g01bk returns the lower tail, upper tail and point probabilities associated with a Poisson distribution.
Public Shared Sub g01bk ( _ rlamda As Double, _ k As Integer, _ <OutAttribute> ByRef plek As Double, _ <OutAttribute> ByRef pgtk As Double, _ <OutAttribute> ByRef peqk As Double, _ <OutAttribute> ByRef ifail As Integer _ )
public: static void g01bk( double rlamda, int k, [OutAttribute] double% plek, [OutAttribute] double% pgtk, [OutAttribute] double% peqk, [OutAttribute] int% ifail )
- Type: System..::..DoubleOn entry: the parameter of the Poisson distribution.Constraint: .
- Type: System..::..Int32On entry: the integer which defines the required probabilities.Constraint: .
- Type: System..::..Double%On exit: the lower tail probability, .
- Type: System..::..Double%On exit: the upper tail probability, .
- Type: System..::..Double%On exit: the point probability, .
Let denote a random variable having a Poisson distribution with parameter . Then
The mean and variance of the distribution are both equal to .
Knüsel L (1986) Computation of the chi-square and Poisson distribution SIAM J. Sci. Statist. Comput. 7 1022–1036
Errors or warnings detected by the method:
On entry, . On entry, . On entry, .
Results are correct to a relative accuracy of at least on machines with a precision of or more decimal digits, and to a relative accuracy of at least on machines of lower precision (provided that the results do not underflow to zero).
The time taken by g01bk depends on and . For given , the time is greatest when , and is then approximately proportional to .
This example reads values of and from a data file until end-of-file is reached, and prints the corresponding probabilities.