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Functions

PROBMED Function

computes cumulative probabilities for the sample median.

Syntax

PROBMED

where

is the sample size.

is the point of interest; that is, the PROBMED function calculates the probability that the median is less than or equal to .

Description

The PROBMED function computes the probability that the sample median is less than or equal to for a sample of independent, standard normal random variables (mean 0, variance 1).

Let represent the sample size and represent the th order statistic. Then, when is odd, the function calculates

     

where

     

and B, where is the gamma function. If is even, the PROBMED function calculates

     
     

where B and and are the standard normal cumulative distribution function and density function, respectively.

For more information, refer to David (1981).

Examples

The statements

data;
   b=probmed(5,-0.1);
   put b;
run;

result in a value of 0.4256380897.

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