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Parameters Estimation of the 3-Component Mixture Models of Exponential Family under Bayesian Paradigm

Thesis Info

Access Option

External Link

Author

Tahir, Hafiz Muhammad

Supervisor

Muhammad Aslam

Program

PhD

Institute

Quaid-I-Azam University

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2017

Thesis Completion Status

Completed

Subject

Statistics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/10412/1/Complete%20Thesis.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726839171

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This thesis is concerned with the problem of estimating the parameters of the 3-component mixture models of the members of one parameter Exponential family using type-I right censored data under Bayesian paradigm. The models include: (i) Exponential distribution (ii) Rayleigh distribution (iii) Pareto distribution and (iv) Burr Type-XII distribution. In the Bayesian perspective, these 3-component mixtures of distributions get either no or least consideration in literature so far. Also, the reliability analysis of the 3-component mixtures of distributions is presented in this study. The expressions for the Bayes estimators and their posterior risks using the non-informative and the informative priors under squared error loss function, precautionary loss function and DeGroot loss function are derived. The censored sampling environment is considered due to its popularity in reliability theory and survival analysis. When prior information is available, elicitation of hyperparameters through prior predictive method based on predictive probabilities is given. The posterior predictive distribution for a future observation and the Bayesian predictive interval are constructed. In addition, the limiting expressions for the Bayes estimators and posterior risks under different loss functions are derived. To examine, numerically, the performance of the Bayes estimators under different loss functions, we have simulated Bayes estimates and posterior risks for different sample sizes, test termination times and parametric values. Further, to highlight the practical significance of each 3- component mixture, the Bayesian analysis of the real life mixture data sets is conducted. At the end of this thesis, the conclusion is presented. Some recommendations for future research are also given.
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اہلیہ سید ابوالحسن علی ندوی

اہلیہ سید ابوالحسن علی ندوی
۱۵ دسمبر کو مجلسِ عاملہ کے صدر، مولانا سید ابوالحسن علی ندوی مدظلہ کی اہلیہ محترمہ کا انتقال ہوگیا، جو بڑی نیک بخت اور عابدہ، زاہدہ خاتون تھیں․․․․․․ اﷲ تعالیٰ مرحومہ کی مغفرت فرمائے اور حضرت مولانا کے غم و اندوہ کو زایل کرے، آمین۔
(ضیاء الدین اصلاحی، جنوری ۱۹۹۰ء)

احادیث ِنزو لِ مسیح ابن مریم علیہما السلام میں قادیانیوں کی تاویلات کا تنقیدی جائزہ A Critical Review of Interpretations of Qādiyānies in Aḥadīth of Nuzūl Al-Masīḥ Ibn e Maryam (علیہما السلام)

The negation of the crucifixion and murder of Maseeh علیہ السلام and the ascension to heaven are mentioned in the Holy Qur'an and the revelation to the earth is mentioned in the authentic Ahadith. The Holy Qur'an and Hadith do not contradict each other on the ascension and revelation of Maseeh علیہ السلام. Mirza Ghulam Ahmed Qadiyani interpret those thirty verses of the Holy Qur'an are about the death of Maseeh علیہ السلام which have nothing to do with his death. The Hadiths of the revelation of Maseehعلیہ السلام benefit from the Holy Qur'an, not derived from any Ijtihad or Israelism. The word death is not mentioned for Essa علیہ السلام in the Holy Qur'an. It is not possible for the Hadith to describe the return of Essa علیہ السلام to earth before the Day of Judgment and let his death be mentioned in the Holy Qur'an. Otherwise, instead of stating the meaning of Holy Qur'an, the Hadith will contradict the Qur'an. The Qur'an mentions the ascension of Essa علیہ السلام to heaven and the Hadith describes the revelation to the earth. There is not a single Hadith that indicates that Essa علیہ السلام refers to Mirza Ghulam Ahmed of Qadian and his descent means that is born from the mothes’s womb, or it is a descent as buroz (بروزی).

Prevalence and Factors Associated With Female Sexual Dysfunction Amongst Women Using Hormonal and Non-Hormonal Contraception at the Aga Khan University Hospital Nairobi Clinics

Background: Female sexual function is a complex phenomenon. It integrates all the body systems and is influenced by a variety of factors. Contraceptives have been shown to have variable effects on female sexual function, but there have not been adequately powered studies on this in our setting. Justification: The prevalence of female sexual dysfunction (FSD) has been shown to vary among different population subsets globally. The associations of different factors with FSD have also shown variable conclusions that are not generalizable to our setting. In Kenya there is a high discontinuation rate of contraception and this is mainly attributed to its related side effects. This has created a need to study the prevalence of, and the significant factors affecting FSD among those using contraception in our setting. Objectives and methods: The aim of the study was to determine the prevalence of FSD among women using hormonal and those using non-hormonal contraception and to examine the factors associated with it. A cross-sectional study was conducted at clinics within AKUHN. Consecutive sampling of women of reproductive age using either hormonal or non-hormonal contraception was done. Two questionnaires, one on demographic profiles and the other on the female sexual function index (FSFI) were completed. Independent associations of the factors with the outcome variables were assessed using Chi square test of association and variables with a P< 0.25 used in the multivariate analysis. Factors associated with FSD were determined using binary logistic regression. Results: A total of 566 participants were included. The prevalence of FSD among those using hormonal and those using non-hormonal contraception was 51.5% and 29.6% respectively (P<0.0001). Using logistic regression we found that the factors that were associated with FSD were presence of chronic illness and use of chronic medication, self-employment and unemployment statuses, alcohol intake and history of miscarriage(s). Conclusions and recommendations: There was a high prevalence of FSD in our setting. There was a strong association between hormonal contraception and FSD amongst those using it. More studies on this topic in different settings are recommended to investigate effect of each type of hormonal method on FSD.