نبی کریم ﷺ کا مہنج اصلاحی مکی دور کے تناظر میں

Before the prophecy of Prophet (S. A. W) the overall state of Arabs was so spoilt that even it was impossible for pedagogue and rectifier to show them the right path because it was not merely the matter of rectification of faith or preaching of right path neither to make them get rid of false beliefs nor to ameliorate the society. For the fulfilment of such type of rectification the preachers and guides are always there in the society and the reparation continues or carries on. The real muddle was to eliminate the arrogance and detrimental idolism which was so incessant generation to generation in the long run that the preaching and teaching of Prophet and the endeavor of guides were ineffective for them. It was the need of time to establish such type of shelter in which people of world could refuge in it. The remedy of this issue to bring into existence such type of human who was entirely different from the primitive human being. So Holy prophet (S. A. W) came as reformist. There are many golden aspects of prophet’s (S. A. W) reformation in a society, Makk฀ life is also one of them. It is not only changed and revolutionized the whole of the human history but also changed political, social and moral scenario of world. Methodology which our Holy prophet adopted it was the first Methodology that respected and valued human wisdom along with being on right path. In this article the same view point has been discussed. The following are the main points: 1. Preacher’s conformity in words and deeds. 2. Clear mandate to set the target. 3. Perseverance to achieve the set goal. 4. The best policy for the betterment of society. 5. The key points for the leadership.

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.