CDF Chi Square Distribution Function

Returns a value from the Chi-square cumulative probability distribution.

Category:	Probability

Table of Contents

Syntax

CDF('CHISQUARE', x, df <, nc>)

Arguments

x

is a numeric constant, variable, or expression that specifies a random variable.

df

is a numeric constant, variable, or expression that specifies a degrees of freedom parameter.

Range	df > 0

nc

is a numeric constant, variable, or expression that specifies an optional noncentrality parameter.

Range	nc ≥ 0

Details

The CDF function for the chi-square distribution returns the probability that an observation from a chi-square distribution, with df degrees of freedom and the noncentrality parameter nc, is less than or equal to x. This function accepts noninteger degrees of freedom. If nc is omitted or equal to 0, the value returned is from the central chi-square distribution. In the following equation, let and let . The following equation describes the CDF function of the chi-square distribution:

$table with 1 row and 1 column , row1 column 1 , c d f . open prime c h i s q prime comma x comma nu comma lamda close . equals left brace . table with 2 rows and 2 columns , row1 column 1 , 0 , column 2 x less than 0 , row2 column 1 , sum , from , j equals 0 , to , infinity , of . e super negative , lamda over 2 end super . . fraction open , lamda over 2 , close to the j , over j factorial end fraction . p sub c . open x comma nu plus 2 j close , column 2 x greater than or equal to 0 , end table , end table. Click image for alternative formats.$

In the equation, P_c(.,.) denotes the probability from the central chi-square distribution:

table with 1 row and 1 column , row1 column 1 , p sub c . open x comma eh close . equals , p sub g . open , x over 2 , comma , eh over 2 , close , end table. Click image for alternative formats.

In the equation, P_g(y,b) is the probability from the gamma distribution given by the equation:

$table with 1 row and 1 column , row1 column 1 , p sub g . open y comma b close . equals . fraction 1 , over cap gamma , open b close end fraction . integral , from , 0 , to , y , of . e super negative v end super . v super b minus 1 end super . d v , end table. Click image for alternative formats.$

Example

data one;
   y=cdf('CHISQ', 11.264, 11);
   put y=;
run;

data one;
   y=cdf('CHISQ', 11.264, 11);
   put y=;
run;

The preceding statements produce this result:

y=0.57858

Last updated: April 14, 2026