Statistical Properties and Application of Bagui-Liu-Zhang Distribution
Keywords:
Exponential distribution, maximum likelihood method, mixture model, moment generating function, shifted exponential distributionAbstract
This paper extended the work of Bagiu et al. (2020) who defined the probability density function of a new oneparameter continuous distribution through the moment generating function approach. The new distribution called Bagiu-LiuZhang 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.
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