Statistical Inferences to the Parameter and Reliability Characteristics of Gamma-mixed Rayleigh Distribution under Progressively Censored Data with Application

• Published in: Revstat Vol. 23; no. 1; p. 19
• Main Authors: Maiti, Kousik, Kayal, Suchandan
• Format: Journal Article
• Language: English
• Published: Instituto Nacional de Estatistica 01.01.2025; Instituto Nacional de Estatística | Statistics Portugal
• Subjects: Algorithms; Bayes estimates; Bayesian prediction estimates; Censorship; Expectation-Maximization (EM) algorithm; HPD credible interval; Observed Fisher information matrix
• ISSN: 1645-6726; 2183-0371
• DOI: 10.57805/revstat.v23i1.453

* We consider estimation of the model parameters and the reliability characteristics of a gamma-mixed Rayleigh distribution based on progressively type-II censored sample (PT-IICS). The sufficient condition for 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. Confidence intervals using the bootstrap-p and bootstrap-t methods are constructed. Bayes estimates are derived. Highest posterior density (HPD) credible intervals are derived using the importance sampling method. Prediction estimates and associated prediction equal-tail intervals under one-sample and two-sample frameworks are obtained. A simulation study is conducted. Finally, a real dataset is considered and analyzed. Keywords: * EM algorithm; observed Fisher information matrix; Bayes estimates; Bayesian prediction estimates; HPD credible interval. Subject Classification: * 62F10, 62F15, 62F40, 62N01.