# Discrete Gompertz-Lomax Distribution and Its Applications

## Keywords:

Discrete Gompertz-G family of distributions, Lomax distribution, maximum likelihood estimation, quantile function, discretization method## Abstract

A new distribution, called the discrete Gompertz-Lomax distribution, is proposed. It has been developed by combining the properties of two existing distributions, namely discrete Gompertz-G family of distributions and Lomax distribution. Its probability mass function is characterized by a flexible probability function that can exhibit unimodality and reverse J-shape (decreasing). It is interesting that some statistical properties of the discrete Gompertz-Lomax distribution have been discussed, including the quantile function, moments, probability generating function, discrete hazard function and discrete reversed hazard function. The maximum likelihood estimation has been formulated to estimate the unknown parameters of the discrete Gompertz-Lomax distribution. A simulation study and applications of this distribution have been illustrated. The development of the discrete Gompertz-Lomax distribution seems to be a valuable contribution to the field of probability theory and statistics. It has potential applications which data with skewed or decreasing patterns may be encountered.

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