Properties and Parameter Estimation of the Partly-Exponential Distribution

The partly-exponential distribution was introduced in the paper by Atikankul et al. in 2021, but no properties of this distribution have been investigated. In this paper, we derive various theoretical properties such as the cumulative distribution function, the moment generating function, the first three moments, the characteristic function, and the mode. The maximum likelihood estimation is used to estimate the parameters. Moreover, the Wald and the profile likelihood approaches are used for interval estimation. A simulation study is conducted to examine the mean square error and bias of the maximum likelihood estimators, as well as the coverage probability of the both confidence intervals.