naginterfaces.library.stat.inv_cdf_students_t¶
- naginterfaces.library.stat.inv_cdf_students_t(p, df, tail='L')[source]¶
inv_cdf_students_t
returns the deviate associated with the given tail probability of Student’s -distribution with real degrees of freedom.For full information please refer to the NAG Library document for g01fb
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/g01/g01fbf.html
- Parameters
- pfloat
, the probability from the required Student’s -distribution as defined by .
- dffloat
, the degrees of freedom of the Student’s -distribution.
- tailstr, length 1, optional
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., .
- Returns
- xfloat
The deviate associated with the given tail probability of Student’s -distribution with real degrees of freedom.
- Raises
- NagValueError
- (errno )
On entry, .
Constraint: , , or .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- Warns
- NagAlgorithmicWarning
- (errno )
The solution has failed to converge. However, the result should be a reasonable approximation.
- Notes
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
inv_cdf_beta()
.For an inverse asymptotic expansion of Cornish–Fisher type is used. The algorithm is described by Hill (1970).
- References
Hastings, N A J and Peacock, J B, 1975, Statistical Distributions, Butterworth
Hill, G W, 1970, Student’s -distribution, Comm. ACM (13(10)), 617–619