Sample Size Determination for a Nonparametric Upper Tolerance Limit for any Order Statistic
نویسنده
چکیده
A nonparametric upper tolerance limit (UTL) bounds a specified percentage of the population distribution with specified confidence. The most common UTL is based on the largest order statistic (the maximum) where the number of samples required for a given confidence and coverage is easily derived for an infinitely large population. However, for other order statistics such as the second largest, third largest, etc., the equations used to determine the number of samples to achieve a specified confidence and coverage become more complex using the incomplete Beta function as the order statistic decreases from the maximum. This paper uses the theory of order statistics to derive the equations from the incomplete Beta distribution for calculating the sample size for a one-sided nonparametric UTL using any order statistic. SAS code is shown that performs these calculations in a single macro. The number of samples required for various order statistics is compared for the incomplete Beta function, the normal approximation to the binomial and the binomial distribution. Examples of SAS code are shown for each method. The binomial distribution is shown to be the most accurate for calculating the proper order statistic for any number of samples. This paper is for intermediate SAS users of Base SAS who understand statistical intervals, statistical distributions and SAS macros.
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