การประมาณค่าแบบช่วงสำหรับค่าเฉลี่ยประชากรภายใต้การสุ่มตัวอย่างแบบชุดลำดับได้ดุล

Abstract

The purpose of this study is to construct interval estimators for population mean and study interval estimation for finite population mean based on balanced ranked set sampling. Confidence intervals for population mean based on a pivotal quantity. It follows from the central limit theorem. This study constructs interval estimators with 3 methods: approximate confidence intervals from sample variance (first method), approximate confidence intervals from variance of estimator base on sample (second method) and approximate confidence intervals from variance of estimator base on each cycle sample mean (third method). The criteria used to compare the interval estimators are coverage probability and average length. The investigation was done mainly via simulation study. First, a number of set of finite population was generated under three distributions, i.e. Normal, Logistic and Cauchy. The population size ( ) considered are 500, 1,000 and 3,000. And sample size considered are two levels: small ( <30) 5, 10 and 20 and large ( 30) 30, 40 and 50. The mean ( ) considered are 0 and standard deviation ( ) considered are 1 and confidence levels considered are 95% and 99%. The simulation study found that: for population was generated under Normal distribution, the second method yielded confidence interval that had the coverage probability closed to 1- for sample size were 10, 20, 30, 40 and 50 ( k = 2). And the second method had shortest average length. For population was generated under Logistic distribution, the second method yielded confidence interval that had the coverage probability closed to 1- for k = 2 when confidence levels are 99%. And the second method had shortest average length. But population size are 3,000, the second method yielded confidence interval that had the coverage probability more than 1- . And population was generated under Cauchy distribution; first method yielded confidence interval that had the coverage probability closed to 1- for sample size were 20, 30, 40 and 50 when confidence levels are 95%. And the compared average length was found that first method had longest average length.