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Abstract
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In this article, a discrete analogue of an extension to a two-parameter half-logistic model is
proposed for modeling count data. The probability mass function of the new model can be expressed
as a mixture representation of a geometric model. Some of its statistical properties, including hazard
rate function, moments, moment generating function, conditional moments, stress-strength analysis,
residual entropy, cumulative residual entropy and order statistics with its moments, are derived. It is
found that the new distribution can be utilized to model positive skewed data, and it can be used
for analyzing equi- and over-dispersed data. Furthermore, the hazard rate function can be either
decreasing, increasing or bathtub. The parameter estimation through the classical point of view has
been performed using the method of maximum likelihood. A detailed simulation study is carried
out to examine the outcomes of the estimators. Finally, two distinctive real data sets are analyzed to
prove the flexibility of the proposed discrete distribution.
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