The unit two parameters Mirra distribution: Reliability analysis, properties, estimation and applications

To define useful numbers having values from 0 to 1, as percentages, probabilities, and proportions, the unit probability models are often employed in probability and statistics. In this paper, a new two-parameter model on the unit interval, entitled the unit Mirra distribution (UMD) is suggested which is a modification of the Mirra distribution (MD). Various statistical properties of the proposed UMD as the rth moment, variance, inverse moments, and incomplete moments are presented. Also, the distributions of order statistics, coefficients of variation and skewness, stochastics ordering, and median and mean deviations are provided. The reliability functions such the hazard function, survival function, odds function, reversed hazard rate function, and the mean residual function are provided with supported graphical representation. The Lorenz curve, Gini index, and Bonferroni curve of the UMD with some simulations are included. The distribution parameters are estimated based on the maximum likelihood estimation, ordinary least squares estimation, Anderson-Darling and maximum product of spacing's estimation. Finally, two different applications of actual data sets that represent the times to infection of kidney dialysis patients in months and the trade share data on unit interval are carried out to evaluate the model's performance as compared to some competitors. It turns out that the suggested UMD can serve as a good alternative for modeling these data sets.