Gompertz-Poisson distribution is a three-parameter lifetime distribution with increasing, decreasing, increasing-decreasing and unimodal shape failure rate function and a composition of Gompertz and Poisson distributions cut at zero point that in this paper estimated the parameters of the distribution by maximum likelihood method and in order to confirm the calculated estimates, based on random sample with volumes of 100, 200, 300, 400 and 500 of Gompertz-Poisson distribution simulation study was conducted. Also with the help of two real data sets and comparing Gompertz-Poisson distribution with several other distributions of lifetime we show this distribution is a good model for data fitness related to lifetime.
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