Bayesian Estimations of Exponential Distribution Based on Interval-Censored Data with a Cure Fraction

Censored data are considered to be of the interval type where the upper and lower bounds of an event’s failure time cannot be directly observed but only determined between interval inspection times. The analyses of interval-censored data have attracted attention because they are common in the fields...

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Autor principal:	Al Omari Mohammed Ahmed
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/e94ba44ac70d4e11b9f3467159a0a347
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spelling	oai:doaj.org-article:e94ba44ac70d4e11b9f3467159a0a3472021-11-08T02:36:23ZBayesian Estimations of Exponential Distribution Based on Interval-Censored Data with a Cure Fraction2314-478510.1155/2021/9822870https://doaj.org/article/e94ba44ac70d4e11b9f3467159a0a3472021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/9822870https://doaj.org/toc/2314-4785Censored data are considered to be of the interval type where the upper and lower bounds of an event’s failure time cannot be directly observed but only determined between interval inspection times. The analyses of interval-censored data have attracted attention because they are common in the fields of reliability and medicine. A proportion of patients enrolled in clinical trials can sometimes be cured. In some instances, their symptoms mostly disappear without any recurrence of the disease. In this study, the proportion of such patients who are cured is estimated. Furthermore, the Bayesian approach under the gamma prior and maximum likelihood estimation (MLE) is used to estimate the cure fraction depending on the bounded cumulative hazard (BCH) model based on interval-censored data with an exponential distribution. The Bayesian approach uses three loss functions: squared error, linear exponential, and general entropy. These functions are compared with the MLE and used between estimators. Moreover, they are obtained using the mean squared error, which locates the best option to estimate the parameter of an exponential distribution. The results show that the BCH model and lambda parameter of the exponential distribution based on the interval-censored data can be best estimated using the Bayesian gamma prior with a positive loss function of the linear exponential.Al Omari Mohammed AhmedHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Al Omari Mohammed Ahmed Bayesian Estimations of Exponential Distribution Based on Interval-Censored Data with a Cure Fraction
description	Censored data are considered to be of the interval type where the upper and lower bounds of an event’s failure time cannot be directly observed but only determined between interval inspection times. The analyses of interval-censored data have attracted attention because they are common in the fields of reliability and medicine. A proportion of patients enrolled in clinical trials can sometimes be cured. In some instances, their symptoms mostly disappear without any recurrence of the disease. In this study, the proportion of such patients who are cured is estimated. Furthermore, the Bayesian approach under the gamma prior and maximum likelihood estimation (MLE) is used to estimate the cure fraction depending on the bounded cumulative hazard (BCH) model based on interval-censored data with an exponential distribution. The Bayesian approach uses three loss functions: squared error, linear exponential, and general entropy. These functions are compared with the MLE and used between estimators. Moreover, they are obtained using the mean squared error, which locates the best option to estimate the parameter of an exponential distribution. The results show that the BCH model and lambda parameter of the exponential distribution based on the interval-censored data can be best estimated using the Bayesian gamma prior with a positive loss function of the linear exponential.
format	article
author	Al Omari Mohammed Ahmed
author_facet	Al Omari Mohammed Ahmed
author_sort	Al Omari Mohammed Ahmed
title	Bayesian Estimations of Exponential Distribution Based on Interval-Censored Data with a Cure Fraction
title_short	Bayesian Estimations of Exponential Distribution Based on Interval-Censored Data with a Cure Fraction
title_full	Bayesian Estimations of Exponential Distribution Based on Interval-Censored Data with a Cure Fraction
title_fullStr	Bayesian Estimations of Exponential Distribution Based on Interval-Censored Data with a Cure Fraction
title_full_unstemmed	Bayesian Estimations of Exponential Distribution Based on Interval-Censored Data with a Cure Fraction
title_sort	bayesian estimations of exponential distribution based on interval-censored data with a cure fraction
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/e94ba44ac70d4e11b9f3467159a0a347
work_keys_str_mv	AT alomarimohammedahmed bayesianestimationsofexponentialdistributionbasedonintervalcensoreddatawithacurefraction
_version_	1718443147584864256

Bayesian Estimations of Exponential Distribution Based on Interval-Censored Data with a Cure Fraction

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