Calculate parameters required in a Dirichlet distribution

dirichlet_params calculates the 'alpha' values of a Dirichlet distribution from the mean values and one variance value.

Usage

dirichlet_params(mean = mean, variance = variance)

Arguments

mean

numerical vector, same length as variance, containing the mean values of component of a Dirichlet distribution.

variance

numerical vector, with only one non-NA element with a variance value.

Value

The corresponding alpha values for the Dirichlet distribution. If the alpha values are negative the variance should be decreased. A warning is issued in this case.

Details

Input mean vector must contain mean values for each component of the Dirichlet distribution. If one value is missing (signaled with a NA) it is calculated from the sum of all other mean values. In turn, only one variance value must be introduced and all other elements in the variance vector must have an NA.

Examples

# Mean and variance values as input.
m <- c(.3, .23,.27, .2)
v <- c(NA, .1, NA, NA)
alpha <- dirichlet_params(m, v)

# Calculate mean values from alpha.
print(alpha/sum(alpha))
#> [1] 0.30 0.23 0.27 0.20

# Calculate variance values from alpha.
alpha0 <- sum(alpha)
beta <- alpha / alpha0
print(beta*(1-beta)/(1+alpha0))
#> [1] 0.11857708 0.10000000 0.11129305 0.09034444