: PROBMED Function

PROBMED Function

computes cumulative probabilities for the sample median.

Syntax

PROBMED $\text{[math]}$

where

$\text{[math]}$	is the sample size.
$\text{[math]}$	is the point of interest; that is, the PROBMED function calculates the probability that the median is less than or equal to $\text{[math]}$ .

Description

The PROBMED function computes the probability that the sample median is less than or equal to $\text{[math]}$ for a sample of $\text{[math]}$ independent, standard normal random variables (mean 0, variance 1).

Let $\text{[math]}$ represent the sample size and $\text{[math]}$ represent the $\text{[math]}$ th order statistic. Then, when $\text{[math]}$ is odd, the function calculates

$\text{[math]}$

where

$\text{[math]}$

and B $\text{[math]}$ , where $\text{[math]}$ is the gamma function. If $\text{[math]}$ is even, the PROBMED function calculates

$\text{[math]}$

where B $\text{[math]}$ and $\text{[math]}$ and $\text{[math]}$ 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.