The Dirichlet distribution

Generates Dirichlet random variates.

Usage

rdiric(n, shape, dimension = NULL, is.matrix.shape = FALSE)

Arguments

n

number of observations. Note it has two meanings, see is.matrix.shape below.

shape

the shape parameters. These must be positive. If dimension is specifed, values are recycled if necessary to length dimension.

dimension

the dimension of the distribution. If dimension is not numeric then it is taken to be length(shape) (or ncol(shape) if is.matrix.shape == TRUE).

is.matrix.shape

Logical. If TRUE then shape must be a matrix, and then n is no longer the number of rows of the answer but the answer has n * nrow(shape) rows. If FALSE (the default) then shape is a vector and each of the n rows of the answer have shape as its shape parameters.

Details

This function is based on a relationship between the gamma and Dirichlet distribution. Random gamma variates are generated, and then Dirichlet random variates are formed from these.

Value

A n by dimension matrix of Dirichlet random variates. Each element is positive, and each row will sum to unity. If shape has names then these will become the column names of the answer.

References

Lange, K. (2002). Mathematical and Statistical Methods for Genetic Analysis, 2nd ed. New York: Springer-Verlag.

Author

Thomas W. Yee

See also

dirichlet is a VGAM family function for fitting a Dirichlet distribution to data.

Examples

ddata <- data.frame(rdiric(n = 1000, shape = c(y1 = 3, y2 = 1, y3 = 4)))
fit <- vglm(cbind(y1, y2, y3) ~ 1, dirichlet, data = ddata, trace = TRUE)
#> Iteration 1: loglikelihood = 931.05677
#> Iteration 2: loglikelihood = 5343.4329
#> Iteration 3: loglikelihood = 13112.883
#> Iteration 4: loglikelihood = 17923.845
#> Iteration 5: loglikelihood = 18570.779
#> Iteration 6: loglikelihood = 18578.673
#> Iteration 7: loglikelihood = 18578.675
#> Iteration 8: loglikelihood = 18578.675
Coef(fit)
#>    shape1    shape2    shape3 
#> 3.0075279 0.9897924 3.9894108 
coef(fit, matrix = TRUE)
#>             loglink(shape1) loglink(shape2) loglink(shape3)
#> (Intercept)        1.101118      -0.0102601        1.383644