A new class of distributions as a finite functional mixture using functional weights

Abstract

In this paper, we introduce a new family of distributions whose probability density function is defined as a weighted sum of two probability density functions; one is defined as a warped version of the other. We focus our attention on a special case based on the exponential distribution with three parameters, a dilation transformation and a weight with polynomial decay, leading to a new life-time distribution. The explicit expressions of the moments generating function, moments and quantile function of the proposed distribution are provided. For estimating the parameters, the method of maximum likelihood estimation is used. Two applications with practical data sets are given.

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“…By the way, a specialized journal in this field has received the highest IF in 2022 (CA: A Cancer Journal for Clinicians -IF 254.7). But, at the same time, the AABC also publishes studies in scientific areas where the citation potential is traditionally much lower (Mathematical Sciences, e.g., Bouali et al 2021).…”