運用不等機率抽樣法於冪分佈之研究
| Autor: | Mei-Jin Wu, 吳美津 |
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| Rok vydání: | 2011 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 99 Horvitz-Thompson estimator tells us that if the first-order includes probabilities have closely correlated with the corresponding measured val- ues of population units, then the variance of samples could be reduced to zero. Therefore, by using the auxiliary data which have closely correlated with measured values of population units to define the first-order inclu- sion probabilities,we might get an unequal probability design which is more efficient than the simple random sampling procedure. Zhe-wei Ye (2009) designing a simulation experiment to compare the measured values of pop- ulation units and the auxiliary data in different correlation coefficients, the efficiency of an unequal probability design relative to the simple random sampling procedure. We use the Bickel-Doksum sampling procedure and the Sunter sampling procedure as our unequal probability designs. From the simulation experiment results, we think in the population units which are from the distribution which could use the central limit theorom,sample through the simple random sampling procedure is more stable and effi- cient than through the unequal probability designs. In doing the statistical inference of a popution, sometimes the population will show the distribu- tion structure of the heavy tails, namely, a power distribution, such as the Cauchy distribution, this paper is to explore in the populations which show the power distribution structure, could sampling through the unequal prob- ability designs is more stable and efficient than through the simple random sampling procedure. This text, we alse design a similar simulation experi- ment to compare the measured values of population units which show the Cauchy distribution structure and the auxiliary data in different correlation coefficients, the efficiency of an unequal probability design relative to the simple random sampling procedure. We use the Bickel-Doksum sampling procedure and the Sunter sampling procedure as our unequal probability designs. From our simulation experiment results, we think that in the ap- proximate Cauchy distribution struction, whatever the the correlations of the measured values of population units and the auxiliary data, a unequal probability design is more efficient than the simple random sampling design. vi Keywords: Equal Probability Sampling Design, Unequal Probability Sam- pling Design, Inclusion Probability, Simple Random Sampling, Horvitz- Thompson Estimator, Sequential Procedure. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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