Statistical Properties and Application of Bagui-Liu-Zhang Distribution

Abstract

This paper extended the work of Bagiu et al. (2020) who defined the probability density function of a new one-parameter continuous distribution through the moment generating function approach. The new distribution called Bagiu-Liu-Zhang distribution is the distribution of the exponential mixture of the shifted exponential random variable. Properties of the distribution such as its cumulative distribution function (cdf), moments, coefficients of skewness and kurtosis, reliability function and hazard rate function were derived. The maximum likelihood estimator of the model parameter was also determined. We illustrated the usefulness of the distribution by comparing its fit to a real data set to the fit of the exponential distribution to the same data.  The numerical results obtained indicate that the distribution can be a more suitable model for some continuous data than the exponential distribution and several one-parameter distributions.