Estimation of Information Measures for Power-Function Distribution in Presence of Outliers and Their Applications

Abstract

The measure of entropy has an undeniable pivotal role in the field of information theory. This article estimates the Rényi and q-entropies of the power function distribution in the presence of s outliers. The maximum likelihood estimators as well as the Bayesian estimators under uniform and gamma priors are derived. The proposed Bayesian estimators of entropies under symmetric and asymmetric loss functions are obtained. These estimators are computed empirically using Monte Carlo simulation based on Gibbs sampling. Outcomes of the study showed that the precision of the maximum likelihood and Bayesian estimates of both entropies measures improves with sample sizes. The behavior of both entropies estimates increase with number of outliers. Further, Bayesian estimates of the Rényi and q-entropies under squared error loss function are preferable than the other Bayesian estimates under the other loss functions in most of cases. Eventually, real data examples are analyzed to illustrate the theoretical results.

Shrinkage estimation of stress strength reliability P (Y❮X❮Z) for lomax distribution based on records

“…Maximum Likelihood Estimate and Uniformly Minimum Variance Unbiased Estimate of R when Y, Z and X either uniform or exponential random variable with the unknown location parameter was considered by Ivshin (1998) [11] . Hassan et al (2013) [10] focused on the estimate of R= P[Y < 𝑋 < 𝑍], where Y and Z be a random stress and X be a random strength have Weibull Distribution in presence of k outliers. Hameed et al (2020) [9] focused on the estimate of R= P[Y < 𝑋 < 𝑍], when Y, Z and X are independent and that these stress and strength variable follows Kumaraswamy Distribution.…”

Comparison Various Estimation Methods for R = P (Y1 < X < Y2) Utilizing Restricted Generalized Weibull Distribution

“…For the estimate of R = (Y 1 < X < Y 2 ), Amal et al in 2013 developed the ML estimator, MOM estimator, Mix. estimator, and the stresses Y 1 , Y 2 , and the strength X have distribution follow Weibull; [5]. When the stresses Y 1 and Y 2 and the strength X have inverse Rayleigh distribution, Raheem, S.H., Kalaf, B.A., and Salman, A.N.…”

Estimation of Stress Strength Reliability P [Y < X < Z] of Lomax Distribution under Different Sampling Scheme

“…Maximum Likelihood Estimate and Uniformly Minimum Variance Unbiased Estimate of R when Y , Z and X either uniform or exponential random variable with the unknown location parameter was considered by [23]. [24] focused on the estimate of R = P [Y < X < Z], where Y and Z be a random stresses, and X be a random strength, having Weibull distribution in presence of k outliers. [25] focused on the estimate of R = P [Y < X < Z],when Y , Z and X are independent and that these stress and strength variable follows Kumaraswamy Distribution.…”