mnomial.r_function(m)
{
# Data from mnomial.b. Female cancers example.
x_c(14080,12990,6440,4350,3420,3190,2600,2420,1820,1760,23610)

# Simulation from the posterior density for (theta_1,...,theta_l)
pi.post_rdiric.r(10000,x+1)

# posterior Mean, Median and 95%CI for the category-1 probability
mm_summary(pi.post[,1])[3:4]
ci_quantile(pi.post[,1],c(.025,.975)) 

# Alternatively, analytical computation of the posterior mean 
#(x[1]+1)/sum(x+1)

return(mm,ci)
}


# R code for generating n random samples from a Dirichlet(a)
rdiric.r_function(n,a) {
        p <- length(a)
        m <- matrix(nrow=n,ncol=p)
        for (i in 1:p) {
                m[,i] <- rgamma(n,a[i])
        }
        sumvec <- m %*% rep(1,p)
        m / as.vector(sumvec)
}