You can use the \(\text{ChiSquaredCDF}\) function to calculate the cumulative distribution function (CDF) of the chi-squared distribution.

You can use the \chisquaredc backslash command to insert this function.

The following variants of this function are available:

  • \(\text{real } \text{ChiSquaredCDF} \left ( \text{<x>}, \text{<k>} \right )\)

Where \(x\) and \(k\) are scalar values indicating the value of interest and the degrees of freedom respectively. The function is defined for all \(k \in \mathbb{Z}\) where \(k > 0\) and where \(0 < x\) if \(k = 1\) and \(0 \leq x\) for all other values of \(k\).

The value is calculated directly using the relation:

\[\text{ChiSquaredCDF} \left ( x, k \right ) = \text{P} \left ( \frac{k}{2}, \frac{x}{2} \right )\]

Where \(\text{P}\) is the regularized lower gamma function defined as:

\[\text{P} \left ( s, z \right ) = \frac{\gamma \left ( s, x \right )}{\Gamma \left ( s \right )}\]

The chi-squared distribution represents the sum of the squares of \(k\) standard normally distributed random variates.

Figure 116 shows the basic use of the \(\text{ChiSquaredCDF}\) function.


Figure 116 Example Use Of the ChiSquaredCDF Function