The weighted distributions are widely used in many fields such as medicine, ecology and reliability, to name a few, for the development of proper statistical models. Weighted distributions are milestone for efficient modeling of statistical data and prediction when the standard distributions are not appropriate. A good deal of studies related to the weight distributions have been published in the literature. In this article, a brief review of these distributions is carried out. Implications of the differing weight models for future research as well as some possible strategies are discussed. Finally, characterizations of these distributions based on a simple relationship between two truncated moments are presented.

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The distribution of the ratio of two independently distributed Lindley random variables $$X$$ X and $$Y$$ Y , with different parameters, is derived. The associated distributional properties are provided. Furthermore, the proposed ratio distribution is fitted to two applications data (COVID-19 and Bladder Cancer Data), and compared it with some well-known right-skewed variations of Lindley distribution, namely; Lindley distribution, new generalized Lindley distribution, new quasi Lindley distribution and a three parameter Lindley distribution. The numerical result of the study reveals that the proposed distribution of two independent Lindley random variables fits better to the above said data sets than the compared distribution.

Hydrologic design is often based on assessments of large return interval measures; it is vital to be able to conclude them as precisely as possible. Henceforth, the selection of a probability distribution is very crucial for such cases. In view of this scenario, we propose and study a pliant probability distribution for precipitation data analysis. Some mathematical and statistical properties are analyzed. In order to make stronger predictions and judge the realistic return period, we have also characterized the model via Laplace transformation. We have estimated its parameters via the maximum likelihood estimation and constructed its information matrix for developing the confidence belt of population parameters. Moreover, a real‐life setup is also considered by applying the model over precipitation data of diverse regions, including Jacksonville, Florida (USA), Barkhan (Pakistan), British Columbia (Canada), and Alexandria (Egypt). This investigated study is based on various statistical parametric and nonparametric tests, which indicates that the proposed model is one of the better strategies for precipitation data analysis when compared with the famous three‐parameter Kappa model.

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