# Chi-squared distribution Probabilities

Calculator of Chi-squared distribution : probabilities, density function (PDF) and cumulative density function (CDF).

## Chi-squared distribution formulas

X is a random variable following a Chi-squared distribution of parameter `k > 0` (degrees of freedom).

`Gamma(x)` is the gamma function.

### Probability Density Function (PDF)

`f(x) = 1/(2^(k/2)*Gamma(k/2))*x^(k/2-1)*e^(-x/2)`

### Cumulative distribution function (CDF)

`F(x) = \int_-oo^x f(t)\ dt`

`F(x) = (gamma(k/2,x/2))/(Gamma(k/2))`

where `gamma(x)` is the lower incomplete gamma function.

### Probabilities

Probability that X is greater than a :

`P(X > a) = 1 - F(a)`

Probability that X is less than b :

`P(X < b) = F(b)`

Probability that X lies between a and b :

`P(a < X < b) = F(b) - F(a)`

## See also

Inverse Chi-squared distribution

Chi-squared distribution Chart

Statistics Calculators