Page 18 - Contributed Paper Session (CPS) - Volume 5

CPS649 A-Hadi N. Ahmed et al.

A new discrete analog of the continuous Lindley
distribution, with reliability applications
1
A-Hadi N. Ahmed , Ahmed Z. Afify
2
1 Department of Mathematical Statistics, Institute of Statistical Studies & Research, Cairo
University, Egypt
2 Department of Statistics, Mathematics and Insurance, Benha University, Egypt

Abstract
Apart from discretization techniques, we propose and study a new natural
discrete analog of the Lindley distribution as a mixture of geometric and
negative binomial distributions. The proposed model extends some recent
discrete Lindley distributions like the discrete Lindley of Bakouch et al. (2014),
the two-parameter discrete Lindley of Hussain et al. (2016). The new
distribution has many interesting properties which make it superior to many
other discrete distributions, particularly in analyzing overdispersed count data.

Keywords
Discrete Lindley analog; Maximum likelihood; Mean residual life; Negative
binomial distribution; Reliability

1. Introduction
In spite of all the available discrete models. there is still a great need to
create more flexible discrete lifetime distributions to serve many areas like
economics. social sciences. biometrics and reliability studies to suit various
types of count data.
As a consequence. various models that are less restrictive than those
presented in the statistical literature. (see. e.g., Nakagawa and Osaki (1975).
Famoye (1993). among others). are needed.
In order to create a natural discrete analog of Lindley’s distribution (Lindley.
1958). we relied on the well-known fact that the geometric and the negative
binomial distributions are the natural discrete analogs of the exponential and
the gamma distributions. respectively (see. e.g. Nakagawa and Osaki (1975)
and Roy (2004). among others). This fact has motivated us to construct a
natural discrete analog to the continuous Lindley distribution by mixing the
discrete counterparts of the exponential and gamma distributions. apart from,
discretizing continuous distributions. More specifically. a new two-parameter
natural discrete Lindley (TNDL) distribution can be constructed as a mixture of
geometric and negative binomial distributions] with common success
probability  and mixing proportions and .
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