Mathematical Properties, Computational Estimation, and Applications of the Slash Q-Lindley Distribution

Source abstract

This paper introduces the Slash Q-Lindley (SQL) distribution, a new heavy-tailed model for positive data obtained as the ratio of a Q-Lindley variable to an independent power-distributed variable. The SQL inherits the flexibility of the baseline Q-Lindley while adding a tail parameter that controls polynomial decay. Its hazard rate tends to zero and, numerically, is decreasing or unimodal. Explicit expressions for the PDF, CDF, and hazard functions are derived using incomplete gamma and confluent hypergeometric functions. Key properties (moments, order statistics, stochastic ordering, entropy, and stress–strength reliability) are investigated. Parameter estimation is performed via maximum likelihood, Anderson–Darling, Cramér–von Mises, maximum product of spacings, ordinary and weighted least squares, and Bayesian MCMC methods. A simulation study evaluates finite-sample behavior, showing that the Bayesian estimator has the smallest overall rank, followed closely by the maximum product of spacings estimator, with maximum likelihood third. The practical advantage of the SQL is demonstrated on two real heavy-tailed datasets (flood discharges and coastal island areas), where it provides superior fits compared to several competing models based on multiple criteria (Akaike Information Criterion, Bayesian Information Criterion, Kolmogorov–Smirnov statistic, Anderson–Darling statistic, Cramér–von Mises statistic). The SQL offers a tractable and flexible alternative for modeling positive data with extreme values.