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.
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)`