naginterfaces.library.stat.inv_​cdf_​normal

naginterfaces.library.stat.inv_cdf_normal(p, tail='L')[source]

inv_cdf_normal returns the deviate associated with the given probability of the standard Normal distribution.

For full information please refer to the NAG Library document for g01fa

https://www.nag.com/numeric/nl/nagdoc_28.4/flhtml/g01/g01faf.html

Parameters
pfloat

, the probability from the standard Normal distribution as defined by .

tailstr, length 1, optional

Indicates which tail the supplied probability represents.

The lower probability, i.e., .

The upper 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 probability of the standard Normal distribution.

Raises
NagValueError
(errno )

On entry, .

Constraint: , , or .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

Notes

The deviate, associated with the lower tail probability, , for the standard Normal distribution is defined as the solution to

where

The method used is an extension of that of Wichura (1988). is first replaced by .

  1. If , is computed by a rational Chebyshev approximation

    where and , are polynomials of degree .

  2. If , is computed by a rational Chebyshev approximation

    where and , are polynomials of degree .

  3. If , is computed as

    where and , are polynomials of degree .

For the upper tail probability is returned, while for the two tail probabilities the value is returned, where is the required tail probability computed from the input value of .

References

NIST Digital Library of Mathematical Functions

Hastings, N A J and Peacock, J B, 1975, Statistical Distributions, Butterworth

Wichura, 1988, Algorithm AS 241: the percentage points of the Normal distribution, Appl. Statist. (37), 477–484