hyperdirichlet (version 1.5-1)

serum:

Description

Data from Mosimann 1962 detailing serum proteins in white Pekin ducklings.

Usage

data(serum)

Format

A matrix with three columns and 23 rows.

Details

The rows each sum to 1; the values are the relative frequencies of serum proteins in white Pekin ducklings as determined by electrophores.

References

J. E. Mosimann 1962. “On the compound multinomial distribution, the multivariate \(\beta\)-distribution, and correlations among proportions”. Biometrika, volume 49, numbers 1 and 2, pp65-82.

Examples

data(serum)
dhyperdirichlet(serum , HD=dirichlet(4:6),log=TRUE)

f <- function(x){
  if(any(x<0)){
    return(Inf)
  } else {
    return(-sum(dhyperdirichlet(serum , HD=dirichlet(x),include.NC=TRUE,log=TRUE)))
  }
}

fish <- optim(c(3.21,20.38,21.68),f)
triplot(HD=dirichlet(fish$par),l=60,main="increase 'l' for better plot quality")
points(serum[,1]+serum[,2]/2,serum[,2]*sqrt(3)/2,pch=16)