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Abstract
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In this paper, we introduce a new four-parameter generalized version of the Gompertz model which is called Beta-Gompertz (BG) distribution. It includes some well-known lifetime distributions such as Beta-exponential
and generalized Gompertz distributions as special sub-models. This new
distribution is quite flexible and can be used effectively in modeling survival
data and reliability problems. It can have a decreasing, increasing, and
bathtub-shaped failure rate function depending on its parameters. Some
mathematical properties of the new distribution, such as closed-form expressions
for the density, cumulative distribution, hazard rate function, the kth
order moment, moment generating function, Shannon entropy, and the quantile
measure are provided. We discuss maximum likelihood estimation of the
BG parameters from one observed sample and derive the observed Fisher’s
information matrix. A simulation study is performed in order to investigate
the properties of the proposed estimator. At the end, in order to show the
BG distribution flexibility, an application using a real data set is presented.
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