A Compound Class of Geometric and Lifetimes Distributions

Said Hofan Alkarni*
Department of Quantitative Analysis, King Saud University, Riyadh, Saudi Arabia.

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© 2013 Alkarni et al.;

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Quantitative Analysis, King Saud University, Riyadh, Saudi Arabia. E-mail:


A new lifetime class with decreasing failure rateis introduced by compounding truncated Geometric distribution and any proper continuous lifetime distribution. The properties of the proposed class are discussed, including a formal proof of its probability density function, distribution function and explicit algebraic formulae for its reliability and failure rate functions. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. A formal equation for Fisher information matrix is derived in order to obtaining the asymptotic covariance matrix. This new class of distributions generalizes several distributions which have been introduced and studied in the literature.

Keywords: Lifetime distributions, decreasing failure rate, Geometric distribution.