An Estimation For The Mean Life Of Weibull Distribution

Based on complete sample, this thesis estimates the mean life of Weibull distribution. This thesis gives two estimating methods, pivotal quantity and sample space sorting. The method of pivotal quantity contains half-pivotal quantity and whole-pivotal quantity. First, using the method of half-pivotal quantity, get the confidence lower limit of scale parameter, and using the method of maximum likelihood estimation, get estimating value of shape parameter. Then substitute the two parameters results into the formula of mean life of Weibull distribution, and we can obtain the confidence lower limit of mean life. While whole-pivotal quantity method uses pivotal quantity for the two parameters. Sample space sorting method decides an order, then uses the order finding confidence lower limit of mean life. Based on uncomplete sample, this thesis gives a method of same quantiling data filling, converting un-complete data to complete data. Finally, the two methods are analysed and compared through analog computation.