nag_deviates_students_t (g01fbc) returns the deviate associated with the given tail probability of Student's -distribution with real degrees of freedom.
The deviate,
associated with the lower tail probability,
, of the Student's
-distribution with
degrees of freedom is defined as the solution to
For other values of
a transformation to the beta distribution is used and the result obtained from
nag_deviates_beta (g01fec).
For
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).
Not applicable.
The value
may be calculated by using the transformation described in
Section 3 and using
nag_deviates_beta (g01fec). This function allows you to set the required accuracy.
This example reads the probability, the tail that probability represents and the degrees of freedom for a number of Student's -distributions and computes the corresponding deviates.