pollen {hyperdirichlet} | R Documentation

## Serum data from Mosimann 1962

### Description

Data from Mosimann 1962 detailing forest pollen counts

### Usage

    data(pollen)

### Format

A matrix with four columns and 76 rows.

### Details

The rows each sum to 100; the values are counts of four different types of pollen. Each row corresponds to a different level in the core; the levels are in sequence with the first row being most recent and the last row being the oldest.

### 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.

### See Also

`serum`

### Examples

    data(pollen)

    func <- function(x,l){
    ifelse(any(l<0),Inf,
     lfactorial(sum(x)) -sum(lfactorial(x))
        +lgamma(sum(l)) +sum(lgamma  (x+l))
        -sum(lgamma(l)) -lgamma(sum  (x+l))
    )
    }

    start_vec <- c(51.6, 1, 5.3 , 2)

    optim(start_vec , function(l){ -sum(apply(pollen , 1, FUN=func,l=l))})

[Package hyperdirichlet version 1.3-8 Index]