fpois: Fit Homogeneous Poisson to Data and Test Equality of Mean and...

In extRemes: Extreme Value Analysis

Fit Homogeneous Poisson to Data and Test Equality of Mean and Variance

Description

Fit a homogeneous Poisson to data and test whether or not the mean and variance are equal.

Usage

fpois(x, na.action = na.fail, ...)

## Default S3 method:
fpois(x, na.action = na.fail, ...)

## S3 method for class 'data.frame'
fpois(x, na.action = na.fail, ..., which.col = 1)

## S3 method for class 'matrix'
fpois(x, na.action = na.fail, ..., which.col = 1)

## S3 method for class 'list'
fpois(x, na.action = na.fail, ..., which.component = 1)

Arguments

x	numeric, matrix, data frame or list object containing the data to which the Poisson is to be fit.
na.action	function to be called to handle missing values.
...	Not used.
which.col,which.component	column or component (list) number containing the data to which the Poisson is to be fit.

Details

The probability function for the (homogeneous) Poisson distribution is given by:

Pr( N = k ) = exp(-lambda) * lambda^k / k!

for k = 0, 1, 2, ...

The rate parameter, lambda, is both the mean and the variance of the Poisson distribution. To test the adequacy of the Poisson fit, therefore, it makes sense to test whether or not the mean equals the variance. R. A. Fisher showed that under the assumption that X_1, ..., X_n follow a Poisson distribution, the statistic given by:

D = (n - 1) * var(X_1) / mean(X_1)

follows a Chi-square distribution with n - 1 degrees of freedom. Therefore, the p-value for the one-sided alternative (greater) is obtained by finding the probability of being greater than D based on a Chi-square distribution with n - 1 degrees of freedom.

Value

A list of class “htest” is returned with components:

statistic	The value of the dispersion D
parameter	named numeric vector giving the estimated mean, variance, and degrees of freedom.
alternative	character string with the value “greater” indicating the one-sided alternative hypothesis.
p.value	the p-value for the test.
method	character string stating the name of the test.
data.name	character naming the data used by the test (if a vector is applied).

Author(s)

Eric Gilleland

See Also

glm

Examples

data(Rsum)
fpois(Rsum$Ct)

## Not run: 

# Because 'Rsum' is a data frame object,
# the above can also be carried out as:

fpois(Rsum, which.col = 3)

# Or:

fpois(Rsum, which.col = "Ct")

##
## For a non-homogeneous fit, use glm.
##
## For example, to fit the non-homogeneous Poisson model
## Enso as a covariate:
##

fit <- glm(Ct~EN, data = Rsum, family = poisson())
summary(fit)

## End(Not run)

extRemes documentation built on Nov. 19, 2022, 1:07 a.m.