Browsing by Author "Anurag Pathak"

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Assessing the effect of E-Bayesian inference for Poisson inverse exponential distribution parameters under different loss functions and its application
(Taylor and Francis Ltd., 2022) Anurag Pathak; Manoj Kumar; Sanjay Kumar Singh; Umesh Singh
This paper present E-Bayesian and Bayesian estimators of parameters of Poisson inverse exponential distribution (PIED) under Squared error loss function (SELF), General entropy loss function (GELF) and Linear Exponential loss function (LINEX) for progressive type-II censored data with binomial removals (PT-II CBRs). The E-Bayesian and corresponding Bayesian estimators are compared in terms of their risks based on simulated samples from PIED. The proposed methodology is applied to survival time of multiple myeloma patients data. © 2020 Taylor & Francis Group, LLC.
Bayesian estimation of the number of species from Poisson-Lindley stochastic abundance model using non-informative priors
(Springer Science and Business Media Deutschland GmbH, 2024) Anurag Pathak; Manoj Kumar; Sanjay Kumar Singh; Umesh Singh; Sandeep Kumar
In this article, we propose a Poisson-Lindley distribution as a stochastic abundance model in which the sample is according to the independent Poisson process. Jeffery’s and Bernardo’s reference priors have been obtaining and proposed the Bayes estimators of the number of species for this model. The proposed Bayes estimators have been compared with the corresponding profile and conditional maximum likelihood estimators for their square root of the risks under squared error loss function (SELF). Jeffery’s and Bernardo’s reference priors have been considered and compared with the Bayesian approach based on biological data. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.
Bayesian inference for Maxwell Boltzmann distribution on step-stress partially accelerated life test under progressive type-II censoring with binomial removals
(Springer, 2022) Anurag Pathak; Manoj Kumar; Sanjay Kumar Singh; Umesh Singh; Manoj Kumar Tiwari; Sandeep Kumar
This article deals with the estimation problem in step-stress partially accelerated life test of Maxwell Boltzmann distribution in presence of progressive type-II censoring with binomial removals. The maximum likelihood and Bayes estimators of the parameter are obtained under symmetric and asymmetric loss functions. Furthermore, the performances of the obtained estimators are compared in terms of risks. The proposed methodology is illustrated through the time to failure (in days) of Aluminium reduction cells and survival times (in weeks) for male rats that were exposed to a high level of radiation. © 2022, The Author(s) under exclusive licence to The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden.
Bayesian inference: Weibull Poisson model for censored data using the expectation–maximization algorithm and its application to bladder cancer data
(Taylor and Francis Ltd., 2022) Anurag Pathak; Manoj Kumar; Sanjay Kumar Singh; Umesh Singh
This article focuses on the parameter estimation of experimental items/units from Weibull Poisson Model under progressive type-II censoring with binomial removals (PT-II CBRs). The expectation–maximization algorithm has been used for maximum likelihood estimators (MLEs). The MLEs and Bayes estimators have been obtained under symmetric and asymmetric loss functions. Performance of competitive estimators have been studied through their simulated risks. One sample Bayes prediction and expected experiment time have also been studied. Furthermore, through real bladder cancer data set, suitability of considered model and proposed methodology have been illustrated. © 2020 Informa UK Limited, trading as Taylor & Francis Group.
E-Bayesian inference for xgamma distribution under progressive type II censoring with binomial removals and their applications
(Taylor and Francis Ltd., 2024) Anurag Pathak; Manoj Kumar; Sanjay Kumar Singh; Umesh Singh; Manoj Kumar Tiwari; Sandeep Kumar
In this article, we propose E-Bayes estimators of the parameter of xgamma distribution under squared error loss function, general entropy loss function, and linear exponential loss function for progressive type II censored data with binomial removals. The proposed estimators, maximum likelihood estimator, and corresponding Bayes estimators are compared in terms of their risks based on simulated samples from xgamma distribution. The proposed methodology is illustrated on two real data sets of bile duct cancer data and the endurance of deep-groove ball bearings data. © 2023 Informa UK Limited, trading as Taylor & Francis Group.
Model suitability analysis of survival time to ovarian cancer patients data
(Natural Sciences Publishing, 2020) Manoj Kumar; Sandeep K. Maurya; Sanjay K. Singh; Umesh Singh; Anurag Pathak
In this paper, we propose a suitable statistical model for survival time of the ovarian cancer patients data. The proposition followed by checking the suitability of twelve lifetime models through different statistical tools like the value of logarithmic of likelihood, Akaike Information Criterion, Kolmogorov-Smirnov distance and Bayesian Information Criterion. The maximum likelihood estimate of the parameters for the considered models has been obtained. Also, the non-parametric procedure has been used to show the validity of the conclusion. © 2020 Natural Sciences Publishing. All rights reserved.
Statistical Inferences: Based on Exponentiated Exponential Model to Assess Novel Corona Virus (COVID-19) Kerala Patient Data
(Springer Science and Business Media Deutschland GmbH, 2022) Anurag Pathak; Manoj Kumar; Sanjay Kumar Singh; Umesh Singh
In this article, we use exponentiated exponential distribution as a suitable statistical lifetime model for novel corona virus (covid-19) Kerala patient data. The suitability of the model has been followed by different statistical tools like the value of logarithm of likelihood, Kolmogorov–Smirnov distance, Akaike information criterion, Bayesian information criterion. Moreover, likelihood ratio test and empirical posterior probability analysis are performed to show its suitability. The maximum-likelihood and asymptotic confidence intervals for the parameters are derived from Fisher information matrix. We use the Markov Chain Monte Carlo technique to generate samples from the posterior density function. Based on generated samples, we can compute the Bayes estimates of the unknown parameters and can also construct highest posterior density credible intervals. Further we discuss the Bayesian prediction for future observation based on the observed sample. The Gibbs sampling technique has been used for estimating the posterior predictive density and also for constructing predictive intervals of the order statistics from the future sample. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Topp–Leone Poisson Exponential Distribution: A Classical and Bayesian Approach
(Springer, 2023) Anurag Pathak; Manoj Kumar; Sanjay Kumar Singh; Umesh Singh
In this paper, we propose a new three-parameter lifetime distribution, which has increasing, decreasing and constant failure rate. The new distribution can be use on a latent complementary risk scenario. The properties of the proposed distribution are discussed, including a formal proof of its density function and an explicit algebraic formula for its quantiles, skewness, kurtosis, survival and hazard functions. Also, we have been discussed inference aspects of the model proposed via Bayesian inference by using Markov chain Monte Carlo simulation. A simulation study performed in order to investigate the classical, Bayesian properties of the proposed estimators obtained under the assumptions of non-informative priors. Further, the applicability of proposed distribution is illustrated on a real data set. © 2023, The Indian Society for Probability and Statistics (ISPS).