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 wit...

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Bibliographic Details
Published in:Anais da Academia Brasileira de Ciências 2021-01, Vol.93 (2), p.e20181019-e20181019
Main Authors: BOUALI, DALAL LALA, CHESNEAU, CHRISTOPHE, SHARMA, VIKAS KUMAR, BAKOUCH, HASSAN S.
Format: Article
Language:English
Subjects:
exponential distribution
finite mixture
maximum likelihood estimation
moment generating function
MULTIDISCIPLINARY SCIENCES
weighted distribution
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Summary: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.
ISSN:0001-3765
1678-2690
1678-2690
DOI:10.1590/0001-3765202120181019