Alpha Power Transformation of the Lindley Probability Distribution - Shibiru Jabessa Dugasa; Ayele Taye Goshu; Butte Gotu Arero (Journal of Probability and Statistics)
This paper presents the alpha power transformation of the Lindley probability distribution (APTLD), which is a new model with four parameters. The probability density, cumulative distribution, hazard, and survival functions are derived and presented. Its properties including moments, moment-generating and quantile functions are obtained. The maximum likelihood method is derived for parameter estimation of the model. Simulation studies are performed to generate random observations from the model. The new distribution model is fitted to two real datasets, revealing better fit as compared to other five distributions. The new probability distribution reveals interesting properties with the flexible shape of its hazard function and could be considered as a new contribution to the field of statistics and probability theory. The findings of this study can be used as the basis for future research in statistics and probability, as well as in different application areas such as health, engineering, education, and economics.