AWEIGHTED BINOMIALLINDLEYDISTRIBUTIONFORDISCRETEDATA
Authors: TassaddaqHussain
Keywords: Characterization; Poisson distribution; Negative moments; Estimation; Mixture 2000 MSC: 60E05, 62E15
Abstract
In this article we propose a weighted and mixed version of binomial and
discrete Lindley distributions. The weighted distributions are usually
considered for the adjustment of probability of occurrences and removal of
biasedness from the data and mixed distributions are usually used in
heterogeneous and over-dispersed data sets. The proposed model adjusts
the probabilities by removing the bias but contrary to the over-dispersion the
model handles the under dispersion issues. Moreover, various properties
like failure rate, moments, and factorial moments, recurrence relation
between moments, self-decomposability, infinite divisibility and limiting form
of the proposed model are also studied. A simulation is conducted and
estimation problem is discussed via two estimation methods like maximum
likelihood and moments estimation. Performance of the proposed model
over the binomial, discrete gamma, Poisson-Lindley and discrete Lindley is
investigated via some test statistics and two under dispersed real data sets.
We introduce a two parameter discrete distribution, so-called the ??BL
distribution. The new distribution is much more flexible than the binomial,
discrete Lindley distribution and could have increasing and unimodal hazard
rates. We derive explicit algebraic formula for the r
th moment which holds in
generality for any parameter value The estimation procedures for the
parameters of ??BL distribution are also derived considering two estimation
methods whose convergence rate is very high as compare to the others.
The MME method yields global estimates where as MLE yields local
estimates. Since it is not feasible to compare these methods theoretically,
we have presented an extensive simulation study in order to identify the
most efficient procedure. We observed that the MLE provides a large
number of local estimates whereas MME yields global one so we used this
global value as a seed for finding the MLE. Moreover, we have also studied
various mathematical properties including moments, ascending and
descending factorial moments, negative and negative factorial moments,
discrete self-decomposability, and infinite divisibility. Finally, two data-sets
were analyzed for illustrative purposes
Article Type:Original research article
Received: 2022-09-13
Accepted: 2022-10-27
First Published:7/12/2024 9:14:30 PM
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