POWER QUASI LINDLEY DISTRIBUTION: PROPERTIES AND APPLICATION
SAID HOFAN ALKARNI *
Department of Quantitative Analysis, King Saud University, Riyadh, Saudi Arabia.
*Author to whom correspondence should be addressed.
In this paper, we introduce a new class of distributions called power quasi Lindley (PQL) distribution for modeling non-monotone survival data. This class of distributions includes several distributions such as Lindley, power Lindley, quasi Lindley, gamma, and generalized gamma distributions as special cases. Some statistical properties of the PQL distribution are explicitly derived. These properties include the density and hazard rate functions with their behavior, moments, moment-generating function, skewness, kurtosis measures, and quantile function. The maximum likelihood estimation of the parameters and their estimated asymptotic distribution and confidence intervals are also derived. Further, the Rényi entropy is derived as a measure of uncertainty in the proposed model. Finally, an application of the model to a real dataset is presented and compared with the fit attained by other well-known existing distributions.
Keywords: Power quasi Lindley distribution;, Lindley distribution, non-monotone survival data modeling, hazard rate function