Power Quasi-XLindley probability distribution: Its properties, inference and application on engineering data

A new three-parameter probability distribution called the power Quasi-XLindley (PoQXL) distribution is introduced as an extension of the existing Quasi-XLindley distribution. The current study explores its mathematical characteristics including derivation of the moments, mode, moment-generating function, the mean residual life function, quantiles, Rényi entropy, and order statistics. To facilitate practical applications, the estimation of parameters is carried out using the renowned maximum likelihood estimation approach. The efficiency of these derived estimators is thoroughly assessed via a comprehensive simulation study which examines their performance under varying sample sizes and different choices of parameters. The applicability and versatility of the distribution are demonstrated using two engineering-related datasets. These datasets are modeled to exemplify the PoQXL distribution ability to analyze diverse phenomena effectively and to highlight its potential utility in applied areas.