afgen: NN and Anscombe samples

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

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

Usage

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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

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##
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.
##


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