R: NN and Anscombe samples

afgen {binhf} | R Documentation

## NN and Anscombe samples

### Description

Samples binomial Fisz and Anscombe transformed random variables on a grid of binomial probabilities.

### Usage

    afgen(xgrid = seq(0, 1, length = 21), ygrid = seq(0, 1, length = 21), samples = 1000,
    binsize = 32)

### Arguments

`xgrid` | vector of x co-ordinate probabilities.
`ygrid` | vector of x co-ordinate probabilities.
`samples` | the number of samples to draw from each random variable.
`binsize` | the binomial size of the binomial random variables.

### Details

The function produces sampled values from the random variable:
ζ(X_1,X_2)=\frac{X_1-X_2}{ √{ (X_1+X_2)(2*binsize-X_1-X_2)/ 2*binsize }} ,
where X_i are Bin(binsize,p_i) random variables, for all combinations of values of p_1 in xgrid and p_2 in ygrid. For Anscombe's transformation, A=sin^{-1}√{(x+3/8)/(binsize+3/4)}, the values correspond to the random variable with the larger binomial probability.

### Value

`a` | an array of dimensions `length(xgrid)xlength(ygrid)xsamples` of values of binomial Haar-Fisz random variable.
`b` | an array of dimensions `length(xgrid)xlength(ygrid)xsamples` of values of A.

### Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

### References

Anscombe, F.J. (1948) The transformation of poisson, binomial and negative binomial Data, Biometrika,35, 246–254.
Nunes, M. and Nason, G.P. (2009) A multiscale variance stabilization for binomial sequence proportion estimation. Statistica Sinica, 19 (1491–1510).

### See Also

`ansc`

### Examples

    ##
    varvalues<-afgen(xgrid=seq(0,1,length=21),ygrid=seq(0,1,length=21),samples=1000,binsize=32)

    ##creates 1000 samples of the two random variables zeta_B and A for each point
    ##(x,y) for x and y regularly-spaced probability vectors of length 21.
    ##

[Package binhf version 1.0-1 Index]