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Bayesian Analysis of Mixture Distributions

Thesis Info

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Author

Saleem, Muhammad

Program

PhD

Institute

Quaid-I-Azam University

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2010

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1430

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725568960

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In this thesis, we consider type-I mixtures of the members of a subclass of one parameter exponential family. This subclass includes Exponential, Rayleigh, Pareto, a Burr type XII and Power function distributions. Except the Exponential, mixtures of distributions of this subclass get either no or least attention in literature so far. The elegant closed form expressions for the Bayes estimators of the parameters of each of these mixtures are presented along with their variances assuming uninformative and informative priors. The proposed informative Bayes estimators emerge advantageous in terms of their least standard errors. An extensive simulation study is conducted for each of these mixtures to highlight the properties and comparison of the proposed Bayes estimators in terms of sample sizes, censoring rates, mixing proportions and different combinations of the parameters of the component densities. A type-IV sample consisting of ordinary type-I, right censored observations is considered. Bayesian analysis of the real life mixture data sets is conducted as an application of each mixture and some interesting observations and comparisons have been observed. The systems of non-linear equations to evaluate the classical maximum likelihood estimates, the components of the information matrices, complete sample expressions, the posterior predictive distributions and the equations for the evaluation of the Bayesian predictive intervals are derived for each of these mixtures as relevant algebra. The predictive intervals are evaluated in case of the Rayleigh mixture only for a number of combinations of the hyperparameters to look for a trend among the hyperparameters that may lead towards an efficient estimation.
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ایٹمی دھماکے

ایٹمی دھماکے

                                                                                                                عمران قادری

ہندوستان نے جب راجستھان کے علاقے میں جب ایٹمی دھماکے کیے اور سیکورٹی کونسل کی مستقل نشست کے لیے پر تو لنے لگا تب وطن عزیز پاکستان نے ایک ذوالفقار علی بھٹو کو جنم دے رکھا تھا …جن کی نظروں نے اس وقت خطے میں بھارت کی چودھراہٹ کا خواب بھانپ لیا تھا ۔

صد شکر کہ اس وقت جب 1971ء کی جنگ کا ٹائیگر نیازی ہندوستانی جنرل کے سامنے ہتھیار ڈالنے کی تقریب میں دستخط کر رہا تھا ۔ان کی پتلونیں آج بھی ہندوستانی نمائش میں لٹکی ہوئی ہیں مگر جنرل نیازی کے ساتھ قید نوے ہزار پاکستانی افواج کو ذوالفقار علی بھٹو جہاں ہندوستان سے آزاد کر ا لایا وہاں ایک شکست خوردہ قوم اور ملک کا وقار بحال کر نے کا عزم لیے ذوالفقار علی بھٹو عملی جدو جہد میں تھا ساتھ ہی خطے میں ہندوستانی چودھراہٹ کا راستہ روکنے کے لیے اس نے پاکستان میں ایٹم بم کی بنیاد رکھی ۔

عجیب لیڈر تھا قوم سے چندے نہیں مانگے نا ہی قوم کو مہنگائی کے سمندر میں دھکیلا بلکہ قوم کے لیے عربوں میں رزق کے دروازے کھولے ہر پاکستانی کو پاکستان کے امراء کے مقابل لا کھڑا کیا ۔صد خدا کا شکر اس وقت پاکستان میں عمران نیازی جیسا کوئی لیڈر نہیں تھا جو بزدل آج بھی سرکار ی طور پر ہندوستان کے احترام میں یوم تکبیر منانے سے قاصر ہے ۔ذوالفقار علی بھٹو نے اس وقت ٹوٹے ہوئے بکھرے ہوئے مایوس پاکستان میں ہندوستان کی چودھراہٹ تسلیم کر نے سے انکار کیا تھا ۔

تاریخ میں درج ہے کہ امریکہ کے یہودی وزیر خارجہ کسنجر کے وہ الفاظ جو اس نے پاکستان کے ذوالفقار علی بھٹو کو مخالفت کرتے ہوئے...

Women Dealing with Health Problems in Desert: A Case Study of Cholistan

Being a desert, Cholistan has nomadic and semi-nomadic culture with life threatening climatic and geographic conditions. In fact, life in Cholistan revolves around search for water, food and fodder. Health problems are also acute among these desert dwellers. The area is deprived of healthcare services. The existing literature on Cholistan desert contains no scholarship on the ways of dealing with health problems particularly of women. This article is the first of its kind to explore this aspect. Using ethno-methodology, primary data were collected from 50 elderly women through protracted qualitative interviews and participants observation. Thematic analysis technique was used for analyzing the data. The findings of the study reveal that several intertwined factors such as lack of road and transportation facilities, lack of healthcare infrastructure and qualified medical staff, adverse weather conditions, mass illiteracy, ignorance and existence of massive poverty are main factors responsible for poor health of women in the Cholistan. Also, women’s health problems are given little importance because of male dominance and male support and approval is sought by women before getting medical treatment. In addition to this, lack of access and poor awareness about modern healthcare services, make women in Cholistan rely mainly on self-medication and local remedies such as ethnomedication and spiritual healing.

New Methods for Null Steering in the Field of Adaptive Beamforming

In this dissertation two categories of adaptive beamforming algorithms have been studied. In first category the adaptive beamforming has been applied for null steering whereas in second category it has been applied for direction of arrival mismatch problem to avoid performance degradation of the beamformers. New algorithms have been contributed in both categories. In case of first category a specific structure has been proposed which provides independent steering of all the available nulls present in the radiation pattern of an array antenna. The idea is based on decoupling of the complex weights employed with each antenna element to provide adaptively by controlling their values. This results in a proposed specific structure. The proposed structure is further improved by incorporating sidelobe suppression capability. Second Order Cone Programming has been used to get the appropriate set of weights to be utilized in the proposed structure. Similarly, the method for improving beam symmetry around the desired signal direction is also incorporated. These additional features are included over the cost of number of steerable nulls. A tailored Genetic Algorithm is proposed to compute the weight vector required to incorporate the proposed structure for beam symmetry. The second part of dissertation is meant for the second category of adaptive beamformers applied for direction of arrival mismatch problem. Performance of these beamformers degrades severely whenever there is a mismatch between the presumed and actual direction of desired signal impinging on an antenna array. A Robust Generalized Sidelobe Canceller has been proposed in this domain as remedial measure to restore the performance. The major advantage of proposed algorithm is that it provides improved results without broadening the main beam. This feature is an added advantage in comparison with the previously existing techniques. For this purpose the blocking matrix present in GSC has been modified without disturbing the quiescent weight vector. This results in robustness against signal look direction error without broadening the main beam. The simulation results confirm the improved performance of the beamformer. Another approach in this domain is based on diagonal loading of signal and data covariance matrices, involved in subsequent computations. The amount of this diagonal loading level is very critical which must not exceed a specific level to ensure the positive definite behavior of signal covariance matrix. This is a standard requirement for the convergence of existing general rank algorithms. Currently, there exists no reliable criterion for deciding the amount of diagonal loading level. In this context a new algorithm has been contributed to decide the amount of diagonal loading. Proposed algorithm is iterative in nature and uses the beam symmetry around the presumed signal direction to decide the level.