Abstract
In this paper, the inverse gamma power series (IGPS) class of distributions asymmetric is introduced. This family is obtained by compounding inverse gamma and power series distributions. We present the density, survival and hazard functions, moments and the order statistics of the IGPS. Estimation is first discussed by means of the quantile method. Then, an EM algorithm is implemented to compute the maximum likelihood estimates of the parameters. Moreover, a simulation study is carried out to examine the effectiveness of these estimates. Finally, the performance of the new class is analyzed by means of two asymmetric real data sets.
Highlights
In the last few decades, several papers have discussed the derivation of new probabilistic families by compounding different distributions with the power series (PS) model
The exponential PS is introduced in Chahkandi and Ganjali [4], Morais and Barreto-Souza [5] presented the Weibull PS (WPS) class of distributions, Mahmoudi and Jafari [6] defined the generalized exponential PS (GEPS) distributions, Silva et al [7], the extended Weibull PS (EWPS) and Bagheri et al [8], the generalized modified Weibull PS distribution (GMWPS)
Warahena-Liyanage and Pararai [9] introduce the Lindley PS distributions (LPS), Alizadeh et al [10] study the exponentiated power Lindley PS class of distributions, Elbatal et al [11] propose and study a new family of exponential Pareto PS and the Generalized Burr XII PS distribution was given by Elbatal et al [12]
Summary
In the last few decades, several papers have discussed the derivation of new probabilistic families by compounding different distributions with the power series (PS) model. We propose to study the resulting model obtained by compounding the inverse gamma (IG) and the PS distribution introduced by Noack [13]. Where G(x; a) = Γ(a, x)/Γ(a) represents the survival function for the gamma distribution with shape parameter a and scale 1 and Γ(a, b) =. PS (IGPS) probabilistic family is introduced and some properties including the density, survival and hazard functions, moments and statistical ordering are examined. This family is applied to two real data sets.
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