Power Quasi Rama Distribution with Properties and Applications in Reliability Engineering

Abstract

A three-parameter power quasi Rama distribution for modeling over-dispersed and under-dispersed engineering data having increasing or decreasing hazard rates has been introduced and it includes quasi Rama distribution, power Rama distribution, Rama distribution, generalized gamma distribution and one parameter gamma distribution as particular cases.  Its statistical properties including behaviour of its probability density function, cumulative density function for varying values of parameters, moments, survival function, hazard function, mean residual life function and stochastic ordering has been discussed. The estimation of the parameters of the distribution has been discussed using maximum likelihood estimation and maximum product spacing estimation. A simulation study has been carried out to know the consistency of the estimators. As the proposed distribution is suitable for over-dispersed and under-dispersed  engineering data having increasing and deceasing hazard rates, the applications of the proposed distribution has been  tested with three dataset from engineering of various natures  and the goodness of fit shows that power quasi Rama distribution provides a better fit as compared to the generalized power Sujatha distribution, three-parameter power Sujatha distribution, power quasi Lindley distribution, generalized gamma distribution, three-parameter Sujatha distribution and three-parameter generalized Lindley distribution.