Bayesian Estimation of Two-Component Mixture of Gumbel Type II Distribution under Informative Priors

Feroze, Navid; Aslam, Muhammad

doi:10.14419/ijbas.v1i4.397

Cited by 6 publications

(11 citation statements)

References 9 publications

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“…(2)(3)(4)(5)(6)(7)(8)(9) We can derive the Bayes estimate of  based on DLF by using (2-9) in (2-4) to be …”

Section: Bayesian Estimation Under Linex Loss Function (Llf)mentioning

confidence: 99%

“…The Bayes estimate of  based on QLF can be obtained by using (2)(3)(4)(5)(6)(7)(8)(9)(10)(11) in (2-4) to be …”

Section: Bayesian Estimation Under Quadratic Loss Function (Qlf)mentioning

confidence: 99%

“… is the Bayes estimate  of given by (2-6), (2-8), (2-10), (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) and (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14). For more details see Han [9,19].…”

Section: E-bayesian Estimationmentioning

confidence: 99%

“…The E-Bayesian estimate of  based on 1 ( , ) ab  can be computed by using (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) and (3)(4) …”

Section: E-bayesian Estimation Under Quadratic Loss Function (Qlf)mentioning

confidence: 99%

“…Abbas and Tang [7] obtained the Bayes estimators for the parameters of Gumbel distribution under different loss functions and compared these estimates with the similar performed by the maximum likelihood method. Feroze and Aslam [8] derived the Bayesian estimators of the parameters of mixture of two components of Gumbel type-II distribution.…”

Section: Introductionmentioning

confidence: 99%

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E-Bayesian analysis of the Gumbel type-ii distribution under type-ii censored scheme

Reyad

Ahmed²

2015

IJAMS

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“…(2)(3)(4)(5)(6)(7)(8)(9) We can derive the Bayes estimate of  based on DLF by using (2-9) in (2-4) to be …”

Section: Bayesian Estimation Under Linex Loss Function (Llf)mentioning

confidence: 99%

“…The Bayes estimate of  based on QLF can be obtained by using (2)(3)(4)(5)(6)(7)(8)(9)(10)(11) in (2-4) to be …”

Section: Bayesian Estimation Under Quadratic Loss Function (Qlf)mentioning

confidence: 99%

“… is the Bayes estimate  of given by (2-6), (2-8), (2-10), (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) and (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14). For more details see Han [9,19].…”

Section: E-bayesian Estimationmentioning

confidence: 99%

“…The E-Bayesian estimate of  based on 1 ( , ) ab  can be computed by using (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) and (3)(4) …”

Section: E-bayesian Estimation Under Quadratic Loss Function (Qlf)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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E-Bayesian analysis of the Gumbel type-ii distribution under type-ii censored scheme

Reyad

Ahmed²

2015

IJAMS

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Statistical Modeling of Indus River Outflow at Tarbela Dam using Generalized Gumbel Type 2 Distribution

Ateeq,

Qasim,

Kiran

2024

Water Resour Manage

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The Indus River, a lifeline for Pakistan, holds paramount significance for its geography, history, and economy. This research delves into a comprehensive analysis of the river's behavior by introducing a novel statistical framework. Leveraging the Gumbel Type 2 distribution and the Rayleigh distribution, a new generalized Gumbel Type 2 (GG2) distribution is derived, and used for modeling the data about the river's outflow at the Tarbela Dam during 2020-2021. Our study contributes to the understanding of the complex dynamics of the Indus River, aiding in the sustainable management of its resources. The GG2 distribution, designed for extreme value events, adept at modeling positive-valued variables, were combined to model the intricate characteristics of the river's flow. Parameters were estimated using both classical and Bayesian methods, enhancing the accuracy and reliability of our findings. The incorporation of Bayesian techniques adds robustness to our parameter estimates and allows for a more comprehensive uncertainty analysis. The results not only deepen our understanding of the river's behavior but also offer insights crucial for infrastructure planning, flood control, and resource allocation.

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Bayesian Estimation of Gumbel Type-II Distribution under Type-II Censoring with Medical Applications

Abbas

Hussain

Rashid

et al. 2020

Computational and Mathematical Methods in Medicine

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The time to event or survival time usually follows certain skewed probability distributions. These distributions encounter vital role using the Bayesian framework to analyze and project the maximum life expectancy in order to inform decision-making. The Bayesian method provides a flexible framework for monitoring the randomized clinical trials to update what is already known using prior information about specific phenomena under uncertainty. Additionally, medical practitioners can use the Bayesian estimators to measure the probability of time until tumor recurrence, time until cardiovascular death, and time until AIDS for HIV patients by considering the prior information. However, in clinical trials and medical studies, censoring is present when an exact event occurrence time is not known. The present study aims to estimate the parameters of Gumbel type-II distribution based on the type-II censored data using the Bayesian framework. The Bayesian estimators cannot be obtained in explicit forms, and therefore we use Lindley’s approximation based on noninformative prior and various loss functions such as squared error loss function, general entropy loss function, and LINEX (linear exponential) loss function. The maximum likelihood and Bayesian estimators are compared in terms of mean squared error by using the simulation study. Furthermore, two data sets about remission times (in months) of bladder cancer patients and survival times in weeks of 61 patients with inoperable adenocarcinoma of the lung are analyzed for illustration purposes.

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Bayesian Estimation of Two-Component Mixture of Gumbel Type II Distribution under Informative Priors

Cited by 6 publications

References 9 publications

E-Bayesian analysis of the Gumbel type-ii distribution under type-ii censored scheme

E-Bayesian analysis of the Gumbel type-ii distribution under type-ii censored scheme

Statistical Modeling of Indus River Outflow at Tarbela Dam using Generalized Gumbel Type 2 Distribution

Bayesian Estimation of Gumbel Type-II Distribution under Type-II Censoring with Medical Applications

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