The function may be called by the names: g01fbc, nag_stat_inv_cdf_students_t or nag_deviates_students_t.
The deviate, associated with the lower tail probability, , of the Student's -distribution with degrees of freedom is defined as the solution to
For or the integral equation is easily solved for .
For other values of a transformation to the beta distribution is used and the result obtained from g01fec.
For an inverse asymptotic expansion of Cornish–Fisher type is used. The algorithm is described by Hill (1970).
Hastings N A J and Peacock J B (1975) Statistical Distributions Butterworth
Hill G W (1970) Student's -distribution Comm. ACM13(10) 617–619
1: – Nag_TailProbabilityInput
On entry: indicates which tail the supplied probability represents.
The upper tail probability, i.e., .
The lower tail probability, i.e., .
The two tail (significance level) probability, i.e., .
The two tail (confidence interval) probability, i.e., .
, , or .
2: – doubleInput
On entry: , the probability from the required Student's -distribution as defined by tail.
3: – doubleInput
On entry: , the degrees of freedom of the Student's -distribution.
4: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
Note: on any of the error conditions listed below except NE_SOL_NOT_CONVg01fbc returns .
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument had an illegal value.
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
On entry, .
On entry, .
On entry, .
The solution has failed to converge. However, the result should be a reasonable approximation.
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).
8Parallelism and Performance
g01fbc is not threaded in any implementation.
The value 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 .
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 -distributions and computes the corresponding deviates.