Weighted Quasi Rama Distribution with Properties and Applications in Engineering
Rama Shanker, Mousumi Ray, Hosenur Rahman Prodhani, Jintu Boruah
Abstract
In this study, a novel weighted quasi Rama distribution is proposed, which generalizes the Rama, weighted Rama, and quasi Rama distributions for modeling lifetime data. Several statistical properties of the proposed distribution have been explored, including moment-based measures such as the coefficients of variation, skewness, and kurtosis, as well as the index of dispersion. The behavior of the hazard function is also examined, demonstrating flexibility with increasing, decreasing, and upside-down bathtub shapes depending on parameter values. Parameter estimation is carried out using the method of maximum likelihood. A simulation study employing the acceptance-rejection method is conducted to assess the consistency of the maximum likelihood estimators. Given its capacity to model both under-dispersed and over-dispersed data, the proposed distribution is applied to two real lifetime datasets from engineering—one under-dispersed and the other over-dispersed. Comparative analysis of goodness-of-fit is performed against several existing two-parameter and three-parameter distributions, both weighted and unweighted. Results show that the proposed distribution offers a significantly better fit across the datasets considered.
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