Question

I am using the fitdist function in the fitdistrplus package in R.
I have the following data (that I read using read.table):

A <- structure(list(V1 = c(-0.00707717, -0.000947418, -0.00189753, 
-0.000474947, -0.00190205, -0.000476077, 0.00237812, 0.000949668, 
0.000474496, 0.00284226, -0.000473149, -0.000473373, 0, 0, 0.00283688, 
-0.0037843, -0.0047506, -0.00238379, -0.00286807, 0.000478583, 
0.000478354, -0.00143575, 0.00143575, 0.00238835, 0.0042847, 
0.00237248, -0.00142281, -0.00142484, 0, 0.00142484, 0.000948767, 
0.00378609, -0.000472478, 0.000472478, -0.0014181, 0, -0.000946522, 
-0.00284495, 0, 0.00331832, 0.00283554, 0.00141476, -0.00141476, 
-0.00188947, 0.00141743, -0.00236351, 0.00236351, 0.00235794, 
0.00235239, -0.000940292, -0.0014121, -0.00283019, 0.000472255, 
0.000472032, 0.000471809, -0.0014161, 0.0014161, -0.000943842, 
0.000472032, -0.000944287, -0.00094518, -0.00189304, -0.000473821, 
-0.000474046, 0.00331361, -0.000472701, -0.000946074, 0.00141878, 
-0.000945627, -0.00189394, -0.00189753, -0.0057143, -0.00143369, 
-0.00383326, 0.00143919, 0.000479272, -0.00191847, -0.000480192, 
0.000960154, 0.000479731, 0, 0.000479501, 0.000958313, -0.00383878, 
-0.00240674, 0.000963391, 0.000962464, -0.00192586, 0.000481812, 
-0.00241138, -0.00144963)), .Names = "V1", row.names = c(NA, 
-91L), class = "data.frame")

I ran the following command:

fitdist(A$V1,"norm",method="mge",gof="CvM")

and it generates the following:

Fitting of the distribution ' norm ' by maximum goodness-of-fit 
Parameters:
  estimate
1       NA
2       NA
Warning message:
In pnorm(q, mean, sd, lower.tail, log.p) : NaNs produced

given the above error message, I ran the below:

> mu=mean(A$V1)
> sigma=sd(A$V1)
> mu
[1] -0.0003091273
> sigma
[1] 0.002051825
> pnorm(A$V1,mu,sigma)
 [1] 0.0004859313 0.3778682282 0.2194235651 0.4677942525 0.2187728328
 [6] 0.4675752645 0.9048490462 0.7302272325 0.6487379052 0.9377179215
[11] 0.4681427154 0.4680993016 0.5598779146 0.5598779146 0.9373956798
[16] 0.0451612910 0.0152074342 0.1559769817 0.1061704134 0.6494763806
[21] 0.6494350178 0.2914741494 0.8024493726 0.9056899734 0.9874187360
[26] 0.9043830715 0.2936417791 0.2933012328 0.5598779146 0.8009684336
[31] 0.7300820807 0.9770270687 0.4682727654 0.6483730677 0.2944326177
[36] 0.5598779146 0.3780342225 0.1082503682 0.5598779146 0.9614622560
[41] 0.9373152170 0.7995942319 0.2949940199 0.2205866970 0.7999587855
[46] 0.1583537921 0.9036385181 0.9031740418 0.9027096003 0.3791890228
[51] 0.2954414771 0.1095934742 0.6483327428 0.6482924162 0.6482520879
[56] 0.2947687275 0.7997772412 0.3785308577 0.6482924162 0.3784483801
[61] 0.3782828856 0.2200710780 0.4680124750 0.4679688685 0.9612699580
[66] 0.4682295443 0.3781172281 0.8001429585 0.3782000541 0.2199411992
[71] 0.2194235651 0.0042152418 0.2918187280 0.0429384302 0.8029149383
[76] 0.6496008197 0.2164182554 0.4667778828 0.7319136560 0.6496837100
[81] 0.5598779146 0.6496421754 0.7316179594 0.0426934572 0.1533157552
[86] 0.7324331764 0.7322844499 0.2153633562 0.6500594259 0.1527813896
[91] 0.2891573876

So now I am confused why I got the above error message regarding NaN. Anyone have any suggestions what might be the reason and the fix?

for the cauchy distribution, I have tried the following:

`> fitdist(A$V1*10^9,"cauchy",method="mle")
Error in fitdist(A$V1 * 10^9, "cauchy", method = "mle") : 
  the function mle failed to estimate the parameters, 
                with the error code 100
In addition: Warning message:
In dcauchy(x, location, scale, log) : NaNs produced
> fitdist(A$V1*10^5,"cauchy",method="mle")
Error in fitdist(A$V1 * 10^5, "cauchy", method = "mle") : 
  the function mle failed to estimate the parameters, 
                with the error code 100
In addition: Warning message:
In dcauchy(x, location, scale, log) : NaNs produced
> fitdist(A$V1*10^5,"cauchy",method="mge",gof="CvM")
Fitting of the distribution ' cauchy ' by maximum goodness-of-fit 
Parameters:
  estimate
1       NA
2       NA
Warning message:
In pcauchy(q, location, scale, lower.tail, log.p) : NaNs produced
> fitdist(A$V1*10^5,"cauchy",method="mge",gof="AD")
Fitting of the distribution ' cauchy ' by maximum goodness-of-fit 
Parameters:
  estimate
1       NA
2       NA
Warning message:
In pcauchy(q, location, scale, lower.tail, log.p) : NaNs produced
> fitdist(A$V1*10^9,"cauchy",method="mge",gof="AD")
Fitting of the distribution ' cauchy ' by maximum goodness-of-fit 
Parameters:
  estimate
1       NA
2       NA
Warning message:
In pcauchy(q, location, scale, lower.tail, log.p) : NaNs produced
> fitdist(A$V1+10^3,"cauchy",method="mle")
Error in fitdist(A$V1 + 10^3, "cauchy", method = "mle") : 
  the function mle failed to estimate the parameters, 
                with the error code 100
In addition: Warning message:
In dcauchy(x, location, scale, log) : NaNs produced

Any suggestions on the fix for this…thanks!

Answer 1

Answer below.

library(fitdistrplus)


A <- structure(list(V1 = c(-0.00707717, -0.000947418, -0.00189753, 
-0.000474947, -0.00190205, -0.000476077, 0.00237812, 0.000949668, 
0.000474496, 0.00284226, -0.000473149, -0.000473373, 0, 0, 0.00283688, 
-0.0037843, -0.0047506, -0.00238379, -0.00286807, 0.000478583, 
0.000478354, -0.00143575, 0.00143575, 0.00238835, 0.0042847, 
0.00237248, -0.00142281, -0.00142484, 0, 0.00142484, 0.000948767, 
0.00378609, -0.000472478, 0.000472478, -0.0014181, 0, -0.000946522, 
-0.00284495, 0, 0.00331832, 0.00283554, 0.00141476, -0.00141476, 
-0.00188947, 0.00141743, -0.00236351, 0.00236351, 0.00235794, 
0.00235239, -0.000940292, -0.0014121, -0.00283019, 0.000472255, 
0.000472032, 0.000471809, -0.0014161, 0.0014161, -0.000943842, 
0.000472032, -0.000944287, -0.00094518, -0.00189304, -0.000473821, 
-0.000474046, 0.00331361, -0.000472701, -0.000946074, 0.00141878, 
-0.000945627, -0.00189394, -0.00189753, -0.0057143, -0.00143369, 
-0.00383326, 0.00143919, 0.000479272, -0.00191847, -0.000480192, 
0.000960154, 0.000479731, 0, 0.000479501, 0.000958313, -0.00383878, 
-0.00240674, 0.000963391, 0.000962464, -0.00192586, 0.000481812, 
-0.00241138, -0.00144963)), .Names = "V1", row.names = c(NA, 
-91L), class = "data.frame")

#your data are very small 
summary(A$V1)

#fit dist does not converge with parameter
fitdist(A$V1,"norm",method="mge",gof="CvM")

#arguments are correctly specified
?fitdist

#equivalent call of mgedist -> same problem
mgedist(A$V1,"norm",gof="CvM")

#with uniform distribution it works
fitdist(A$V1,"unif",method="mge")

#as well as with mme and mle
fitdist(A$V1,"norm",method="mme")
fitdist(A$V1,"norm",method="mle")

#so the problem comes with the mean or the sd parameters of the normal distribution.
#as returns a result, sd is the problem
mgedist(A$V1,"norm",gof="CvM", fix.arg=list(sd=sd(A$V1)), start=list(mean=0))

#fixing a lower bound for sd returns a result
mgedist(A$V1,"norm",gof="CvM", lower=c(-1, .01))

#but the appropriate answer to your problem is to rescale your data.
#it works perfectly.
mgedist(1000*A$V1,"norm",gof="CvM", lower=c(-1, 1e-3))
#we don't even need to use lower bounds.
mgedist(1000*A$V1,"norm",gof="CvM")


#looking at the source code of mgedist, one can see, that the distance
#of Cramer von Mises is defined as follows.
fnobj <- function(par, fix.arg, obs, pdistnam) {
                n <- length(obs)
                s <- sort(obs)
                theop <- do.call(pdistnam, c(list(q = s), as.list(par), 
                  as.list(fix.arg)))
                1/(12 * n) + sum((theop - (2 * seq(1:n) - 1)/(2 * 
                  n))^2)
            }

#a NaN is produced with negative sd            
fnobj(c(1,1), NULL, A$V1, pnorm)
fnobj(c(mean=1,sd=1), NULL, A$V1, pnorm)
fnobj(c(mean=0,sd=0), NULL, A$V1, pnorm)
fnobj(c(mean=0,sd=-1), NULL, A$V1, pnorm)