Abstract
The paper introduces a new probability distribution, which is weighted version of the Prakaamy distribution. The paper explores various statistical properties of the Weighted Prakaamy (WP)distribution including probability density function (PDF), cumulative distribution function (CDF), moments, moment generating function, characteristics function, reliability analysis, ordered statistics, maximum likelihood estimation of parameters, entropies, likelihood ratiotest, and Bonferroni and Lorenz curves. The paper uses simulations to evaluate the performance of maximum likelihood estimators. The authorsapply the WP distribution to various real-life data sets from fields of engineering and medical science. This empirical analysis aims to evaluate the performance of the distribution in modeling and predicting real-world phenomena. The paper suggests that WP distribution outperforms other probability distributions including Prakaamy distribution, Exponential distribution, Erlang Truncated Exponential distribution, Power Lindley distribution and Lindley distribution.
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