  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 $k$th 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 this proposed estimator for parameters. At
the end, in order to show the BG distribution flexibility, an application using
a real data set is presented.
