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Home > Bayesian Analysis of Some Randomly Censored Lifetime Distributions

Bayesian Analysis of Some Randomly Censored Lifetime Distributions

Thesis Info

Access Option

External Link

Author

Danish, Muhammad Yameen

Supervisor

Muhammad Aslam

Program

PhD

Institute

Allama Iqbal Open University

City

Islamabad

Province

Islamabad

Country

Pakistan

Thesis Completing Year

2016

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/7555/1/PHD%20Full%20%28Thesis%29.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725569370

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The thesis presents the Bayesian analysis of some two-parameter lifetime distributions in presence of random censoring. It is well known that for the distributions having shape parameter(s), the conjugate joint prior distributions of shape and scale parameters do not exist while computing the Bayes estimates. In this thesis it is assumed that the shape and scale parameters have independent gamma priors. In case of no prior information about the parameters, the commonly used noninformative priors on the shape and scale parameters are considered. It is observed that the closedform expressions for the Bayes estimators cannot be obtained; four different methods of Bayesian computation are proposed in the crucial places to obtain the approximate Bayes estimates. Among these two are based on analytical approximation, namely, the Lindley’s approximation and the Tierney-Kadane’s approximation; and two are based on Monte Carlo sampling that are importance sampling and Gibbs sampling. For each model, we use three different methods of estimation: maximum likelihood, analytical approximation and Monte Carlo sampling. Simulation studies are carried out to observe the behavior of the Bayes estimators and to compare with the maximum likelihood estimators of the unknown parameters, the hazard function and the reliability function for different sample sizes, different priors, different loss functions, different loss function parameter values and for different censoring rates. The analysis of real data examples is performed in a noble way to illustrate the proposed 10 methodology. Several model fitness measures are taken into consideration to check the goodness-of-fit of the proposed models
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مفتی سید عمیم الاحسان مجددی

مولانا مفتی عمیم الاحسان صاحب مجددی برکتی
ڈھاکے ایک خط سے ابھی چند روز ہوئے یہ معلوم کرکے بے حد افسوس ہواکہ مولانا مفتی سید عمیم الاحسان صاحب مجددی برکتی داعی اجل کولبیک کہہ کراس خاکدان عالم سے رخصت ہوگئے۔ مولانا اپنے زمانے کے بلندپایہ اور وسیع النظر ومحقق عالم تھے۔ فقہ وحدیث آپ کے خاص فن تھے جن میں بڑی گہری نظر رکھتے تھے۔درس کے علاوہ افتا اورتصنیف وتالیف کابھی مشغلہ تھااور اسی سلسلے میں متعدد اہم کتابیں آپ کے قلم کی مرہون رقم ہیں۔ علاوہ ازیں نہایت متقی، متورع اورصاحب باطن بھی تھے۔زندگی کاایک بڑاحصہ کلکتہ میں بسر ہوا۔تقسیم کے بعد ڈھاکہ چلے گئے اوروہاں کے مدرسۂ عالیہ میں پروفیسر حدیث وفقہ ہوگئے تھے۔ ڈھاکہ میں عید کی نماز مولانا نے ہی پڑھائی تھی۔اس کے بعد طبیعت خراب ہوگئی جس کاسلسلہ دس روز تک چلتارہا یہاں تک کہ ۲۷/اکتوبر کوساڑھے چاربجے صبح طائر روح قفس عنصری سے پرواز کرگیا۔ ناظم ندوۃ المصنفین اورایڈیٹر برہان سے بڑی محبت کرتے اورخلوص رکھتے تھے اس لیے ہم لوگوں کے لیے یہ ذاتی حادثہ بھی ہے۔اﷲ تعالیٰ انھیں کروٹ کروٹ جنت عطاکرے اوران کے مدراج ومراتب بڑھائے۔آمین ثم آمین [نومبر۱۹۷۴ء]

 

A Proposed Islamic Microfinance Impact Assessment Methodology

Impact assessment of microfinance programs have been remained the foremost concern of microfinance stakeholders for optimal policy measures. The existing literature regarding the impact assessment varies from parametric to experimental methods to evaluate the performance of microfinance programs across the world however; the literature is lacking a single measure to reveal maximum possible changes in socioeconomic variables resulting from microfinance institutions’ intervention. This study aims to develop a composite index for evaluating the performance of microfinance programs in multi-dimensional contexts. The study exposes a set of eight “diverse indicators” to evaluate the performance of a microfinance program on a wider socioeconomic scale. The dimensions of the index are consist of economic (Income, saving) and socioeconomic (poverty, access to basic facilities, family empowerment) indicators. The changes in deprivations of household, based on the selected indicators, reveal the intensity of success of a microfinance program towards their goals. Finally, we have developed an index by the interaction of incidence and intensity of socioeconomic deprivations. The index is named as “Multidimensional Microfinance Deprivation Index”. This is an index developed in the same line as multidimensional poverty index. The implications of this study are three folds; firstly, it will open up a new dimension of literature in the field of microfinance including Islamic microfinance by instigating an important area. Secondly, it may provide a better alternative to microfinance’s stakeholders to investigate the impact assessment of microfinance programs on a wider socioeconomic scale rather than a few economic. Last but not the least, the study integrates diverse socioeconomic indicators, after assigning weights and adjustment to portray an overall picture of the performance of microfinance in terms of uplifting the socioeconomic conditions of the poor and financially marginalized people.

Development of Integrated Activity Based Mathematics Curriculum at Secondary Level in North West Frontier Province, Pakistan

Mathematics is an important subject and it is the key to advancement in society. Keeping in mind the importance of mathematics in daily life, the present study was designed on the development of an integrated activity based curriculum of mathematics at secondary level in the North West Frontier Province of Pakistan. Recently the name ‘North West Frontier Province’ has been changed officially. The new name is ‘Khyber Pakhtoonkhwa (KPK)’. Therefore hereafter ‘Khyber Pakhtoonkhwa (KPK)’ will be used through out the thesis. The study was aimed; (a) To pinpoint various branches of knowledge which mathematics teachers add/discuss in teaching of mathematics at secondary level through real life integrated activities in applied situation (b) To know up to what extent mathematics teachers use real life integrated activities in applied situation implementing their current secondary level mathematics curriculum (c) To find mathematics teachers’ beliefs about the role and importance of real life integrated activities in mathematics teaching at secondary level (d) To explore mathematics teachers views about various barriers that will prevent or make difficult to use real life integrated activities at secondary level in mathematics teaching (e) To identify what assessment practices mathematics teachers at secondary level use in mathematics teaching and (f) To develop a model of integrated activity based mathematics curriculum at secondary level. This study was carried on in two phases. The population of the study was all secondary level mathematics teachers and students in the province of KPK, Pakistan. In first phase mixed method approach was used. The sample of the study in this phase was selected through multi stage proportionate random sampling method. Total 8 out of 24 vii (33% of the population) districts were included in the sample. Two districts were randomly selected from each cluster (called Zone) already made by KPK public service commission. After selecting districts from each district 1/3 schools each from Urban and rural were randomly selected and then three mathematics teachers from each sample rural school and six mathematics teachers from each sample urban school were chosen randomly for survey. In this way total 681 mathematics teachers 465 from rural and 216 from urban constituted the sample of descriptive part of the study. Also total 32 teachers four from each district two each from urban and rural were included in the sample for interview using purposive sample. While experimental research was carried out using post test only equivalent group experimental design in second phase of the study. Total 60 students of grade 10, 30 for experimental group and 30 for control group of Government Higher Secondary School (GHSS) No.1 Peshawar cant were the sample in second phase of the study. Purposive sampling method was used for school selection and the students were selected through pair random sampling on the basis of the scores they achieved in mathematics in their 9th grade annual examination. In the experiment, use of integrated activity based curriculum units and traditional method of teaching were independent variables while students’ achievement and their retention score were dependent variables. After collection of data, descriptive statistics Percentage, Chi Square Test, Wilcoxon Two Sample Test and Two-independent Sample t-Test were used for analyzing data and drawing conclusion. On the basis of findings the conclusions drawn from first phase of the study were that majority of the teachers didn’t discuss other branches of knowledge in mathematics teaching through real life integrated activities in applied situation, teachers didn’t use real life integrated activities in applied situation using current mathematics curriculum and teachers assessed students through the reproduction of the same questions as given in their textbook. The over all perception of mathematics teachers was positive towards the use of real life integrated activities in applied situation in mathematics teaching. However unavailability of guide book, lack of fund, time constraint, inappropriate training, rote learning based examination system and load of work were considered as barriers in use of integrated activities in mathematics teaching. The conclusion extracted from the second phase was that students’ achievement can be enhanced through the use of real life activities in applied situation in teaching mathematics. Their understanding of using mathematics in real life can be improved, when students are practically involved in the process by using integrated activities in teaching of mathematics.