naginterfaces.library.stat.prob_f¶
- naginterfaces.library.stat.prob_f(f, df1, df2, tail='L')[source]¶
prob_f
returns the probability for the lower or upper tail of the or variance-ratio distribution with real degrees of freedom.For full information please refer to the NAG Library document for g01ed
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/g01/g01edf.html
- Parameters
- ffloat
, the value of the variate.
- df1float
The degrees of freedom of the numerator variance, .
- df2float
The degrees of freedom of the denominator variance, .
- tailstr, length 1, optional
Indicates whether an upper or lower tail probability is required.
The lower tail probability is returned, i.e., .
The upper tail probability is returned, i.e., .
- Returns
- pfloat
The probability for the lower or upper tail of the or variance-ratio distribution with real degrees of freedom.
- Raises
- NagValueError
- (errno )
On entry, .
Constraint: or .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, and .
Constraint: and .
- (errno )
The probability is too close to or . is too far out into the tails for the probability to be evaluated exactly. The result tends to approach if is large, or if is small. The result returned is a good approximation to the required solution.
- Notes
The lower tail probability for the , or variance-ratio distribution, with and degrees of freedom, , is defined by:
for , , .
The probability is computed by means of a transformation to a beta distribution, :
and using a call to
prob_beta()
.For very large values of both and , greater than , a normal approximation is used. If only one of or is greater than then a approximation is used, see Abramowitz and Stegun (1972).
- References
Abramowitz, M and Stegun, I A, 1972, Handbook of Mathematical Functions, (3rd Edition), Dover Publications
Hastings, N A J and Peacock, J B, 1975, Statistical Distributions, Butterworth