# install.packages("univariateML") # Frank.Nielsen@acm.org
# The Harmonic mean of two independent Cauchy distributions (l1,s1) and (l2,s2) is a Cauchy distribution (l12,s12)
library("univariateML")
n <- 100000
l1 <- 1.5
s1 <- 1
l2 <- 2
s2 <- 3
x1 <- rcauchy(n,l1,s1)
x2 <- rcauchy(n,l2,s2)
h12<- 2*x1*x2/(x1+x2)
mlcauchy(h12)
#l12
2*(l1*s2*s2+l2*s1*s1+l1*l2*l2+l1*l1*l2)/((s1+s2)*(s1+s2)+(l1+l2)*(l1+l2))
#s12
2*(s1*s2*s2+(s1*s1+l1*l1)*s2+l2*l2*s1)/((s1+s2)*(s1+s2)+(l1+l2)*(l1+l2))
# Running the above script, we get [1] 1.840708  [1] 1.610619