scholarly journals Bayesian Analysis of Inverted Kumaraswamy Mixture Model with Application to Burning Velocity of Chemicals

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Farzana Noor ◽  
Saadia Masood ◽  
Mehwish Zaman ◽  
Maryam Siddiqa ◽  
Raja Asif Wagan ◽  
...  
Keyword(s):  
Bayesian Analysis ◽  
Mixture Model ◽  
Bayesian Method ◽  
Burning Velocity ◽  
Likelihood Estimation ◽  
Empirical Bayesian ◽  
Squared Error ◽  
Linex Loss ◽  
Empirical Bayesian Method ◽  
Better Than

Burning velocity of different chemicals is estimated using a model from mixed population considering inverted Kumaraswamy (IKum) distribution for component parts. Two estimation techniques maximum likelihood estimation (MLE) and Bayesian analysis are applied for estimation purposes. BEs of a mixture model are obtained using gamma, inverse beta prior, and uniform prior distribution with two loss functions. Hyperparameters are determined through the empirical Bayesian method. An extensive simulation study is also a part of the study which is used to foresee the characteristics of the presented model. Application of the IKum mixture model is presented through a real dataset. We observed from the results that Linex loss performed better than squared error loss as it resulted in lower risks. And similarly gamma prior is preferred over other priors.

Data Processing and Technology Application in Bayes and Empirical Bayes Reliability Analysis of Parameter of Ailamujia Distribution

2014 ◽  
Vol 951 ◽  
pp. 249-252
Author(s):  
Hui Zhou
Keyword(s):  
Empirical Bayes ◽  
Bayes Estimators ◽  
Conjugate Prior ◽  
Likelihood Estimator ◽  
Empirical Bayesian ◽  
Technology Application ◽  
Inverse Gamma ◽  
Squared Error ◽  
Linex Loss ◽  
Empirical Bayes Estimators

The estimation of the parameter of the ЭРланга distribution is discussed based on complete samples. Bayes and empirical Bayesian estimators of the parameter of the ЭРланга distribution are obtained under squared error loss and LINEX loss by using conjugate prior inverse Gamma distribution. Finally, a Monte Carlo simulation example is used to compare the Bayes and empirical Bayes estimators with the maximum likelihood estimator.

scholarly journals The Bühlmann–Straub Estimation of Claim Means in Random B-F Reserve Model

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Zhang Yi ◽  
Wen Limin ◽  
Li Zhilong
Keyword(s):  
Prior Distribution ◽  
Personal Experience ◽  
Bayesian Method ◽  
Historical Data ◽  
Credibility Theory ◽  
Empirical Bayesian ◽  
Sample Distribution ◽  
Empirical Bayesian Method ◽  
Chain Ladder ◽  
Bayesian Estimators

In the B-F reserve model, it is a very critical step to estimate the claim means of the accident year. However, the traditional method uses the prior estimators of the claim means based on the personal experience of actuaries or historical data. This method inevitably carries the subjectivity of the actuary himself. In this paper, a stochastic B-F model is established, and a prior distribution is constructed for the claim means in the accident year. The idea of the credibility theory is used to derive the linear Bayesian estimators of claim means. Finally, the empirical Bayesian method is used to estimate the first two moments of the prior distribution, and the empirical Bayesian estimators of the claim means and the corresponding reserves are derived. The estimators obtained in this paper do not depend on the specific forms of the sample distribution and the prior distribution and can be used directly in practice. In the numerical simulation, our estimates are compared with the traditional B-F estimates and the chain ladder estimates. It is verified that the estimates given in this paper have small mean square error.

scholarly journals Robust Bayesian Analysis of Lifetime Data from Maxwell Distribution

2018 ◽  
Vol 48 (1) ◽  
pp. 38-55
Author(s):  
M. S. Panwar ◽  
Sanjeev K Tomer
Keyword(s):  
Bayesian Analysis ◽  
Real Data ◽  
Type I ◽  
Lifetime Data ◽  
Maxwell Distribution ◽  
Data Set ◽  
Squared Error ◽  
Robust Bayesian Analysis ◽  
Linex Loss ◽  
Mean Lifetime

In this paper, we consider robust Bayesian analysis of lifetime data from the Maxwell distribution assuming an $\varepsilon$-contamination class of prior distributions for the parameter. We obtain robust Bayes estimates of the parameter and mean lifetime under squared error and LINEX loss functions in presence of uncensored as well as Type-I progressively hybrid censored lifetime data. A real data set is analysed for numerical illustrations.

scholarly journals Bayesian Analysis of Cancer Data Using a 4-Component Exponential Mixture Model

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Farzana Noor ◽  
Saadia Masood ◽  
Yumna Sabar ◽  
Syed Bilal Hussain Shah ◽  
Touqeer Ahmad ◽  
...  
Keyword(s):  
Bayesian Analysis ◽  
Mixture Model ◽  
Graphical Representation ◽  
Age Groups ◽  
Model Parameters ◽  
Jeffreys Prior ◽  
Female Population ◽  
Cancer Data ◽  
Linex Loss ◽  
Exponential Mixture

Cancer is among the major public health problems as well as a burden for Pakistan. About 148,000 new patients are diagnosed with cancer each year, and almost 100,000 patients die due to this fatal disease. Lung, breast, liver, cervical, blood/bone marrow, and oral cancers are the most common cancers in Pakistan. Perhaps smoking, physical inactivity, infections, exposure to toxins, and unhealthy diet are the main factors responsible for the spread of cancer. We preferred a novel four-component mixture model under Bayesian estimation to estimate the average number of incidences and death of both genders in different age groups. For this purpose, we considered 28 different kinds of cancers diagnosed in recent years. Data of registered patients all over Pakistan in the year 2012 were taken from GLOBOCAN. All the patients were divided into 4 age groups and also split based on genders to be applied to the proposed mixture model. Bayesian analysis is performed on the data using a four-component exponential mixture model. Estimators for mixture model parameters are derived under Bayesian procedures using three different priors and two loss functions. Simulation study and graphical representation for the estimates are also presented. It is noted from analysis of real data that the Bayes estimates under LINEX loss assuming Jeffreys’ prior is more efficient for the no. of incidences in male and female. As far as no. of deaths are concerned again, LINEX loss assuming Jeffreys’ prior gives better results for the male population, but for the female population, the best loss function is SELF assuming Jeffreys’ prior.

scholarly journals An approximate empirical Bayesian method for large-scale linear-Gaussian inverse problems

2018 ◽  
Vol 34 (9) ◽  
pp. 095001 ◽  
Author(s):  
Qingping Zhou ◽  
Wenqing Liu ◽  
Jinglai Li ◽  
Youssef M Marzouk
Keyword(s):  
Inverse Problems ◽  
Large Scale ◽  
Bayesian Method ◽  
Empirical Bayesian ◽  
Empirical Bayesian Method
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