A GENERALIZED POWER SUJATHA DISTRIBUTION WITH PROPERTIES AND APPLICATIONS

This paper introduces a generalized power Sujatha distribution as an extension of the two-parameter generalization of Sujatha distribution, initially proposed for analyzing and modeling lifetime data in medical and engineering fields. The existing generalization of Sujatha distribution, being two-parameter, may not always provide a satisfactory fit for certain lifetime data from both theoretical and practical perspectives. The generalized power Sujatha distribution is presented as a comprehensive model, encompassing both the Generalization of Sujatha distribution and the Sujatha distribution as particular cases, specifically for the analysis of data in medical and engineering domains. The paper delves into the statistical properties of the proposed distribution, examining the behavior of its probability density function and cumulative distribution function across varying parameter values. Additionally, the first four raw moments of the distribution are derived and provided. The expressions for the hazard rate function and mean residual life function are obtained, and their behaviors under different parameter values are discussed. Stochastic ordering, a valuable tool for comparing stochastic nature, is also explored. The method of maximum likelihood is discussed for parameter estimation, and a simulation study is conducted to assess the performance of maximum likelihood estimates as sample sizes increase. To validate the applicability of the distribution, two real lifetime data sets from medical and engineering fields are analyzed. The goodness of fit of the generalized power Sujatha distribution is evaluated using the Akaike Information criterion and Kolmogorov-Smirnov statistic. The results demonstrate that the proposed distribution offers a closer fit compared to three-parameter power Quasi Lindley distribution, Three-parameter Sujatha distribution, Generalized gamma distribution, and twoparameter Generalizations of Sujatha distribution, as well as Weibull distribution and one-parameter Sujatha distribution. Given its superior fit over Power Quasi Lindley and Weibull distributions, particularly in the context of modeling and analyzing data from medical and engineering fields, the paper concludes by recommending the generalized power Sujatha distribution as the preferred choice over the considered distributions for such applications.