An analysis of the $q$-analogues of the Aradhana lifetime distribution
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The primary aim of this research is to explore the $q$-analogues of the Aradhana distribution and investigate their distributional and statistical properties. To achieve this, a comprehensive mathematical analysis is conducted, modeling the $q$-analogues of probability density function, cumulative distribution function, examining their shapes, obtaining the $q$-analogues of moments and related measures, and the cumulative distribution functions of order statistics. Furthermore, the $q$-analogues of the central moment, moment generating function, reliability function, stress-strength reliability, and stochastic ordering concepts for non-negative $q$-continuous random variables are introduced, and these distributional functions are derived for the proposed $q$-distribution. The unknown parameters of the proposed $q$-distribution are estimated using the method of moments. Several simulation studies are conducted to evaluate and compare the effectiveness of the estimators, utilizing data generated through $q$-Monte Carlo simulations.
Abstract
The primary aim of this research is to explore the $q$-analogues of the Aradhana distribution and investigate their distributional and statistical properties. To achieve this, a comprehensive mathematical analysis is conducted, modeling the $q$-analogues of probability density function, cumulative distribution function, examining their shapes, obtaining the $q$-analogues of moments and related measures, and the cumulative distribution functions of order statistics. Furthermore, the $q$-analogues of the central moment, moment generating function, reliability function, stress-strength reliability, and stochastic ordering concepts for non-negative $q$-continuous random variables are introduced, and these distributional functions are derived for the proposed $q$-distribution. The unknown parameters of the proposed $q$-distribution are estimated using the method of moments. Several simulation studies are conducted to evaluate and compare the effectiveness of the estimators, utilizing data generated through $q$-Monte Carlo simulations.