عصر حاضر کی تناظر میں عرف اور عادت کی شرعی حیثیت: ایک تجزیاتی مطالعہ

The unique feature of Islam is its comprehensive code of life. This proves its indispensability and worth as the universal order which accommodates complex issues of human life without compromising on its fundamentals. Hence, it is a matchless way of life on this planet. Keeping in view the modern specification of the current age in respect of those countries which tend to modify their legislations and their political, economic and social institutions as per Islamic framework. In this regard, a part from the fundamental and core Islamic sources of jurisprudence like the holy Quran, traditions of the holy Prophet (Hadith), consensus of Muslim scholars (Ijma) and Analogy (Qias), there are other sources like ‘Decorum’ (Istihsan) and ‘Arbitrariness’ (Masalih e Mursalah) to play their effective and significant jurisprudential role to address the numerous social issues by honoring the customs and norms already prevailing in any particular society. The article under discussion speaks of the distinct characteristic of Islam that it is a religion of nature and takes care of natural necessities of human life. Already prevailing customs and norms in human society are not subject to disregard or straight rejection. Islam puts a considerable endeavor not to confront the wisdom of the society by sweeping its norms and customs unnecessarily. Conditions imposed by Islam to formulate any society are specious enough which accommodate many of the customs and encompass overwhelming norms in it. But being the sincere guardian of the humanity, on the other hand, it does not miss its significant reformative role to play with reference to those customs and norms which appear contrary to its fundamentals

Mean Estimation in Adaptive Cluster Sampling Using Auxiliary Information

In this dissertation, generalized simple and exponential type estimators have been developed using the information of single and two auxiliary variables for the estimation of rare and clustered population mean in adaptive cluster sampling designs. The proposed estimators are specifically developed for different situations of clustered populations in simple adaptive cluster sampling, stratified adaptive cluster sampling and systematic adaptive cluster sampling designs. In Chapter 1, the discussion has been made about the situations of rare and clustered population in which the conventional sampling designs may not be appropriate in order to achieve even moderate precision. The use of adaptive cluster sampling design along with the process in the presence of auxiliary information is also discussed. Comparison of adaptive cluster sampling with conventional sampling design and some advantages and disadvantages has also been given. Furthermore, stratified adaptive cluster sampling and systematic adaptive cluster sampling has been illustrated in the same Chapter with the detail sampling process. In Chapter 2, the literature regarding the use of auxiliary information in conventional sampling designs, adaptive cluster sampling, stratified adaptive cluster sampling and systematic adaptive cluster sampling have been discussed whereas Chapter 3 contains some basic estimators that already developed in conventional sampling designs, adaptive cluster sampling, stratified adaptive cluster sampling and systematic adaptive cluster sampling designs. The major contribution of this dissertation appears from Chapter 4 by proposing modified ratio and regression-cum-modified ratio estimators using the information of single auxiliary variable in adaptive cluster sampling by utilizing the average values of the networks with simple random sampling without replacement. The expressions of approximate bias and mean square error for the proposed estimators have been derived. The generalized form for the proposed estimators has been suggested by introduction the unknown constants. The expressions of approximate bias and mean square error have been derived for the generalized form and optimum properties have been discussed. Many conventional and non-conventional parameters of the auxiliary variable have been used as special cases of the proposed estimators. The efficiency issues in adaptive cluster sampling have also been discussed. Theoretical comparisons have been made of the proposed estimators with existing estimators. An extensive numerical study is conducted by using real and artificial population data sets for all the estimators to evaluate their performance. In Chapter 5, weighted exponential ratio-product type estimator have been developed using single auxiliary variable in adaptive cluster sampling for the situations in which the relationship between the survey variable and the auxiliary variable is non-linear. The expressions of approximate bias and mean square error have been derived. A simulation study is conducted to evaluate the performance of the proposed estimator with existing exponential type estimators. In Chapter 6, a generalized semi-exponential type estimator has been suggested based on two auxiliary variables in adaptive cluster sampling. Some exponential and non-exponential type estimators have been discussed, as the special cases of the proposed estimator. The expressions of estimated bias and minimum mean square error have been derived. A simulation study is conducted on simulated populations generated by Poisson cluster process and Ecodist Package in R, to examining the performance of proposed estimator in adaptive cluster sampling design. In Chapter 7, modified ratio and regression-cum-modified ratio estimators have been developed using the information of single auxiliary variable in stratified adaptive cluster sampling. The generalized form for the proposed estimators has been suggested by introduction the unknown constants. The expressions of approximate bias and mean square error have been derived and optimum properties have been discussed. Theoretical comparisons have been made of the proposed estimators with existing estimators. An extensive numerical study is conducted by using real and artificial population data sets for all the estimators to evaluate their performance. In Chapter 8, a generalized semi-exponential type estimator has been suggested based on two auxiliary variables by utilizing the average values of the networks in stratified adaptive cluster sampling. Some exponential and nonexponential type estimators have been discussed, as the special cases of the proposed estimator. The expressions of approximate bias and minimum mean square error have also been derived. A simulation study is conducted using the simulated populations generated by Poisson cluster process at different level of rarity and aggregation to examining the performance of proposed estimator in stratified adaptive cluster sampling design. In Chapter 9, modified ratio and regression-cum-modified ratio estimators have been developed using the information of single auxiliary variable in systematic adaptive cluster sampling. The generalized form for the proposed estimators has been suggested by introducing the unknown constants. The expressions of approximate bias and mean square error have been derived and optimum properties have been discussed. Theoretical comparison has been made of the proposed estimators with existing estimators. A numerical study is conducted by using artificial population data sets taken from Thompson (2012) for all the estimators to evaluate their performance.