# \(\text{ChiSquaredQuantile}\)¶

You can use the \(\text{ChiSquaredQuantile}\) function to calculate the quantile function of the chi-squared distribution. The quantile function is the inverse of the cumulative distribution function.

You can use the `\chisquaredq`

backslash command to insert this function.

The following variants of this function are available:

\(\text{real } \text{ChiSquaredQuantile} \left ( \text{<p>}, \text{<k>} \right )\)

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:

Where \(\gamma\text{Inv}\) is the inverse lower gamma function. evaluated for the second term.

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

Figure 118 shows the basic use of the \(\text{ChiSquaredQuantile}\) function.