Bayesian estimation and classification for two logistic populations with a common location

Pushkal Kumar, Manas Ranjan Tripathy () and Somesh Kumar
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Pushkal Kumar: National Institute of Technology Rourkela
Manas Ranjan Tripathy: National Institute of Technology Rourkela
Somesh Kumar: Indian Institute of Technology Kharagpur

Computational Statistics, 2023, vol. 38, issue 2, No 7, 748 pages

Abstract: Abstract The problems of estimation and classification for two logistic populations with a common location and different scale parameters are considered. The MLEs of the associated parameters are derived by solving a system of non-linear equations numerically as they do not have closed-form expressions. The asymptotic confidence intervals and bootstrap confidence intervals are derived numerically. Bayes estimators for the associated parameters using Lindley’s approximation method with respect to three types of priors, namely the vague prior, Jeffrey’s prior and conjugate prior, are also derived numerically. Further, Bayes estimators using the Markov chain Monte Carlo (MCMC) method that uses the Metropolis-Hastings algorithm are also derived. Moreover, using these MCMC samples, the highest posterior density (HPD) credible confidence intervals are also derived for the associated parameters. The point estimators are compared through their bias and mean squared error, whereas the interval estimators are compared through coverage probabilities and expected lengths using the Monte-Carlo simulation method numerically. Based on these estimators, certain classification rules are derived to classify a new observation into one of the two logistic populations under the same model set-up. The expected probability of misclassification for each classification rule is computed numerically to evaluate their performances. Finally, two real-life examples are considered where the datasets have been satisfactorily modeled by using the logistic distribution with a common location, and the estimation and classification methodologies have been demonstrated.

Keywords: Approximate Bayes estimator; Asymptotic confidence interval; Bootstrap confidence interval; Classification rule; HPD credible interval; Lindley’s approximation; Markov chain Monte Carlo Method; Maximum likelihood estimator; Numerical comparison; Probability of misclassification; 62F10; 62F15; 62F40; 62F99 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00180-022-01247-y

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