مولوی فیروز الدین ڈسکوی

حضرت ہندہ رضی اللہ عنہا سے متعلق تاریخی روایات کا تحقیقی جائزہ

Some Historians have blamed on Hadrat Hind (R.A) that she mutilated the corpse and chewed the liver of Hadrat Hamza (R.A), which is the cruelty of a specific group of the opponents of Companions. But the Text Book Board of KPK has included exactly these narrations in the curriculum of Urdu compulsory of fifth class. Firstly, this incident was happened before accepting Islam, and when she accepted Islam then there is no blame can be raised upon her on this incident. But definitely, these narrations impact the mind of children. It was necessary to test the authenticity of these narrations before including in curriculum. In this article, some Historical narrations regarding Hadrat Hind (R.A) have been chosen, and some authentic narrations from Ahadith Books have been presented in order to reject these Historical narrations in a scholarly manner.

Multivariate Ratio and Exponential Estimators for Population Variance in Two-Phase Sampling Using Multi-Auxiliary Variables

In this dissertation, multivariate ratio and regression-cum-exponential type estimators have been proposed for estimating the finite population variance using the multi-auxiliary variables under two-phase sampling scheme. In Chapter 1, the discussion about the use of auxiliary information, twophase sampling procedure, variance estimation is given. The literature related to the use of multi-auxiliary variables, variance estimation under two-phase sampling and some modified estimators are discussed in Chapter 2. The major contribution of this dissertation appears in Chapter 3, 4, 5, 6 and 7. The multivariate ratio-type estimators along with some special cases are discussed in Chapter 3. These estimators are discussed for the three situations, the partial information, the full information and the no information. The expressions for variance covariance matrices are computed for multivariate cases and the univariate cases have also been discussed. In Chapter 4, the multivariate regression-cum-exponential estimators along with the special cases and the minimum variance covariance expressions are discussed. Further these estimators are also derived for the full and the no information cases. The optimum values for the constants have also been discussed. The real life Canadian climate data is used to check the efficiency of our proposed (ratio and regression-cum-exponential) estimators, in Chapter 5. Chapter 6 is based on the simulation studies. In simulation studies, we used two models to demonstrate the performance of our proposed estimators. The last Chapter of this dissertation contains the conclusions about our proposed and existing estimators and it is discussed how our proposed estimators are more efficient than existing estimators.