getting parameters for the lognormal and gamma to match given values for first and second moment

parsFromMoments.R

### I use these to generate data for teaching examples 
lnparFromMoments <- function(expectation, variance){
  m <- expectation; s2 <- variance ; m2 <- m^2
  mu <- log(m2/sqrt(s2+m2))
  sigma2 <- log(1+s2/m2)
  c(mu, sqrt(sigma2)) 
}

gammaparFromMoments <- function(expectation, variance, scale = FALSE){
  m <- expectation; s2 <- variance ; m2 <- m^2 
  shape_alpha <- m2/s2
  rate_beta <- m/s2
  if(scale) {shape_kappa <- shape_alpha; scale_theta <- 1/rate_beta}
  if(!scale) return(c(shape_alpha, rate_beta))
  if(scale) return(c(shape_kappa, scale_theta))
}

meansd <- function(x) c(mean(x), sd(x)) 
meanvar <- function(x) c(mean(x), var(x)) 

# (a<- lnparFromMoments(4,1.5))
# meanvar(exp(rnorm(10000, a[1],a[2])))
# (a<- gammaparFromMoments(160,5, scale = TRUE))
# meanvar(rgamma(10000, shape = a[1], scale = a[2]))

scale01 <- function(x) (x-min(x))/diff(range(x))