rdiric.RdGenerates Dirichlet random variates.
rdiric(n, shape, dimension = NULL, is.matrix.shape = FALSE)number of observations.
Note it has two meanings, see is.matrix.shape below.
the shape parameters. These must be positive.
If dimension is specifed, values
are recycled if necessary to length 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).
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.
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.
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.
Lange, K. (2002). Mathematical and Statistical Methods for Genetic Analysis, 2nd ed. New York: Springer-Verlag.
dirichlet is a VGAM family function for
fitting a Dirichlet distribution to data.
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