Intervened Exponential Distribution: Properties and Applications

Abstract

This manuscript aims to study the intervention-based probability model. Statistical and reliability properties such as the expressions for, cumulative density function (CDF), mean deviations about mean and median, rth order central and non-central moments, ”generation functions” for moments have been derived. Moreover, the expression for reliability function, hazard rate, reverse hazard rate, aging intensity, mean residual life function, stress-strength reliability, and entropy metrics due to R´enyi and Shannon are also derived. Monte Carlo simulation study performance of maximum likelihood estimates (MLEs) has been carried out, followed by calculations of Average Bias (ABias), and Mean Square Error (MSE). The applicability of the model in real-life situations has been discussed by analyzing the two real-life data sets.

Estimation for the Parameters of Power Rayleigh Distributions Using Double Ranked Set Sampling with an Application to Wind Speed Data

“…To increase the flexibility of the Rayleigh distribution, Bhat and Ahmad [67] proposed the PR distribution with the power transformation technique. Using the transformation 𝑋 = 𝑌 1 𝜂 , where Y follows the Rayleigh distribution with parameters 𝜂 and 𝜃, the PR distribution is obtained as follows…”