Exploring the fundamental properties and MGF of a 3-component mixture of power distributions: a simulation study

This paper estimates the parameters of the 3-component mixture of power distributions. The expressions of fundamental properties of the said distribution are presented, and for judgment, the numerical results of mean, median, variance, mode and skewness are evaluated. The closed-form expressions of the reliability properties, the statistical properties and necessary inequality measures are discussed. The trend of reliability measures is shown with the help of numerical results and graphs by taking different values of parameters and proportion parameters. The mathematical expressions of certain related statistical functions are derived from the reliability functions, the moment generating function, the characteristics function, the probability generating function, and the factorial moment generating function. The expressions of essential entropies, Shannon’s entropy, the B-entropy and Renyi’s entropy, are derived. The mathematical expressions of inequality indexes, the Gini index, the Lorenz curve, the Bonferroni curve, the Zinga index, the Atkinson index and the generalized entropy index are also analysed. The RF, the HRF, the CHR, the RHR, the MRL, and the MWT functions are derived in reliability analysis. The numerical values and graphs for different parameters and proportion components are discussed to judge the behaviour of reliability properties.