سیرت طیبہ پر استشراقی فکر کے اعتراضات کے اسباب و عوامل کا تاریخی و ارتقائی جائزہ

Over the course of time and with the rapid increase in human population need for mutual relations become crucial. Resultantly on behalf of this closeness, separation, anti-standpoints and comparisons also emerged. As the time passed by hatred and hypocrisy and other social vices spread on large scale. Thus human society was waiting for such liberator who may lead and work for the betterment of this society. With the dawn of Islamic civilization all such issues were not only resolved but also provided with a model for containing the difference of opinion and multiple traditions under its unique worldview. Islamic History presents itself as a model where the minorities were provided with the opportunities of participating in political, social, educational and collective affairs. Thus in a society where tyranny, injustice, un-forbearance, religious intensity, terrorism and the activities of violating the human rights were very common, were substituted by the Islamic ideal  of forbearance. It is argued here that the solution of all these issues was only in religion contrary to what is being claimed about an idea of social harmony where religion is not given its due position. Today its our dire need to develop a sense of harmony, modesty, affection and peacefulness among the masses of various religions of Pakistani society. It is further argued that for this very noble cause all the religious scholars and their followers can come forward playing their pertinent role.  

Estimation of Covariance Matrix and Inference About Regression Coefficients and Autocorrelation in Heteroskedastic Regression Models

Beta Exponentiated Weibull distribution (BEWD) is an extension of the exponentiated Weibull distribution which involves two additional shape parameters. Interestingly, the additional parameters control the tails weights of the distribution and affect skewness and kurtosis of the distribution. The five-parameter BEWD is a generalized distribution in modelling lifetimes of various industrial products. Its density and hazard curves are widely heterogeneous in their shapes. Three subfamilies of the BEWD family emerge under three parameter subspaces with the property that the members of each subfamily display similar density curves. It is found that some members of the BEWD family in one of the parameter subspaces approximately behave like a normal distribution. BEWD assumes decreasing, increasing or a bathtub behaviour. Using a sample hazard curve, and so a prior understanding of restrictions on the BEWD parameters we find estimates of parameters for fitting BEWD. These estimates based on maximum likelihood are essentially more efficient than when no such knowledge about the sample hazard curve is used. Characterizations based on truncated moments and hazard rate function are obtained. Simulation study of BEWD is performed in both ways; without the knowledge of parametric conditions and using parametric constraints and compare the results. Real data applications of the proposed approach support the better fitting of BEWD than other models. A generalization of BEWD is introduced in which a transmuted parameter is added and its behaviour is studied, named as Transmuted Beta Exponentiated Weibull Distribution (TBEWD). Different mathematical properties including moments, characteristic function, skewness, kurtosis and mode are being discussed. The transmuted parameter affects the basic characteristics, shape of density function and other properties of BEWD. Characterizations of TBEWD based on truncated moments and hazard rate function are also derived. The maximum likelihood estimation (MLE) is used to estimate the model parameters. Simulation Study is performed to test the efficiency of MLEs. Various aspects of this distribution are explored in the context of its applications, which include its subfamilies displaying reasonable similarity with regard to their hazard curves. The parametric restrictions so discovered are found useful in fitting this distribution. A number of applications of TBEWD model are also given.