# Unit-Gompertz Distribution with Applications

## DOI:

https://doi.org/10.6092/issn.1973-2201/8497## Keywords:

Gompertz distribution, Maximum likelihood estimators, Monte Carlo simulation## Abstract

The transformed family of distributions are sometimes very useful to explore additional properties of the phenomenons which non-transformed (baseline) family of distributions cannot. In this paper, we introduce a new transformed model, called the unit-Gompertz (UG) distribution which exhibit right-skewed (unimodal) and reversed-J shaped density while the hazard rate has constant, increasing, upside-down bathtub and then bathtub shaped hazard rate. Some statistical properties of this new distribution are presented and discussed. Maximum likelihood estimation for the parameters that index UG distribution are derived along with their corresponding asymptotic standard errors. Monte Carlo simulations are conducted to investigate the bias, root mean squared error of the maximum likelihood estimators as well as the coverage probability. Finally, the potentiality of the model is presented and compared with three others distributions using two real data sets.

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*Statistica*,

*79*(1), 25–43. https://doi.org/10.6092/issn.1973-2201/8497

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