ‘J’ shaped; Shannon and Rényi entropy
Bathtub shaped hazard rate function; convex-concave shaped; ExpIntegralE function; regularized incomplete gamma function; reverse ‘J’ shaped; Shannon and Rényi entropy
Summary:
Up to present for modelling and analyzing of random phenomenons, some statistical distributions are proposed. This paper considers a new general class of distributions, generated from the logit of the gamma random variable. A special case of this family is the Gamma-Uniform distribution. We derive expressions for the four moments, variance, skewness, kurtosis, Shannon and Rényi entropy of this distribution. We also discuss the asymptotic distribution of the extreme order statistics, simulation issues, estimation by method of maximum likelihood and the expected information matrix. We show that the Gamma-Uniform distribution provides great flexibility in modelling for negatively and positively skewed, convex-concave shape and reverse `J' shaped distributions. The usefulness of the new distribution is illustrated through two real data sets by showing that it is more flexible in analysing of the data than of the Beta Generalized-Exponential, Beta-Exponential, Beta-Pareto, Generalized Exponential, Exponential Poisson, Beta Generalized Half-Normal and Generalized Half-Normal distributions.
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