Abstract
Considering the sum of the independent and non-identically distributed random variables is a most important topic in many scientific fields. An extension of the exponential distribution based on mixtures of positive distributions is proposed by Gómez et al. (Rev Colomb Estad 37:25–34, 2014). Distribution of the sum of the independent and non-identically distributed random variables is obtained using inverse transformation of the moment generating function. A saddlepoint approximation is used to approximate the derived distribution. Simulations are used to investigate the accuracy of the saddlepoint approximation. Parameters are estimated by the maximum likelihood method. The method is illustrated by the analysis of real data.
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Research of the H. Murakami was supported by JSPS KAKENHI Grant Number 18K11199.
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Kitani, M., Murakami, H. On the distribution of the sum of independent and non-identically extended exponential random variables. Jpn J Stat Data Sci 3, 23–37 (2020). https://doi.org/10.1007/s42081-019-00046-y
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DOI: https://doi.org/10.1007/s42081-019-00046-y