On Bayesian inference of reliability parameter in Burr-type XII model based on imprecise data: a survey on fuzzy modelling

Iman Makhdoom; Abbas Pak

doi:https://doi.org/10.59170/stattrans-2024-008

On Bayesian inference of reliability parameter in Burr-type XII model based on imprecise data: a survey on fuzzy modelling

Iman Makhdoom Department of Statistics, Payame Noor University(PNU), P.O.Box,19395-4697 Tehran, Iran ORCID:https://orcid.org/0000-0002-2768-1024 , Abbas Pak Department of Computer Sciences, Faculty of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran ORCID:https://orcid.org/0000-0003-2388-3523 Statistics in Transition new series, vol. 25, 2024, 1, pages: 125-143 Published online: 6 March 2024 https://doi.org/10.59170/stattrans-2024-008 Citation: Makhdoom, I., Pak, A., 2024. On Bayesian inference of reliability parameter in Burr-type XII model based on imprecise data: a survey on fuzzy modeling. Statistics in Transition new series, 25(1), pp. 125-143. https://doi.org/10.59170/stattrans-2024-008.

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ABSTRACT

There are always two major sources of uncertainty in measurements related to lifetime surveys: variation among the observations and imprecision of individual observation called fuzziness. The typical statistical analysis is based on variation among the observations and does not consider the imprecision due to individual observation. However, ignoring the imprecision of individual observations may cause losing information and getting misleading results. It is mandatory to analyse such data, to extend the real numbers classically and Bayesian estimation methods to fuzzy numbers. Inference on the Burr-type (BT) XII model, based on precise measurements, is carried out by researchers, yet the problem of estimating parameters, in the presence of fuzzy data, remains unresolved. We are estimating the BT XII distribution parameters and their corresponding reliability when the available data are in the fuzzy numbers. The maximum likelihood estimation (MLE), the Bayesian method and the method of moments are used for estimating parameters. Finally, these estimators are compared via a Monte-Carlo simulation study.

KEYWORDS

Bayesian estimation, Burr-type XII distribution, Maximum likelihood estimates, Markov chain Monte Carlo, EM algorithm, Fuzzy data analysis

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