Abstract
In this article, an extension of the transmuted-G family is proposed, in the so-called Poison transmuted-G family of distributions. Some of its statistical properties including quantile function, moment generating function, order statistics, probability weighted moment, stress-strength reliability, residual lifetime, reversed residual lifetime, Rényi entropy and mean deviation are derived. A few important special models of the proposed family are listed. Stochastic characterizations of the proposed family based on truncated moments, hazard function and reverse hazard function, are also studied. The family parameters are estimated via the maximum likelihood approach. A simulation study is carried out to examine the bias and mean square error of the maximum likelihood estimators. The advantage of the proposed family in data fitting is illustrated by means of two applications to failure time data sets.
Highlights
In the last decades, many generalized families of continuous models have been introduced by extending classical probability models and applied to model various phenomena
We propose a new extension of the T-G model having two parameters α and β by considering the T-G as the baseline distributions in the P-G family of distributions, in the so-called Poison transmuted-G (PT-G) family of distributions
1.1 Important sub models Here we provide some special cases of the PT-G family of distributions and list their main distributional characteristics. ➢ The PT- exponential (PT-E) distribution
Summary
Many generalized families of continuous models have been introduced by extending classical probability models and applied to model various phenomena. The cumulative distribution function (cdf, for short) and probability density function (pdf, for short) of the T-G family can be expressed respectively as follows. The pdf and cdf of the PT-G family can be expressed respectively as follows f. Consider the exponential model with scale parameter λ > 0, g(x) = λe−λx and G(x) = 1 − e−λx, x > 0, for the PT-E model, the pdf and hrf respectively are f. Equations (5) and (6) can be expressed as infinite series expansion to show that the PT-G can be written as a linear combination of T-G as well as a linear combination of exponentiated-G distributions These expressions will be helpful to study the mathematical characteristics of the PT-G family.
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