The deviate,
${t}_{p}$ associated with the lower tail probability,
$p$, of the Student's
$t$-distribution with
$\nu $ degrees of freedom is defined as the solution to
For other values of
$\nu <3$ a transformation to the beta distribution is used and the result obtained from
g01fec.
For
$\nu \ge 3$ an inverse asymptotic expansion of Cornish–Fisher type is used. The algorithm is described by
Hill (1970).
The results should be accurate to five significant digits, for most argument values. The error behaviour for various argument values is discussed in
Hill (1970).
The value
${t}_{p}$ may be calculated by using the transformation described in
Section 3 and using
g01fec. This function allows you to set the required accuracy.
Internal changes have been made to this function as follows:
- At Mark 27: The algorithm underlying this function has been altered to improve the accuracy in cases where ${\mathbf{df}}<3$.
For details of all known issues which have been reported for the NAG Library please refer to the
Known Issues.
This example reads the probability, the tail that probability represents and the degrees of freedom for a number of Student's $t$-distributions and computes the corresponding deviates.