The Transmuted Kumaraswamy Burr III Distribution:Estimation and Applications
This study introduces a new probability distribution referred to as the Transmuted Kumaraswamy Burr III distribution (KwB III) using the Quadratic Rank Transmuted Map (QRTM) proposed by Shaw et al. (2007). The statistical properties of the distribution were thoroughly invested, including the moments, moment generating function, mean, quantiles and random number generator, Rényi entropy, order statistics and the reliability analysis. A simulation study was carried out to evaluate the performance of the MLEs, and showed that the estimators were nearly unbiased and that the mean squared error (MSE) decreased with increasing sample size, confirming efficiency and consistency.
In addition, the study applied several information criteria, such as -2 log-likelihood (), the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), corrected Akaike Information Criterion (AICc), and Hannan-Quinn information criterion (HQIC) to evaluate model fit and compare the proposed distribution with existing alternatives. Overall, findings demonstrate that the proposed distribution is flexible, statistically robust, and suitable for modelling various types of data, especially when classical models are inadequate.
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