HYPERBOLIC COSINE - F FAMILY OF DISTRIBUTIONS WITH AN APPLICATION TO EXPONENTIAL DISTRIBUTION

Abstract

A new class of distributions called the hyperbolic cosine – F (HCF) distribution is introduced and its properties are explored.This new class of distributions is obtained by compounding a baseline F distribution with the hyperbolic cosine function. This technique resulted in adding an extra parameter to a family of distributions for more flexibility. A special case with two parameters has been considered in details namely; hyperbolic cosine exponential (HCE) distribution. Various properties of the proposed distribution including explicit expressions for the moments, quantiles, moment generating function, failure rate function, mean residual lifetime, order statistics, stress-strength parameter and expression of the Shannon entropy are derived. Estimations of parameters in HCE distribution for two data sets obtained by eight estimation procedures: maximum likelihood, Bayesian, maximum product of spacings, parametric bootstrap, non-parametric bootstrap, percentile, least-squares and weighted least-squares. Finally these data sets have been analyzed for illustrative purposes and it is observed that in both cases the proposed model fits better than Weibull, gamma and generalized exponentialdistributions.

Keywords

• Hyperbolic cosine function,Exponential distribution,Mean residual life time,Maximum product of spacings,Maximum likelihood estimation,Bootstrap.

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