Bivariate Semi-parametric Singular Family of Distributions and its Applications

Debasis Kundu ()
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Debasis Kundu: Indian Institute of Technology Kanpur

Sankhya B: The Indian Journal of Statistics, 2022, vol. 84, issue 2, No 18, 846-872

Abstract: Abstract In this paper we introduce a very general class of bivariate semi-parametric distributions whose marginals belong to the proportional hazard class, and it has a singular component. This model can be used quite effectively to analyze a bivariate data set when there are ties. Note that the Marshall-Olkin bivariate exponential distribution is a special case of the proposed class. We derive several properties of the proposed distribution, and it is observed that it has a very convenient copula structure. Hence, several dependence properties and dependence measures can be obtained based on the copula. The main feature of the proposed distribution is that we do not use any specific parametric form of the base line distribution, instead we have assumed that the base line distribution has piecewise constant hazard function. It makes the proposed family a very flexible family. The maximum likelihood estimators cannot be obtained in explicit form, and we have used a very convenient EM algorithm to compute the maximum likelihood estimators. Simulation experiments have been performed to see the effectiveness of the proposed EM algorithm. Finally we have used this model to analyze a dependent competing risks data. Two data sets have been analyzed and the results are quite satisfactory.

Keywords: Bivariate singular distribution; copula; maximum likelihood estimators; EM algorithm; asymptotic distribution; lehmann family of distributions; Primary 62F10; Secondary 62F03, 62H12 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13571-022-00289-y

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