ESTIMATION OF THE SCALE PARAMETER OF THE WEIBULL PROBABILITY DENSITY FUNCTION BY USE OF ONE ORDER AND OF M ORDER STATISTICS.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING
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Two estimators of the scale parameter O of the Weibull probability density function are developed by use of one and of m order statistics. In the development it is assumed that the shape parameter K is known or can be determined by some method. The location, or threshold, parameter C is assumed to be zero. The background of the Weibull p.d.f. is presented briefly, and the development of the distribution of order statistics, the moments of order statistics, the distribution of Weibull order statistics, and the moments of the Weibull order statistics are shown in detail. The single-order-statistic estimator development is based on the expected value of the ith order statistic. To obtain a linear m-order-statistic estimator the method of Lagrangian multipliers is used to obtain multipliers k sub i that will give a minimum variance unbiased estimator. The constraint used in this method is that the sum of the k sub i must be equal to the number of values m used where m is the truncation point. For example, with n15, m7, the seven k sub i must sum to 7. The m multipliers are then applied to the one-order-statistic estimators to determine an estimator for the scale parameter based on m order statistics. Author
- Statistics and Probability
- Manufacturing and Industrial Engineering and Control of Production Systems