ccompgof {compositions} R Documentation

## Compositional Goodness of fit test

### Description

Goodness of fit tests for count compositional data.

### Usage

PoissonGOF.test(x,lambda=mean(x),R=999,estimated=missing(lambda))
ccompPoissonGOF.test(x,simulate.p.value=TRUE,R=1999)
ccompMultinomialGOF.test(x,simulate.p.value=TRUE,R=1999)


### Arguments

 x a dataset integer numbers (PoissonGOF) or count compositions (compPoissonGOF) lambda the expected value to check against R The number of replicates to compute the distribution of the test statistic estimated states whether the lambda parameter should be considered as estimated for the computation of the p-value. simulate.p.value should all p-values be infered by simulation.

### Details

The compositional goodness of fit testing problem is essentially a multivariate goodness of fit test. However there is a lack of standardized multivariate goodness of fit tests in R. Some can be found in the energy-package.

In principle there is only one test behind the Goodness of fit tests provided here, a two sample test with test statistic.

\frac{\sum_{ij} k(x_i,y_i)}{\sqrt{\sum_{ij} k(x_i,x_i)\sum_{ij} k(y_i,y_i)}}

The idea behind that statistic is to measure the cos of an angle between the distributions in a scalar product given by

 (X,Y)=E[k(X,Y)]=E[\int K(x-X)K(x-Y) dx] 

where k and K are Gaussian kernels with different spread. The bandwith is actually the standarddeviation of k.
The other goodness of fit tests against a specific distribution are based on estimating the parameters of the distribution, simulating a large dataset of that distribution and apply the two sample goodness of fit test.

### Value

A classical "htest" object

 data.name The name of the dataset as specified method a name for the test used alternative an empty string replicates a dataset of p-value distributions under the Null-Hypothesis got from nonparametric bootstrap p.value The p.value computed for this test

### Missing Policy

Up to now the tests can not handle missings.

### Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

### References

Aitchison, J. (1986) The Statistical Analysis of Compositional Data Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.

fitDirichlet,rDirichlet, runif.acomp, rnorm.acomp,

### Examples

## Not run:
x <- runif.acomp(100,4)
y <- runif.acomp(100,4)

erg <- acompGOF.test(x,y)
#continue
erg
unclass(erg)
erg <- acompGOF.test(x,y)

x <- runif.acomp(100,4)
y <- runif.acomp(100,4)
dd <- replicate(1000,acompGOF.test(runif.acomp(100,4),runif.acomp(100,4))$p.value) hist(dd) dd <- replicate(1000,acompGOF.test(runif.acomp(20,4),runif.acomp(100,4))$p.value)
hist(dd)
dd <- replicate(1000,acompGOF.test(runif.acomp(10,4),runif.acomp(100,4))$p.value) hist(dd) dd <- replicate(1000,acompGOF.test(runif.acomp(10,4),runif.acomp(400,4))$p.value)
hist(dd)
dd <- replicate(1000,acompGOF.test(runif.acomp(400,4),runif.acomp(10,4),bandwidth=4)$p.value) hist(dd) dd <- replicate(1000,acompGOF.test(runif.acomp(20,4),runif.acomp(100,4)+acomp(c(1,2,3,1)))$p.value)

hist(dd)

x <- runif.acomp(100,4)
acompUniformityGOF.test(x)

dd <- replicate(1000,acompUniformityGOF.test(runif.acomp(10,4))\$p.value)

hist(dd)

## End(Not run)


[Package compositions version 2.0-8 Index]