A Flexible Unit Distribution Based on a Half-Logistic Map with Applications in Stochastic Data Modeling

In this manuscript, a new two-parameter stochastic distribution is proposed and obtained by a continuous half-logistic transformation of the quasi-Lindley (QL) distribution to the unit interval. The resulting distribution, named the quasi-Lindley half-logistic unit (QHU) distribution, is examined in terms of its key stochastic properties, such as asymmetry conditions, shape and modality, moments, etc. In addition, the stochastic dominance of the proposed distribution with respect to its parameters is considered, and it is shown that the QHU distribution, in contrast to the QL distribution that is always positively asymmetric, can have both asymmetric forms. The parameters of the QHU distribution are estimated by the maximum likelihood (ML) method, and the asymptotic properties of thusly obtained estimators are examined. Finally, an application of the proposed distribution in modeling some real-world phenomena is also presented.