pottwhitt

This statistic can be used to test for homogeinity among all
the relative risks. The test statistic is:$$E_+ \sum_{i=1}^n \frac{O_i(O_i-1)}{E_i}$$
If we supposse that the data are generated from a multinomial model,
this is the locally U.M.P. when considering the next hypotheses:
<table class="table">
<tr><td>$H_0$</td><td>:</td><td>$\theta_1 = \ldots = \theta_n=\lambda$</td></tr>
<tr><td>$H_1$</td><td>:</td><td>$\theta_i \sim Ga(\lambda^2/\sigma^2, \lambda/\sigma^2)$</td></tr>
</table>
Notice that in this case, $\lambda$ is supposed to be unknown.
The alternative hypotheses means that relative risks come all from a Gamma
distribution with mean $\lambda$ and variance
$\sigma^2$.
pottwhitt.stat is the function to calculates the value of the statistic
for the data.
pottwhitt.boot is used when performing a non-parametric bootstrap.
pottwhitt.pboot is used when performing a parametric bootstrap.

htest

A set of functions for the detection of spatial clusters
of disease using count data. Bootstrap is used to estimate
sampling distributions of statistics.

Virgilio Gf3mez-Rubio

DCluster

Functions for the Detection of Spatial Clusters of Diseases

pottwhitt function

This statistic can be used to test for homogeinity among all
the relative risks. The test statistic is:

$$E_+ \sum_{i=1}^n \frac{O_i(O_i-1)}{E_i}$$
If we supposse that the data are generated from a multinomial model,
this is the locally U.M.P. when considering the next hypotheses:
<table class='table'>
<tr><td>$H_0$</td><td>:</td><td>$\theta_1 = \ldots = \theta_n=\lambda$</td></tr>
<tr><td>$H_1$</td><td>:</td><td>$\theta_i \sim Ga(\lambda^2/\sigma^2, \lambda/\sigma^2)$</td></tr>
</table>


Notice that in this case, $\lambda$ is supposed to be unknown.
The alternative hypotheses means that relative risks come all from a Gamma
distribution with mean $\lambda$ and variance
$\sigma^2$.
pottwhitt.stat is the function to calculates the value of the statistic
for the data.
pottwhitt.boot is used when performing a non-parametric bootstrap.
pottwhitt.pboot is used when performing a parametric bootstrap.

\(H_0\)	:	\(\theta_1 = \ldots = \theta_n=\lambda\)
\(H_1\)	:	\(\theta_i \sim Ga(\lambda^2/\sigma^2, \lambda/\sigma^2)\)

pottwhitt: Potthoff-Whittinghill's Statistic for Overdispersion

Description

Arguments

References

See Also