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

Yıl 2016, Cilt: 29 Sayı: 4, 811 - 829, 19.12.2016

Omid Kharazmi Ali Saadatinik

Öz

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.

Anahtar Kelimeler

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

Kaynakça

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