Interval estimation of the parameters of the weibull and extreme value distributions by upper record value

• Main Authors: Hsin-Ying Huang, 黃欣盈
• Other Authors: 吳忠武
• Format: Others
• Language: zh-TW
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/24725685259212019149

碩士 === 淡江大學 === 統計學系 === 90 === We assume that can be a sequence of independent and identically Weibull distribution random variables with probability density function as given where （> 0）and （> 0）are two parameters (also see Weibull (1939)or Johnson, Kotz and Baladrishnan (1994))。Let be the upper record values of Weibull distribution, where and U(1)=1。We can find 100(1- )﹪confidence interval of the parameter and the joint confidence regions of the parameters( )。In addiction ,we define a rule (ex: the shortest of the confidence interval length, minimization the sample mean square error, or minimization the confidence region area) to find the best interval estimation of the parameter and the exact joint confidence regions of the parameters( )。We expect to extend the method to other distributions as Extreme-value distribution with probability density function as given where and are location parameter and scale parameter, respectively. Finally, we also give some examples and simulation to evaluate the method.