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Bayesian Approach to the Mixture Models

Thesis Info

Access Option

External Link

Author

Noor, Farzana

Program

PhD

Institute

Quaid-I-Azam University

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2014

Thesis Completion Status

Completed

Subject

Statistics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/2317/1/2806S.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676724532337

Similar


This thesis deals with Bayesian inference of mixture densities using censored data. Type-I and type-II mixtures are considered that belong to two or one parameter exponential family. Selection of distribution is made keeping in view the novelty and applicability. These include Inverse Weibull, Pareto type-II, shifted exponential distribution and lastly mixture of Burr type XII and Rayleigh distributions that belong to type-II mixture model. These mixture distributions have not been explored so far in Bayesian setup. Bayes estimators for the parameters of the mixture models are derived in closed forms using type-I right censoring. To conduct Bayesian analysis, Informative (Gamma and Squared Raylegh) priors and non-informative (Uniform and Jeffreys) priors are considered while three loss functions, Squared Error Loss Function, Weighted loss function and Quadratic loss function are employed. A wide simulation study is made to scrutinize the properties of proposed Bayes estimators. Parameters of the mixture model are also tested through hypothesis testing procedure for inverse Weibull and Pareto type- II models. For the inverse Weibull mixture model when all parameters are unknown Bayes estimators can not be obtained in closed forms thus Gibbs sampling and Importance sampling techniques are used to obtain Bayes estimates in this case. Bayesian predictive density is used to obtain Bayes predictive intervals and reliability estimator. Predictive intervals for one and two sample prediction are also obtained that help to predict failure times of future observations. Bayes estimators using limiting form are also derived. Though type-I right censoring is considered throughout the dissertation, however, shifted exponential distribution is also explored through progressive censoring scheme. For the said case, Bayes estimators, credible intervals, Expected test termination time which is considered very useful for life testing experiments, are derived and evaluated. Applications of these mixtures are also presented by applying a real data set in each case.
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بنات النبی (اثبات اربعہ)

بنات النبی اثبات بنات اربعہ
اعتراض نمبر۱۶۸
شیعہ آپؐ کی ایک بیٹی تسلیم کرتے ہیں اور باقی گرو ہ چار بیٹیاں مانتے ہیں۔
جواب: حضرت سیدنا ابن عباس سے روایت ہے کہ آپؐ کے پہلے فرزند اعلان نبوت سے پہلے مکہ میں پیدا ہوئے۔ وہ قاسم تھے اور آپ کی کنیت ابو القاسم انھیں سے تھی۔ پھر جو اولاد ہوئی وہ سیدہ زینب، سیدہ رقیہ، سیدہ فاطمہ اور سیدہ ام کلثوم تھیں پھر جو اسلام میں (اعلان نبوت کے بعد) پیدا ہوئے وہ حضرت عبد اللہؓ تھے جن کا نام طیب و طاہر رکھا گیا۔۔( اثبات بنات اربعہ ص ۲۷)
ابن اسحاق نے کہا کہ نبی کریم کی تمام اولاد پاک سیدہ خدیجہ ؓ کے بطن اقدس سے ہے سوائے حضرت ابراھیم ؓ کے (حضور کے ایک صاحب زادے جو ماریہ قبطیہ سے تھے)۔ حضرت قاسم آپ کے صاحب زادے تھے جن سے آپ کی کنیت (ابو القاسم) تھی اور طیب و طاہر اور سیدہ زینب ، رقیہ، ام کلثوم اور فاطمہ۔(حوالہ بالا)
سورہ کوثر کی شان نزول میں اکثر مفسرین نے آنحضرت ؐ کی چار شہزادیاں تحریر کی ہیں جن میں شیعہ کتب کے حوالہ جات بھی دیے ہیں۔
اما م قسطلانی فرماتے ہیں کہ’’ تم جان لو کہ نبی مکرم کی جملہ اولاد جن پر علماء کا اتفاق ہے ان میں سے چھ ہیں۔ان میں سب سے پہلے حضرت عبداللہ و حضرت قاسم اور آخر حضرت ابراھیم اور آپ ؐ کی چار صاحب زادیاں ہیں جن میں بڑی زینبؓ ہیں اور حضرت رقیہؓ اور حضرت ام کلثومؓ اور حضرت فاطمہؓ ان سے اصغر ہیں ‘ یہ صحیح قول ہے اور چاروں صاحب زادیوں نے اسلام کا زمانہ پایا ہے اور آپؐ کے ساتھ ہجرت مدینہ کی ہے۔
امام یوسف بن اسماعیل نبھانی فرماتے ہیں کہ آپؐ کی چار صاحب زادیاں تھیں۔(۱) حضرت زینبؓ (۲) حضرت...

پاکستانی نوجوان’’ فکری انحراف، اسباب اور سدباب‘‘ اسوہ حسنہ کی روشنی میں

The Pakistani youth are engaged day and night in a struggle for attainment of education, technology, and status. But what is deplorable is that they have forgotten their cultural values, ethics, code of life, and religious identity in order to unite with external powers in becoming part of the drive for development and they have become ignorant of their fundamental responsibilities as a member of the Muslim Ummah. What are the priorities and issues facing Muslims on the local, national, and international levels? Especially in Europe and America the Muslim youth are standing at the crossroads. They are undergoing a religious, ideological, and moral decline. History is eye witness to how the Muslim youth made valuable sacrifices in all walks of life and persevered in making incredible achievements. Moreover, it is the three-fold ideological, cultural, and emotional invasion of the anti-Islamic forces which has been the cause of a weakening of faith in the Muslim Ummah in general and the young generation in particular, since ideology is of primary significance for any nation, religion, movement, or group. It is true that nations are formed and sustained on the basis of ideology. The moment the ideological base is weakened, decline and dissolution become the fate of nations. They are unaware of how it is our foremost national duty and an urgent need to develop scholars who would propagate the Islamic agenda. Contrastively, the anti-Islamic forces are engaged in engendering their representatives. Hence, in order to safeguard our youth from ideological and religious dissolution it is necessary that educational and cultural steps are taken in society in advance so that our youth are provided with a wholesome environment free of ideological dissolution. An outline of the article is given below: The importance and significance of the prime of youth, The ideological propensities of the youth, The causes of dissension in youth, The remedy of dissension, are discussed in detail in this article.

Parental and Peer Influence on Career Decision Making Self Efficacy of Youth and its Relationship With Their Identity Development

Attachment, either parental or peer, is an eternal affectional bond of substantial intensity, and becomes of prime importance in the physical and psychological development of adolescents. This study was aimed to investigate the relationship of parental and peer attachment bonds with career decision making self efficacy (CDMSE) and identity development (Id-Dev) among adolescents and post- adolescents. The study was carried out in three phases: Phase-I constituted of evaluation of the language used in the instruments, Phase-II was a pilot study in which pre-testing of the scales was carried out to assess psychometric properties of the scales used in the main study, and also to see applicability of the research design, Phase-III covered the main study accomplishment. A criterion was formulated to screen the desired sample and the participants in the age range of 17 to 25 years belonging to middle socioeconomic class were included in the study. It was ensured that only those participants were included whose both parents were alive and living together. Care was also taken to include those participants who were day scholars and not residing in hostel. Non-probability purposive sampling was used in the main study of the research and total sample collected was 550 adolescents and post- adolescents studying in different government colleges and universities of Rawalpindi and Islamabad including both males (n = 300) and females (n = 250). All participants were asked to complete a separate demographic sheet so as to have a clear picture of their background. Scales used in study were Inventory of Parent and Peer Attachment-R (IPPA-R), Career Decision-Making Self-Efficacy Scale-Short Form (CDMSE-SF), and the Extended Objective Measure of Ego Identity Status (EOM-EIS-2). Correlations, t-test, regression analysis was conducted for testing hypotheses. Predictability of variables i.e. predicting level of CDMSE & Id-Dev in relation to parental and peer attachment bonds was also assessed. Findings of the study revealed that there was a positive relationship among the variables studied (i.e. CDMSE & parental and peer attachment bonds & Id-Dev and parental as well as peer attachment bonds). It highlighted that when more and more parental and peer attachment bonds are there, more will be CDMSE that also influences a healthy Id- Dev of the youngsters. The outcome of this result signify the contribution of both parents well as peers attachment bonds in predicting CDMSE of adolescents and post-adolescents, however parental attachment bonds are more powerful in prediction of CDMSE as compared to peers attachment bonds. Results of present study denote, both parents and peers attachment bonds play their role in prediction of Id-Dev among adolescents & post-adolescents yet peer attachment bonds more powerfully predict Id-Dev in comparison to parental attachment bonds. Findings of present study suggested that females were relatively more involved in maintaining interpersonal identity as compared to males. The results of the study suggest the further need for clarifying how the parental and peer attachment works in different family structures with variable socioeconomic background and covering different age groups of the sample