Calculate alpha parameters of Dirichlet distribution.
Function to calculate the α parameters of the Dirichlet distribution based on the method of moments (MoM) using the mean μ and standard deviation σ of the random variables of interest.
dirichlet_params(p.mean, sigma)
p.mean |
Vector of means of the random variables. |
sigma |
Vector of standard deviation of the random variables (i.e., standard error). |
numeric vector of method-of-moment estimates for the alpha parameters of the dirichlet distribution
Based on methods of moments. If μ is a vector of means and σ is a vector of standard deviations of the random variables, then the second moment X_2 is defined by σ^2 + μ^2. Using the mean and the second moment, the J alpha parameters are computed as follows
α_i = \frac{(μ_1-X_{2_{1}})μ_i}{X_{2_{1}}-μ_1^2}
for i = 1, …, J-1, and
α_J = \frac{(μ_1-X_{2_{1}})(1-∑_{i=1}^{J-1}{μ_i})}{X_{2_{1}}-μ_1^2}
Fielitz BD, Myers BL. Estimation of parameters in the beta distribution. Dec Sci. 1975;6(1):1–13.
Narayanan A. A note on parameter estimation in the multivariate beta distribution. Comput Math with Appl. 1992;24(10):11–7.
p.mean <- c(0.5, 0.15, 0.35) p.se <- c(0.035, 0.025, 0.034) dirichlet_params(p.mean, p.se)
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