naginterfaces.library.stat.prob_chisq_noncentral¶
- naginterfaces.library.stat.prob_chisq_noncentral(x, df, rlamda, tol=0.0, maxit=100)[source]¶
prob_chisq_noncentral
returns the probability associated with the lower tail of the noncentral -distribution.For full information please refer to the NAG Library document for g01gc
https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/g01/g01gcf.html
- Parameters
- xfloat
The deviate from the noncentral -distribution with degrees of freedom and noncentrality parameter .
- dffloat
, the degrees of freedom of the noncentral -distribution.
- rlamdafloat
, the noncentrality parameter of the noncentral -distribution.
- tolfloat, optional
The required accuracy of the solution. If
prob_chisq_noncentral
is entered with greater than or equal to or less than (seemachine.precision
), the value of is used instead.- maxitint, optional
The maximum number of iterations to be performed.
- Returns
- pfloat
The probability associated with the lower tail of the noncentral -distribution.
- Raises
- NagValueError
- (errno )
On entry, and .
Constraint: if .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
The initial value of the Poisson weight used in the summation of Equation (1) (see Notes) was too small to be calculated. The computed probability is likely to be zero.
- (errno )
The solution has failed to converge in iterations. Consider increasing or .
- (errno )
The value of a term required in Equation (2) (see Notes) is too large to be evaluated accurately. The most likely cause of this error is both and are too large.
- (errno )
The calculations for the central chi-square probability has failed to converge. A larger value of should be used.
- Notes
The lower tail probability of the noncentral -distribution with degrees of freedom and noncentrality parameter , , is defined by
where is a central -distribution with degrees of freedom.
The value of at which the Poisson weight, , is greatest is determined and the summation (1) is made forward and backward from that value of .
The recursive relationship:
is used during the summation in (1).
- References
NIST Digital Library of Mathematical Functions