- Type: System..::..DoubleOn entry: the deviate from the noncentral -distribution with degrees of freedom and noncentrality parameter .Constraint: .
- Type: System..::..DoubleOn entry: , the degrees of freedom of the noncentral -distribution.Constraint: .
- Type: System..::..DoubleOn entry: , the noncentrality parameter of the noncentral -distribution.Constraint: if or if .
- Type: System..::..Double
- Type: System..::..Int32On entry: the maximum number of iterations to be performed.Suggested value: . See [Further Comments] for further discussion.Constraint: .
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).
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
Note: g01gc may return useful information for one or more of the following detected errors or warnings.
Errors or warnings detected by the method:
If on exit , , or , then g01gc returns .
On entry, , or , or and , or , or .
- The initial value of the Poisson weight used in the summation (1) was too small to be calculated. The value of is likely to be zero.
- The solution has failed to converge in maxit iterations.
- The calculations for the central probability has failed to converge. This is an unlikely error exit. A larger value of tol should be used.
The number of terms in (1) required for a given accuracy will depend on the following factors:
|(i)||The rate at which the Poisson weights tend to zero. This will be slower for larger values of .|
|(ii)||The rate at which the central probabilities tend to zero. This will be slower for larger values of and .|
This example reads values from various noncentral -distributions, calculates the lower tail probabilities and prints all these values until the end of data is reached.