On sums of dependent random lifetimes under the time-transformed exponential model

Jorge Navarro (), Franco Pellerey () and Julio Mulero ()
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Jorge Navarro: Universidad de Murcia
Franco Pellerey: Politecnico di Torino
Julio Mulero: Universidad de Alicante

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2022, vol. 31, issue 4, No 1, 879-900

Abstract: Abstract For a given pair of random lifetimes whose dependence is described by a time-transformed exponential model, we provide analytical expressions for the distribution of their sum. These expressions are obtained by using a representation of the joint distribution in terms of bivariate distortions, which is an alternative approach to the classical copula representation. Since this approach allows one to obtain conditional distributions and their inverses in simple form, then it is also shown how it can be used to predict the value of the sum from the value of one of the variables (or vice versa) by using quantile regression techniques.

Keywords: Dependence models; C-convolution; Distorted distributions; Quantile regression; Confidence bands; 62N05; 62H05 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11749-022-00805-2

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