Browsing by Author "Kumar, K"

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    On Estimation of Shannon’s Entropy of Maxwell Distribution Based on Progressively First-Failure Censored Data
    (2024-02) Kumar, K; Kumar, I; Ng, H
    Shannon’s entropy is a fundamental concept in information theory that quantifies the uncertainty or information in a random variable or data set. This article addresses the estimation of Shannon’s entropy for the Maxwell lifetime model based on progressively first-failure-censored data from both classical and Bayesian points of view. In the classical perspective, the entropy is estimated using maximum likelihood estimation and bootstrap methods. For Bayesian estimation, two approximation techniques, including the Tierney-Kadane (T-K) approximation and the Markov Chain Monte Carlo (MCMC) method, are used to compute the Bayes estimate of Shannon’s entropy under the linear exponential (LINEX) loss function. We also obtained the highest posterior density (HPD) credible interval of Shannon’s entropy using the MCMC technique. A Monte Carlo simulation study is performed to investigate the performance of the estimation procedures and methodologies studied in this manuscript. A numerical example is used to illustrate the methodologies. This paper aims to provide practical values in applied statistics, especially in the areas of reliability and lifetime data analysis.
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    On Estimation of Shannon’s Entropy of Maxwell Distribution Based on Progressively First-Failure Censored Data
    (2024-02) Kumar, K; Kumar, I
    Shannon’s entropy is a fundamental concept in information theory that quantifies the uncertainty or information in a random variable or data set. This article addresses the estimation of Shannon’s entropy for the Maxwell lifetime model based on progressively first-failure-censored data from both classical and Bayesian points of view. In the classical perspective, the entropy is estimated using maximum likelihood estimation and bootstrap methods. For Bayesian estimation, two approximation techniques, including the Tierney-Kadane (T-K) approximation and the Markov Chain Monte Carlo (MCMC) method, are used to compute the Bayes estimate of Shannon’s entropy under the linear exponential (LINEX) loss function. We also obtained the highest posterior density (HPD) credible interval of Shannon’s entropy using the MCMC technique. A Monte Carlo simulation study is performed to investigate the performance of the estimation procedures and methodologies studied in this manuscript. A numerical example is used to illustrate the methodologies. This paper aims to provide practical values in applied statistics, especially in the areas of reliability and lifetime data analysis.
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    Stochastic modeling and parameter estimation of turbogenerator unit of a thermal powerplant under classical and Bayesian inferential framework
    (2023-10) Kumar, A; Chaudhary, R; Kumar, K
    Theworkreported in present study deals with the development of a novel stochastic model andestimation of parameters to assess reliability characteristics for a turbogenerator unit of thermal power plant under classical and Bayesian frameworks. Turbogenerator unit consists of five components namely turbine lubrication, turbine governing, generator oil system, gen erator gas system and generator excitation system. The concepts of cold standby redun dancy andWeibull distributed random variables are used in development of stochastic model. The shape parameter for all the random variables is same while scale parameter is different. Regenerative point technique and semi-Markov approach are used for evaluation of reliability characteristics. Sufficient repair facility always remains available in plant as well as repair done by the repairman is considered perfect. As the life testing experiments are time consuming, so to highlight the importance of proposed model Monte Carlo simulation study is carried out. A comparative analysis is done between true, classical and Bayesian results of MTSF, availability and profit function.
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    Stochastic modeling and parameter estimation of turbogenerator unit of a thermal power plant under classical and Bayesian inferential framework
    (2023-10) Kumar, A; Chaudhary, R; Kumar, K; Saini, M; Saini, D
    The work reported in present study deals with the development of a novel stochastic model and estimation of parameters to assess reliability characteristics for a turbogenerator unit of thermal power plant under classical and Bayesian frameworks. Turbogenerator unit consists of five components namely turbine lubrication, turbine governing, generator oil system, gen erator gas system and generator excitation system. The concepts of cold standby redun dancy and Weibull distributed random variables are used in development of stochastic model. The shape parameter for all the random variables is same while scale parameter is different. Regenerative point technique and semi-Markov approach are used for evaluation of reliability characteristics. Sufficient repair facility always remains available in plant as well as repair done by the repairman is considered perfect. As the life testing experiments are time consuming, so to highlight the importance of proposed model Monte Carlo simulation study is carried out. A comparative analysis is done between true, classical and Bayesian results of MTSF, availability and profit function.