Parameterize gamma distribution with mode and SD

gamma_mode_sd.R

#Parameterize gamma distribution with mode and SD

#Choose summary stats for the gamma
xmode <- 1 #mode of distribution
xsd <- 0.5 # SD 

#Calculate gamma parameters
beta <- (xmode + sqrt(xmode^2 + 4*xsd^2 ) ) / ( 2 * xsd^2 )
alpha <- 1 + xmode * beta

#Plot gamma
x <- seq(0.01, 4, length.out = 1000)
fx <- dgamma(x, shape = alpha, rate = beta) 
#NB stan language is same parameterization as R defaults: shape and rate

plot(x, fx, type = "l")
abline(v = FP_mode)

rx <- rgamma(10000, shape = alpha, rate = beta)
sd(rx)