Home > A Class of Generalized Estimators of Population Means Using Auxiliary Variables in Single and Two Phase Sampling With Properties of the Estimators
A Class of Generalized Estimators of Population Means Using Auxiliary Variables in Single and Two Phase Sampling With Properties of the Estimators
In this study generalized exponential ratio type estimators have been proposed for estimating the finite population mean, using the information from single and two auxiliary variables, under sampling design such as single and two phase sampling. For each proposed estimator bias of order two and mean square error of order one are derived using single and two phase equal probability sampling with single and two auxiliary variables. A class of these estimators have been developed and their bias of order one and mean square errors of order one have been derived. Mathematical comparison has been furnished of the generalized proposed estimators with the existing estimators. Shrinkage estimators of the proposed estimators have been defined along with their mean square errors for single and two phase sampling. To put side by side the proposed estimators with existing estimators, numerical study has been carried out with single and two phase equal probability sampling. It is experiential that the proposed estimators are more efficient than simple random sampling, Ratio, Bhal and Tuteja (1991), Samiuddin and Hanif (2006), Sisodia and Dwivedi (1981), Upadhyaya (1999), Singh and Tailor (2003) and Noor-ul-Amin and Hanif (2012) and others. In case of unequal probability sampling the proposed estimator is also more efficient than the simple random sampling, Ratio, Bhal and Tuteja (1991), Sisodia and Dwivedi (1981) and Singh and Tailor (2003). To study the properties of the estimators, simulation has been carried out and it is evident that the proposed estimators are consistent estimators of population mean. It also shows that normal distribution is the most significant fitted distribution on the proposed estimators.
مولانا عبدالحفیظ بلیاوی افسوس ہے کہ دارالعلوم ندوۃ العلماء کے استاذ مولانا عبدالحفیظ صاحب بلیاوی نے وفات پائی وہ ادب کے استاد تھے، عربی زبان و لغت پر ان کی نظر بڑی گہری و وسیع تھی، انہوں نے لغت کی کئی کتابیں لکھیں، ان میں مصباح اللغات اور اردو عربی ڈکشنری چھپ گئی ہیں بعض مسودے کی شکل میں ہیں، دینی علوم میں بھی پوری دستگاہ رکھتے تھے، ان کی پوری زندگی عربی زبان کی تلاش و تحقیق میں گذر ی، ان کی وفات سے عربی زبان کا ایک بڑا ماہر اٹھ گیا، اﷲ تعالیٰ اس شیدائے علم کی مغفرت فرمائے۔ (شاہ معین الدین ندوی، ستمبر ۱۹۷۱ء)
The main Focus of Islam is to promote a healthy social setup. It is evident that a healthy society is a structure and framework of individuals' peaceful interactions. If the individuals are ofgood character with sound personalities, the society becomes a symbol of happiness and tranquility. It is clear that individuals face different situations in daily life and the way these matters are dealt with, depict the emotional aspect of their personality. Islam neither promotes ascetism nor it advocates to become materialistic, rather it strengthens a harmony between the spiritual and material needs. The balanced emotional expressions not only furnish a positive personality but also lead the individual to real success and salvation in this life and in the life hereafter. This article is an effort to identify the dimensions of different emotions, so that the negative emotional trends at individual or social level should not disturb the balance of the community life. (Note: Main components of the development of the personality are referred as cognitive, behavioral, and Emotional. Thefirst two components have been discussed in Issue No. 19th / 2008, whereas the Emotional components are being discussed in this Article.)
This work studies the selected sculptures of the Malakand collection, which represent important and striking features of the Gandhāra Art. The great collection is significant due to its historical importance and variety in the depiction of the postures and events. These sculptures, on one hand, reflect the traditions and practices of Buddhism in Gandhāra and, on the other hand, they depict the quality of art, the psyche and devotion of the followers and artists. Many research studies on the art, style and architecture of the Swat valley have been carried out and the present project focuses on systematic documentation and analysis of the collection. Total 134 sculptures of the present collection have been documented and a complete catalogue of the stone sculptures has been made. The classification of the sculptures is based upon the thematic and stylistic analysis and stone material used in the making of the sculptures. To establish the chronology and to give the proper place of origin, the sculptures of present collection were deeply and thoroughly studied from the perspective of Zonal Workshops mentioned by M. Farooq Swati in the Swat valley. During the present research on Malakand collection; it is observed that the art had accepted the foreign impact during different periods of time. The quality of art, style and material used for making the sculptures show that the artist kept all the socio- economic and religious conditions of the time in his mind while carving these sculptures. The research methodology of the present study is based on descriptive as well as analytical approach. The architectural elements used for the decoration of stūpas, votive stūpas and monasteries were studied in detail and it was observed that the same pottery, furniture and the architectural elements like Persepolitan andxvii Corinthian pillars continue to the present and are visible in the villages of Malakand and other part of Gandhāra region.