The weighted estimation of the parameters and characterizations of the Makeham distribution based on the censored sample

• Main Authors: Sheng-Chih, Kao, 高聖智
• Other Authors: Jong-Wuu, Wu
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/90005886628969622327

碩士 === 國立嘉義大學 === 應用數學系研究所 === 99 === Many continuous probability distribution, such as Exponential, Weibull etc., has been characterized through conditional expectation on both a non-adjacent and adjacent order statistics. As we know, the Makeham distribution play an important role in modeling human morality and establishing actuarial tables. We will use non-adjacent order statistics to characterize this distribution through conditional expectation and use a adjacent order statistics to characterize this distribution though conditional variance. We extend our result to characterize a distribution with cumulative distribution function , , where , , , and is monotonic and differentiable function of such that as and as . Most important thing in our extension is some of our results can reduce to Wu and Ouyang (1996), Khan et al. (2009), Beg and Kirmani (1978) and Khan and Beg (1987). Beside, we compare estimators of weighted and unweighted least square methods for the parameters of Makeham distribution by using the sample mean square error under the Monte Carlo simulation. We find out that the weighted least square methods have smaller sample mean square error than unwieghted least square methods. No matter what the size of sample, among the weighted least square methods, it sugguested to use to esitmate and weighted is choosed to be , .