Omega \({{\omega}}\)—Type Probability Models: A Parametric Modification of Probability Distributions

A mathematical approach to developing new distributions is reviewed. The method which composes of integration and the concept of a normalizing constant, allows for primitive interjection of new parameter(s) in an existing distribution to form new model(s), called Omega-Type probability models. A probability distribution is proposed from a root model, Lindley distribution, and some properties, such as the series representation of the density and cumulative distribution functions, shape of the density, hazard and survival functions, moments and related measures, quantile function, order statistics, parameter estimation and interval estimate, were studied. Amidst the usual hazard and survival shapes, a constant or uniform trend was realized for the survival function, which projects the possibility of modeling systems that may not terminate over a given period of time. Three different methods of estimation, namely, the Cramer‒von Mises estimator, maximum product of the spacing estimator and maximum likelihood estimator, were used. The modified unimodal shape of the proposed distribution is added as a special feature in the improvements made among the Lindley family of distributions. Finally, two real-life datasets were fitted to the new distribution to demonstrate its economic importance.