Identifiability of finite mixtures using a new transform

Ahmad, K.E.

doi:10.1007/bf00052342

Cited by 32 publications

(21 citation statements)

References 15 publications

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“…In order to verify the statistical consistency of parameter estimation, we need to prove the theoretical identifiability of the aforementioned models for the general Weibull, lognormal and two-parameter Pareto distribution families. For heavy-tailed distributions, the identifiability of finite mixtures of the Weibull, lognormal and Pareto distributions was proven in Ahmad (1988). Here, we apply the results from Ahmad (1988) and Jiang and Tanner (1999) and obtain the conditions required for the identifiability of the models from the previous section.…”

Section: Identifiabilitymentioning

confidence: 97%

Bayesian Adjustment for Insurance Misrepresentation in Heavy-Tailed Loss Regression

Xia

2018

Risks

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In this paper, we study the problem of misrepresentation under heavy-tailed regression models with the presence of both misrepresented and correctly-measured risk factors. Misrepresentation is a type of fraud when a policy applicant gives a false statement on a risk factor that determines the insurance premium. Under the regression context, we introduce heavy-tailed misrepresentation models based on the lognormal, Weibull and Pareto distributions. The proposed models allow insurance modelers to identify risk characteristics associated with the misrepresentation risk, by imposing a latent logit model on the prevalence of misrepresentation. We prove the theoretical identifiability and implement the models using Bayesian Markov chain Monte Carlo techniques. The model performance is evaluated through both simulated data and real data from the Medical Panel Expenditure Survey. The simulation study confirms the consistency of the Bayesian estimators in large samples, whereas the case study demonstrates the necessity of the proposed models for real applications when the losses exhibit heavy-tailed features.

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Section: Identifiabilitymentioning

confidence: 97%

Bayesian Adjustment for Insurance Misrepresentation in Heavy-Tailed Loss Regression

Xia

2018

Risks

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“…Therefore, a mixture of Exponentiated Weibull components is identifiable. Identifiability of mixtures has been discussed by several authors, including Teicher (1963), AL-Hussaini and Ahmad (1981) and Ahmad (1988).…”

Section: −T α and H(·) = F (·)mentioning

confidence: 99%

Bayesian Prediction Based on Generalized Order Statistics from a Mixture of Two Exponentiated Weibull Distribution Via MCMC Sumulation

Abushal¹,

AL-Zaydi²

2012

IJSP

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This paper is concerned with the problem of obtaining the maximum likelihood prediction (point and interval) and Bayesian prediction (point and interval) for a future observation from mixture of two exponentiated Weibull (MTEW) distributions based on generalized order statistics (GOS). We consider one-sample and two-sample prediction schemes using the Markov chain Monte Carlo (MCMC) algorithm. The conjugate prior is used to carry out the Bayesian analysis. The results are specialized to upper record values.

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“…Here, we discussed the problem of identifiability of finite mixture of Gumbel distributions. Discussions of the identifiability of a mixtures may be found in several articles, including Teicher (1960Teicher ( , 1961Teicher ( , 1963Teicher ( , 1967, Yakowitz (1970), Al-Hussaini and Ahmad (1981), Fraser et al (1981), Ahmad (1982Ahmad ( , 1988, Ahmad and Abd-ElHakim (1990), and Kont (1983), among others.…”

Section: Identifiabilitymentioning

confidence: 99%

Estimation of a Discriminant Function Based on Small Sample Size from a Mixture of Two Gumbel Distributions

Ahmad¹,

Jaheen²,

Modhesh³

2010

Communications in Statistics - Simulation and Computation

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The identifiability of finite mixture of Gumbel distributions is proved. A procedure is presented for finding maximum likelihood estimates for the four parameters of a mixture of two Gumbel distributions, using classified and unclassified observations. A nonlinear discriminant function for a mixture of two Gumbel distributions is derived and estimated based on small sample size. Throughout simulation experiments, the performance of the corresponding estimated nonlinear discriminant function is investigated.

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Identifiability of finite mixtures using a new transform

Abstract: Identifiability, mixtures, Weibull, lognormal, chi, pareto, power function,

Cited by 32 publications

References 15 publications

Bayesian Adjustment for Insurance Misrepresentation in Heavy-Tailed Loss Regression

Bayesian Adjustment for Insurance Misrepresentation in Heavy-Tailed Loss Regression

Bayesian Prediction Based on Generalized Order Statistics from a Mixture of Two Exponentiated Weibull Distribution Via MCMC Sumulation

Estimation of a Discriminant Function Based on Small Sample Size from a Mixture of Two Gumbel Distributions

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