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Generalized Residual Entropy and Upper Record Values
Full text linkIn this communication, we deal with a generalized residual entropy
of record values and weighted distributions. Some results on
monotone behaviour of generalized residual entropy in record values
are obtained. Upper and lower bounds are presented. Further, based
on this measure, we study some comparison results between a random
variable and its weighted version. Finally, we describe some
estimation techniques to estimate the generalized residual entropy
of a lifetime distribution
Some Results on a Generalized Residual Entropy based on Order Statistics
Full text linkIn the present paper, we discuss some monotone properties of the GRE of order (α, β) in order statistics under various assumptions. It is shown that monotone properties are preserved under the formation of a parallel system but not under the formation of a series system. A counter example is presented. Bounds of the GRE of order statistics are obtained. The GRE of parallel and series systems are shown to be monotone function of the number of observations of a given sample. Numerical simulation is carried out for verification of the theoretical results. Maximum likelihood estimators of GRE of X, X1:n and Xn:n are obtained when independent data are drawn from exponential distribution
Statistical Inferences to the Parameter and Reliability Characteristics of Gamma-mixed Rayleigh Distribution under Progressively Censored Data with Application
Full text linkThe purpose of the present paper is two-fold. First, we consider the estimation of the unknown model parameters and the reliability characteristics of a gamma-mixed Rayleigh distribution when a progressively type-II censored sample (PT-IICS) is available. The sufficient condition for the existence and uniqueness of the maximum likelihood estimates (MLE) is obtained. We compute MLEs using the expectation-maximization (EM) algorithm. Asymptotic confidence intervals are constructed. For comparison purposes, confidence intervals using bootstrap-p and bootstrap-t methods are also constructed. Bayes estimates are derived with respect to the squared error, LINEX, and the entropy loss functions. Two approximation techniques (Lindley and importance sampling) are used for the computation of the Bayes estimates. Further, the highest posterior density (HPD) credible intervals are derived using the importance sampling method. Second, we consider the problem of Bayesian prediction. Prediction estimates and the associated prediction equal-tail intervals under one-sample and two-sample frameworks are obtained. A simulation study is conducted the comparison the methods of estimation and prediction. Finally, a real dataset is considered and analyzed for the purpose of illustration
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