Bayesian statistics provides a theory of inference which enables us to narrate the results of observation with hypothetical predictions and it provides the only generic tool for incorporating new experimental evidence and updating the existing information. In most of the pragmatic situations in Statistics, we have to deals with comparisons. One such comparing technique is the paired comparisons. The method of paired comparison has been widely employed to remove some of the difficulties involved in the simultaneous comparison of several objects. This method is being used in experimentation and research methodologies in which subjective judgment is involved. So it has become demanding to tract the attention of many of the Bayesian analytics. In recent years, many models for paired comparisons have been devised. The present study contributes to the theory of Bayesian Statistics by presenting Bayesian analysis for four different paired comparison models: the Davidson model with order effect, the Rao-Kupper model with order effect, the van Barren model VI and the amended Davidson model. For the analysis, both the noninformative and informative priors are used. The joint posterior distributions and the marginal posterior distributions of the parameters of the models are derived, the posterior estimates (means and modes) of the parameters, the predictive probabilities for future single paired comparison and the posterior probabilities for comparing the two parameters are calculated. The use of the Gibbs sampling procedure is also given in this study. The analysis has been performed for three and four treatments. An interesting amendment has been made in the Davidson model to accommodate the no preference category for those respondents who genuinely have no preference as well as those who have not been able to distinguish between the two treatments/objects. We give the Bayesian analysis of the amended model using both the noninformative and the informative priors. For using the informative prior, the hyperparameters are elicited through the prior predictive distribution. Those values of the hyperparameters are elicited at which the difference between the confidence levels characterized by the hyperparameters in prior predictive distribution and the elicited confidence levels of expert is the minimum. For the analysis, the entire calculation of the posterior estimates, the predictive and the preference probabilities and the marginal distributions along with their graphical presentations as well as the posterior probabilities for testing of hypotheses of comparing parameters is carried out mainly in SAS package. For the novelty of our work, an assessment that has been done by comparing the posterior estimates, the predictive probabilities for future single paired comparison and the posterior probabilities of hypotheses for comparing parameters of the said three models has also been included. The small data set is also considered for the analysis of the models. Finally, some ideas for future research has also been proposed and appendices carrying some important programs designed in SAS and Mathematica packages have been added.
بہت کم لوگ ایسے ہوا کرتے ہیں جنہیں قدرت شعری صلاحیت سے نوازتی ہے۔ اقبال پر شعری کیفیت طاری ہوتی تو وہ دیر تک جاری رہتی تھی۔ اقبال نے پندرہ سال کی عمر میں شعر کہنا شروع کیا۔ آپ نے اپنا فکری پیغام شاعری کے وسیلے سے عام کیا۔ خطوط، خطبات، مضامین اور مقالے وغیرہ اقبال کے فکری اسالیب کے نمونے ہیں۔ خطوط کی تعداد تو بہت ہی زیادہ ہے۔ انہیں کلیات کی صورت کجا بھی کیا گیا ہے۔ شعری کلام کی ترتیب کے وقت اقبال نے کلام کا بہت سا معقول حصہ حذف کر دیا جسے باقیات کے نام سے جمع کیا گیا۔ اقبال کی بعض انگریزی تصانیف کے اردو تراجم ہوئے۔ بہت سی تصانیف کے نئے ایڈیشن سامنے آئے۔ پروفیسر عبد الحق نے سابقہ مونوگراف کی طرح اس میں بھی تصانیف کا مختصر تعارف پیش کیا ہے۔
During the Arab Rule in Sindh, there had been great and featured research work in all fields of Islamic knowledge particularly in the field of Qurʾān, Hadīth and biography of Prophet Muḥammad PBUH. After the Arabs, The Kalhora’s period is known as the golden period of education, literature and civilization in the history of Sindh. Prior to this, the scholars of Sindh had written various voluminous works on Islamic knwoledge in Arabic and Persian. During this period, a movement initiated amongst the scholars of Sindh, which encouraged them for writing and compiling books in local Sindhi Language inspite of vernacular Arabian and Persian languages. As such, a remarkable work of authorship and compilation had been made in various fields including Islamic studies in general and in the field of biography of Hazrat Muḥammad PBUH, which thereafter remained continued in the days of Talpur’s, British Rule and till to date. This paper is the analytical survey of Sīrah Literature being produced in Sindh from 1947 to 2015 CE in local Sindhi Language.
Banks plays vital role in capitalist economy. During the period of financial turmoil, it has been viewed that
banks lost a huge capital due to non-recovery of loans from customers. Since there are two type of banks
working in Pakistan therefore this thesis analyse which banks performance was better during the financial
crunch. The objective of this thesis is to determine the factor affecting the profitability of Islamic and
Conventional banks in Pakistan during the period 2008 — 2012.
Data was collected through financial books of seventeen conventional and five Islamic banks. Two dependent
variables i.e. Return on Asset and Return on Equity were used to determine the profitability of Islamic and
conventional banks in Pakistan. Whereas Liquidity, Credit Risk, Capitalization, Efficiency, Bank Size, Economic
Performance, Inflation and a dummy variable were used as Independent variables. Panel Data analysis is used
to find out the result of secondary data. Initially the analysis was conducted on whole industry, which then
applied on Islamic and Conventional banks separately.
The results shows mixed trend for whole industry as well as separately. Liquidity is insignificant in the industry
whereas the same result was obtained in separate analysis of Islamic and Conventional banks. Credit risk is
significant and negatively correlated for whole industry as well as for separate banking segment i.e. Islamic and
Conventional. Capitalization is significant in industry with ROE but showing a direct relationship. Same result
is shown in Islamic and Conventional Banking Industry. However, it is also significant with ROA in Conventional
banks showing an inverse relation. Efficiency is positively correlated and significant with ROA and ROE in
industry and Islamic banks, whereas it is insignificant with ROE in conventional banks. Bank size shows same
result for all analysis i.e. positive correlation and significance.
The results of inflation and GDP are significant for conventional banks but having an inverse relation. Whereas
GDP showing insignificant results in Islamic banks. While inflation is, significant but positively correlated with
ROA. The results depicts that certain factor plays different role while determining the profitability of banks
during certain conditions and type of banks. A same factor may be beneficial for conventional banks in certain
time period whereas the same may be impacting negatively due to change of circumstances.