Errors while trying to fit gamma distribution with R fitdistr{MASS}

Question

I have a problem with fitdistr{MASS} function in R. I have this vector:

a <- c(26,73,84,115,123,132,159,207,240,241,254,268,272,282,300,302,329,346,359,367,375,378, 384,452,475,495,503,531,543,563,594,609,671,687,691,716,757,821,829,885,893,968,1053,1081,1083,1150,1205,1262,1270,1351,1385,1498,1546,1565,1635,1671,1706,1820,1829,1855,1873,1914,2030,2066,2240,2413,2421,2521,2586,2727,2797,2850,2989,3110,3166,3383,3443,3512,3515,3531,4068,4527,5006,5065,5481,6046,7003,7245,7477,8738,9197,16370,17605,25318,58524)

and I want to fit a gamma distribution to the data with a command:

fitted.gamma <- fitdistr(a, "gamma")

but I have such error:

Error in optim(x = c(26, 73, 84, 115, 123, 132, 159, 207, 240, 241, 254,  : 
non-finite finite-difference value [1]
In addition: Warning messages:
1: In densfun(x, parm[1], parm[2], ...) : NaNs produced
2: In densfun(x, parm[1], parm[2], ...) : NaNs produced
3: In densfun(x, parm[1], parm[2], ...) : NaNs produced
4: In densfun(x, parm[1], parm[2], ...) : NaNs produced

So I tried with initializing the parameters:

(fitted.gamma <- fitdistr(a, "gamma", start=list(1,1)))

The object fitted.gamma is created but when printed, creates an error:

Error in dn[[2L]] : subscript out of bounds

Do you know what is happening or maybe know some other R functions to fit univariate distributions by MLE?

Thanks in advance for any help or response.

Kuba

Answer 1

Always plot your stuff first, you scaling is far offfffffff.

library(MASS)
a <- c(26,73,84,115,123,132,159,207,240,241,254,268,272,282,300,302,329,346,359,367,375,378, 384,452,475,495,503,531,543,563,594,609,671,687,691,716,757,821,829,885,893,968,1053,1081,1083,1150,1205,1262,1270,1351,1385,1498,1546,1565,1635,1671,1706,1820,1829,1855,1873,1914,2030,2066,2240,2413,2421,2521,2586,2727,2797,2850,2989,3110,3166,3383,3443,3512,3515,3531,4068,4527,5006,5065,5481,6046,7003,7245,7477,8738,9197,16370,17605,25318,58524)
## Ooops, rater wide
plot(hist(a))
fitdistr(a/10000,"gamma") # gives warnings
# No warnings
fitted.gamma <- fitdistr(a/10000, dgamma,  start=list(shape = 1, rate = 0.1),lower=0.001)

Now you can decide what to do with the scaling

Answer 2

For data that clearly fits the gamma distribution, but is on the wrong scale (i.e., as if it had been multiplied/divided by a large number), here's an alternative approach to fitting the gamma distribution:

fitgamma <- function(x) {
  # Equivalent to `MASS::fitdistr(x, densfun = "gamma")`, where x are first rescaled to 
  # the appropriate scale for a gamma distribution. Useful for fitting the gamma distribution to 
  # data which, when multiplied by a constant, follows this distribution
  if (!requireNamespace("MASS")) stop("Requires MASS package.")

  fit <- glm(formula = x ~ 1, family = Gamma)
  out <- MASS::fitdistr(x * coef(fit), "gamma")
  out$scaling_multiplier <- unname(coef(fit))
  out
}

Usage:

set.seed(40)
test <- rgamma(n = 100, shape = 2, rate = 2)*50000
fitdistr(test, "gamma") # fails
dens_fit <- fitgamma(test) # successs
curve(dgamma(x, 2, 2), to = 5) # true distribution
curve(dgamma(x, dens_fit$estimate['shape'], dens_fit$estimate['rate']), add=TRUE, col=2) # best guess
lines(density(test * dens_fit$scaling_multiplier), col = 3)