naginterfaces.library.univar.ci_​poisson

naginterfaces.library.univar.ci_poisson(n, xmean, clevel)[source]

ci_poisson computes a confidence interval for the mean parameter of the Poisson distribution.

For full information please refer to the NAG Library document for g07ab

https://www.nag.com/numeric/nl/nagdoc_28.6/flhtml/g07/g07abf.html

Parameters
nint

, the sample size.

xmeanfloat

The sample mean, .

clevelfloat

The confidence level, , for two-sided interval estimate. For example gives a confidence interval.

Returns
tlfloat

The lower limit, , of the confidence interval.

tufloat

The upper limit, , of the confidence interval.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

When using the relationship with the gamma distribution the series to calculate the gamma probabilities has failed to converge.

Notes

Given a random sample of size , denoted by , from a Poisson distribution with probability function

the point estimate, , for is the sample mean, .

Given and this function computes a confidence interval for the parameter , denoted by [], where is in the interval .

The lower and upper confidence limits are estimated by the solutions to the equations

where .

The relationship between the Poisson distribution and the -distribution (see page 112 of Hastings and Peacock (1975)) is used to derive the equations

where is the deviate associated with the lower tail probability of the -distribution with degrees of freedom.

In turn the relationship between the -distribution and the gamma distribution (see page 70 of Hastings and Peacock (1975)) yields the following equivalent equations;

where is the deviate associated with the lower tail probability, , of the gamma distribution with shape parameter and scale parameter . These deviates are computed using stat.inv_cdf_gamma.

References

Hastings, N A J and Peacock, J B, 1975, Statistical Distributions, Butterworth

Snedecor, G W and Cochran, W G, 1967, Statistical Methods, Iowa State University Press