Fitting Weibull using method of moments in R

Question

I am trying to fit a Weibull distribution using method of moments to my data in RStudio. I don't know about the necessary commands and packages one needs to fit distributions such as Weibull or Pareto. Specifically I am trying to estimate the shape parameter k and the scale λ.

I use this code to generate my data:

a <- rweibull(100, 10, 1)

Answer 1

Here is a function to estimate the Weibull distribution parameters with the method of moments.

weibull_mom <- function(x, interval){
  mom <- function(shape, x, xbar){
    s2 <- var(x, na.rm = TRUE)
    lgamma(1 + 2/shape) - 2*lgamma(1 + 1/shape) - log(xbar^2 + s2) + 2*log(xbar)
  }
  xbar <- mean(x, na.rm = TRUE)
  shape <- uniroot(mom, interval = interval, x = x, xbar = xbar)$root
  scale <- xbar/gamma(1 + 1/shape)
  list(shape = shape, scale = scale)
}


set.seed(2021)    # Make the results reproducible
a <- rweibull(100, 10, 1)
weibull_mom(a, interval = c(1, 1e6))
#$shape
#[1] 9.006623
#
#$scale
#[1] 0.9818155

The maximum likelihood estimates are

MASS::fitdistr(a, "weibull")
#     shape        scale   
#  8.89326148   0.98265852 
# (0.69944224) (0.01165359)
#Warning messages:
#1: In densfun(x, parm[1], parm[2], ...) : NaNs produced
#2: In densfun(x, parm[1], parm[2], ...) : NaNs produced