بدصورت غربت
یہ کیسی تنہائی ہے
میں یادوں کے سیلاب میں بہتا جا رہا ہوں
میرے ایک ہاتھ میں خواہش اور دوسرے میں محرومیاں ہیں
پائوں میں غربت کی زنجیریں ہیں
گلے میں ضرورتوں کا طوق ہے
مجبوریاںسیاہ حلقے بن کرنکھوں کے گرد لپٹی ہیں
پلکوں پہ جمی اداسی
قطرہ قطرہ پگھلتی کھردرے رخساروں پہ گرتی ہے
میرے نیلے ہونٹ جن پہ دوپہر کی جلتی خشک دڑاڑیں ہیں
The relationship between English (in what this term comes to mean as a language, as a discipline of studies, and as a synecdoche of Western culture) and our culture as Muslim Pakistanis has developed over a period of time since the British colonization. The history of this cultural interaction may be divided into three broad phases: the initial, the middle, and the present. The strategy adopted in this paper is based upon the argument that this relationship may be traced through some of the most representative figures of our culture, such as, Shibli, Iqbal, Faiz etc. In each phase of this interaction. The present essay on Shibli deals with the first phase of our cultural interaction with English. It adopts what may be termed as an analogical approach to the issue as it intends to engage with what I think to be rather unwarranted psychoanalytic forays of some of our critics into the psycho-dynamics of such culturally representative figures like Shibli in their relationship with English. The paper exploits the analogy first used by Sheikh Muhammad Ikram, and later employed by Nasir Abbas Nayyar that Shibli’s attitude towards English was the same as his attitude towards his step-mother at home. English, in other words, was a step-mother for Shibli, and for the generations represented through his figure in this early phase of our cultural interaction with the language. Shibli’s terms of engagement with his step-mother, and analogically with English, is the subject of this essay.
In this dissertation, a class of Hartley Ross type unbiased estimators is proposed for estimation of finite population mean under adaptive cluster sampling and stratified adaptive cluster sampling. Hartley Ross type unbiased estimator is also proposed utilizing two auxiliary variables. These estimators employ information on known parameters of the auxiliary variable. The variances of proposed class of unbiased estimators are obtained up to first degree of approximation. Computations related to proposed estimators are illustrated via numerical example. Proposed estimators are more efficient than the usual mean estimator, ratio and modified ratio estimators in adaptive cluster sampling and stratified adaptive cluster sampling under certain realistic conditions. Exponential-ratio-type and difference-type estimators are propounded for general parameter in adaptive cluster sampling and stratified adaptive cluster sampling. The proposed estimators coherently utilize information on two auxiliary variables in three different situations i-e. none, partial and full information about population parameters of auxiliary variables. The proposed estimators for general parameter can be used to estimate the population mean, population coefficient of variation, population standard deviation and population variance of the variable of interest. Proposed estimators are also presented to be used with multi auxiliary variables. Difference-type estimators are recommended for estimation of population coefficient of variation under adaptive cluster sampling. Proposed estimators utilize mean, ranks and coefficient of variation of auxiliary variables. Difference-type and difference-cum-exponential-ratio-type estimators are presented utilizing two auxiliary variables for estimation of general parameter under adaptive cluster sampling and stratified adaptive cluster sampling. These estimators utilize auxiliary information in terms of ranks, variances and means of auxiliary variables. Such estimators are generalized for multi auxiliary variables. xviii Generalized ratio-type and ratio-exponential-type estimators are proposed for population mean under adaptive cluster sampling based on modified Horvitz-Thompson estimator. The proposed estimators utilize auxiliary information in combination of conventional measures (coefficient of skewness, coefficient of variation, correlation coefficient, covariance, coefficient of kurtosis) and robust measures (tri-mean, Hodges-Lehmann, mid-range) to increase efficiency. Finally, three new sampling schemes are proposed to select initial sample in adaptive cluster sampling. These schemes are proposed adopting, ranked set sampling to increase precision of estimates. Usual Hansen-Hurwitz and Horvitz-Thompson estimators for population mean under adaptive cluster sampling are modified for employment under the proposed schemes. Procedures related to the proposed schemes are also illustrated with the help of examples. Expressions for bias and mean square error of proposed estimators are derived using first order of approximation. Empirical and simulation studies are conducted to evaluate the proposed estimators. Behaviors of existing and proposed estimators are analyzed for several initial sample sizes and at different levels of correlation between study and auxiliary variables. Comparisons of existing and proposed estimators are also illustrated. The results reveal that whenever the efficiency conditions are fulfilled, proposed estimators performed more efficiently than competing estimators for estimation of population mean, population variance and population coefficient of variation. The proposed estimators are found to be more efficient under both adaptive cluster sampling and stratified adaptive cluster sampling. The sampling schemes which are recommended by adopting ranked set sampling are found to be more efficient than adaptive cluster sampling when initial sample is drawn by simple random sampling without replacement.