naginterfaces.library.stat.prob_​binomial

naginterfaces.library.stat.prob_binomial(n, p, k)[source]

prob_binomial returns the lower tail, upper tail and point probabilities associated with a binomial distribution.

For full information please refer to the NAG Library document for g01bj

https://www.nag.com/numeric/nl/nagdoc_28.6/flhtml/g01/g01bjf.html

Parameters
nint

The parameter of the binomial distribution.

pfloat

The parameter of the binomial distribution.

kint

The integer which defines the required probabilities.

Returns
plekfloat

The lower tail probability, .

pgtkfloat

The upper tail probability, .

peqkfloat

The point probability, .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, and .

Constraint: .

(errno )

On entry, is too large to be represented exactly as a double precision number.

(errno )

On entry, the variance exceeds .

Notes

Let denote a random variable having a binomial distribution with parameters and ( and ). Then

The mean of the distribution is and the variance is .

prob_binomial computes for given , and the probabilities:

The method is similar to the method for the Poisson distribution described in Knüsel (1986).

References

Knüsel, L, 1986, Computation of the chi-square and Poisson distribution, SIAM J. Sci. Statist. Comput. (7), 1022–1036