The method used is an extension of that of Wichura (1988). is first replaced by .
(a)
If , is computed by a rational Chebyshev approximation
where and , are polynomials of degree 7.
(b)
If , is computed by a rational Chebyshev approximation
where and , are polynomials of degree 5.
(c)
If , is computed as
where and , are polynomials of degree 6.
4 References
Wichura (1988) Algorithm AS 241: the percentage points of the Normal distribution Appl. Statist.37 477–484
5 Arguments
1:
p – doubleInput
On entry: the probability, , from the standardized Normal distribution.
Constraint:
.
2:
fail – NagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).
6 Error Indicators and Warnings
NE_INTERNAL_ERROR
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.
NE_REAL_ARG_GE
On entry, p must not be greater than or equal to : .
nag_deviates_normal_dist (g01cec) attempts to attain a relative precision of .
8 Further Comments
If is a Normal random variable with mean and variance , the deviate corresponding to a lower tail probability of is , where is the standardized Normal deviate returned by nag_deviates_normal_dist (g01cec).
9 Example
The deviates corresponding to several lower tail probabilities from the standard Normal distribution are calculated and printed.