Bayesian estimation and prediction for Burr‐Rayleigh mixture model using censored data

Noor, Farzana; Sajid, Ahthasham; Shah, Syed Bilal Hussain; Zaman, Mehwish; Gheisari, Mehdi; Mariappan, Vinayagam

doi:10.1002/dac.4094

Cited by 12 publications

(11 citation statements)

References 29 publications

(30 reference statements)

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“…Abu-Taleb et al [10] present Bayes estimation for the parameters of the lifetime distribution when both censoring and survival time are exponentially distributed. Noor et al [11] have analyzed a mixture model by mixing Rayleigh and Burr XII distribution under a Bayesian setup. Abu Zinadah [12] presents maximum likelihood estimation and Bayesian analysis on exponential distribution and exponential pareto under type II censoring.…”

Section: Introductionmentioning

confidence: 99%

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

Noor

Masood

Sabar

et al. 2021

Computational and Mathematical Methods in Medicine

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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.

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Section: Introductionmentioning

confidence: 99%

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

Noor

Masood

Sabar

et al. 2021

Computational and Mathematical Methods in Medicine

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“…After obtaining the MNAR and MLAR model, deviance information criterion (DIC) for each MLAR model is calculated and the model with the smallest DIC is selected. The DIC formula is shown on (8).…”

Section: Repeat Step Two T Times → ∞mentioning

confidence: 99%

“…A method with a mixture model approach has been used in several studies to solve problems that occur in unimodal data [7] [8]. By considering the skewed and the heterogeneity, the mixture model method can improve the accuracy 12 of predictive cases [7] [8]. It has been proven to be better than the separate one [9] [10] and suitable to be applied to the autoregressive (AR) model, a time series model.…”

Section: Introductionmentioning

confidence: 99%

Investment Modelling Using Value at Risk Bayesian Mixture Modelling Approach and Backtesting to Assess Stock Risk

Miftahurrohmah

Wulandari

Dharmawan

2021

JISEBI

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Background: Stock investment has been gaining momentum in the past years due to the development of technology. During the pandemic lockdown, people have invested more. One the one hand, stock investment has high potential profitability, but on the other, it is equally risky. Therefore, a value at risk (VaR) analysis is needed. One approach to calculate VaR is by using the Bayesian mixture model, which has been proven to be able to overcome heavy-tailed cases. Then, the VaR’s accuracy needs to be tested, and one of the ways is by using backtesting, such as the Kupiec test.Objective: This study aims to determine the VaR model of PT NFC Indonesia Tbk (NFCX) return data using Bayesian mixture modelling and backtesting. On a practical level, this study can provide information about the potential risks of investing that is grounded in empirical evidence.Methods: The data used was NFCX data retrieved from Yahoo Finance, which was then modelled with a mixture model based on the normal and Laplace distributions. After that, the VaR accuracy was calculated and then tested by using backtesting.Results: The test results showed that the VaR with the mixture Laplace autoregressive (MLAR) approach (2;[2],[4]) was accurate at 5% and 1% quantiles while mixture normal autoregressive MNAR (2;[2],[2,4]) was only accurate at 5% quantiles.Conclusion: The better performing NFCX VaR model for this study based on backtesting using Kupiec test is MLAR(2;[2],[4]).

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“…Mixture models have been effectively used in many areas such as industrial engineering (Ali et al [1]), biology (Bhattacharya [2]), social sciences (Harris [3]), economics (Jedidi et al [4]), and reliability (Sultan et al [5]). For more detail about the finite mixture models, see Everitt [6], Ali [7], Feroze and Aslam [8], Zhang and Huang [9], Fundi et al [10], Tripathi et al [11], Noor et al [12], and Feroze and Aslam [13].…”

Section: Introductionmentioning

confidence: 99%

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

Noor

Masood

Zaman

et al. 2021

Mathematical Problems in Engineering

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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.

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Bayesian estimation and prediction for Burr‐Rayleigh mixture model using censored data

Cited by 12 publications

References 29 publications

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

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

Investment Modelling Using Value at Risk Bayesian Mixture Modelling Approach and Backtesting to Assess Stock Risk

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

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