منهجية الاشتقاق في اللغة العربية

Language is the identity of a nation, a region and a territory, which serves as a link between the people of that nation and territory. On the other hand, it causes unity, uniformity, brotherhood and love. That’s why study of language has been the subject of conversation of scholars and researchers from the very first day. Wherever human beings exist on this earth planet, there are languages with their noun, verb, preposition and its sub kinds i. E. Present, past and future tense, subject, Object and pronoun. A complete structure of language is founded upon which the learned men have made valuable contribution in various decades. Survival and development of these languages owe to the efforts of these learned people. The current research study is also an effort in which discussion has been made with reference to Arabic language. Arabic is the fourth largest language of the world. It is spoken and understood in Saudi Arabia, U. A. E, Egypt, Syria, Iraq, Iran, Jordon and Morocco. 3 The Universities all over the world, particularly those Universities which have leading role in the present time, not only adopt Arabic Language as medium of instruction but are not second to the Arabs in respect of Arabic Language. The present article discusses the one aspect of this historical grand language namely “derivation”. What is the source of derivation in the Arabic Language? How words are formed and how they are refined. What are different theories regarding derivation. This article is an effort to explain all these aspects

Bayesian Analysis of Mixture Distributions

In this thesis, we consider type-I mixtures of the members of a subclass of one parameter exponential family. This subclass includes Exponential, Rayleigh, Pareto, a Burr type XII and Power function distributions. Except the Exponential, mixtures of distributions of this subclass get either no or least attention in literature so far. The elegant closed form expressions for the Bayes estimators of the parameters of each of these mixtures are presented along with their variances assuming uninformative and informative priors. The proposed informative Bayes estimators emerge advantageous in terms of their least standard errors. An extensive simulation study is conducted for each of these mixtures to highlight the properties and comparison of the proposed Bayes estimators in terms of sample sizes, censoring rates, mixing proportions and different combinations of the parameters of the component densities. A type-IV sample consisting of ordinary type-I, right censored observations is considered. Bayesian analysis of the real life mixture data sets is conducted as an application of each mixture and some interesting observations and comparisons have been observed. The systems of non-linear equations to evaluate the classical maximum likelihood estimates, the components of the information matrices, complete sample expressions, the posterior predictive distributions and the equations for the evaluation of the Bayesian predictive intervals are derived for each of these mixtures as relevant algebra. The predictive intervals are evaluated in case of the Rayleigh mixture only for a number of combinations of the hyperparameters to look for a trend among the hyperparameters that may lead towards an efficient estimation.