Estimate parameters of Frechet distribution using

Question

I'm relatively new in R and I would appreciated if you could take a look at the following code. I'm trying to estimate the shape parameter of the Frechet distribution (or inverse weibull) using mmedist (I tried also the fitdist that calls for mmedist) but it seems that I get the following error :

Error in mmedist(data, distname, start = start, fix.arg = fix.arg, ...) : the empirical moment function must be defined.

The code that I use is the below:

require(actuar)
library(fitdistrplus)
library(MASS)
#values
n=100
scale = 1
shape=3
# simulate a sample
data_fre = rinvweibull(n, shape, scale)
memp=minvweibull(c(1,2), shape=3, rate=1, scale=1)
# estimating the parameters
para_lm = mmedist(data_fre,"invweibull",start=c(shape=3,scale=1),order=c(1,2),memp = "memp")

Please note that I tried many times en-changing the code in order to see if my mistake was in syntax but I always get the same error.

I'm aware of the paradigm in the documentation. I've tried that as well but with no luck. Please note that in order for the method to work the order of the moment must be smaller than the shape parameter (i.e. shape).

The example is the following:

require(actuar)
#simulate a sample
x4  <-  rpareto(1000, 6, 2)

#empirical raw moment
memp  <-  function(x, order)
    ifelse(order == 1, mean(x), sum(x^order)/length(x))


#fit
mmedist(x4, "pareto", order=c(1, 2), memp="memp", 
    start=c(shape=10, scale=10), lower=1, upper=Inf)

Thank you in advance for any help.

Answer 1

You will need to make non-trivial changes to the source of mmedist -- I recommend that you copy out the code, and make your own function foo_mmedist.

1. The first change you need to make is on line 94 of mmedist:

   if (!exists("memp", mode = "function")) 
   

   That line checks whether "memp" is a function that exists, as opposed to whether the argument that you have actually passed exists as a function.

   if (!exists(as.character(expression(memp)), mode = "function"))

2. The second, as I have already noted, relates to the fact that the optim routine actually calls funobj which calls DIFF2, which calls (see line 112) the user-supplied memp function, minvweibull in your case with two arguments -- obs, which resolves to data and order, but since minvweibull does not take data as the first argument, this fails.
   This is expected, as the help page tells you:

   memp A function implementing empirical moments, raw or centered but has to be consistent with distr argument. This function must have two arguments : as a first one the numeric vector of the data and as a second the order of the moment returned by the function.

How can you fix this? Pass the function moment from the moments package. Here is complete code (assuming that you have made the change above, and created a new function called foo_mmedist):

# values
n = 100
scale = 1
shape = 3

# simulate a sample
data_fre = rinvweibull(n, shape, scale)

# estimating the parameters
para_lm = foo_mmedist(data_fre, "invweibull",
                  start= c(shape=5,scale=2), order=c(1, 2), memp = moment)

You can check that optimization has occurred as expected:

> para_lm$estimate
   shape    scale 
2.490816 1.004128 

Note however, that this actually reduces to a crude way of doing overdetermined method of moments, and am not sure that this is theoretically appropriate.