使用R使Gamma分布适合流

Question

Hello I have a monthly average of stream flow for the last 100 years:

Sep <-
c(50504.61, 31903.57, 20575.81, 51250, 20282.16, 19932.05, 22302.73, 
24777.73, 27681.94, 18676.9, 28587.23, 29030.58, 24433.3, 18785.24, 
21913.74, 33662.53, 23215.58, 35792.85, 13766.63, 41484.56, 16209.67, 
74759.93, 19730.94, 61532.38, 24404.35, 14988.49, 24505.1, 19911.57, 
10058.62, 20984.86, 24913.8, 21067.56, 37107.83, 23730.15, 18556.58, 
24130.02, 14550.06, 21667.81, 11748.43, 17464.65, 15869.2, 27497.25, 
13161.09, 14842.04, 15144.44, 18796.16, 24514.99, 14315.39, 17463.56, 
12698.22, 10528.03, 35689.17, 15496.81, 11170.44, 11593.22, 30230.25, 
14554.43, 25971.54, 12939.35, 30981.11, 12630.06, 18271.7, 14998.52, 
21462.35, 39960.48, 23928.06, 20261.68, 23808.23, 12809.67, 18762.68, 
17108.04, 12861.55, 14521.27, 14215.91, 21513.8, 18797.29, 37495.3, 
27068.98, 37775.56, 26099.67, 34931.63, 23563.04, 19916.69, 15545.58, 
19366.38, 27494.53, 22375.44, 27635.01, 18280.28, 26641.43, 18894.12, 
42866.85, 25925.63, 38156.57, 18015.56)

I am trying to fit a Gamma Distribution to the data with the function:

fit.gamma <- fitdist(Sep, distr = "gamma", method = "mle")

and it gives an error:

simpleError in optim(par = vstart, fn = fnobj, fix.arg = fix.arg, obs = data, gr = gradient, ddistnam = ddistname, hessian = TRUE, method = meth, lower = lower, upper = upper, ...): non-finite finite-difference value [2]> Error in fitdist(Sep, distr = "gamma", method = "mle") : the function mle failed to estimate the parameters,
with the error code 100

I am using the packages

library(fitdistrplus)
library(sm)
library(Rlab)
library(MASS)

Any help would be much appreciated

Answer 1

Gamma distribution has two parameters and both are positive. fitdist function uses optim function to find those parameters. However, without any user specified limit, optim will try even (infeasible) negative parameters during iteration resulting in NaNs . Setting the limit lower = c(0, 0) , will fix this error.

Credit to this answer

library(fitdistrplus)

fit.gamma <- fitdist(Sep, distr = "gamma", method = "mle", lower = c(0, 0))

# Check result
plot(fit.gamma)

# Goodness-of-fit statistics
gofstat(fit.gamma)

#> Goodness-of-fit statistics
#>                              1-mle-gamma
#> Kolmogorov-Smirnov statistic  0.09099753
#> Cramer-von Mises statistic    0.16861125
#> Anderson-Darling statistic    1.07423429
#> 
#> Goodness-of-fit criteria
#>                                1-mle-gamma
#> Akaike's Information Criterion    2004.836
#> Bayesian Information Criterion    2009.944

Created on 2018-03-24 by the reprex package (v0.2.0).