# [R] Fitdistr() versus nls()

From: Luca Telloli <telloli_at_cs.unibo.it>
Date: Sat 23 Sep 2006 - 10:35:10 GMT

I'm new to R so I apologize in advance for any big mistake I might be doing. I'm trying to fit a set of samples with some probabilistic curve, and I have an important question to ask; in particular I have some data, from which I calculate manually the CDF, and then I import them into R and try to fit: I have the x values (my original samples) and the y values (P(X<x)).

To attempt the fit I've both fitdistr() and nls(), in the way you can read in the piece of code at the end of the email. Because the fit with all data doesn't work very well, I decided to take a subset of samples randomly chosen (for some random x, the correspondant y is chosen).

The first big problem is that fitdistr and nls, in the way I use them in the code, they don't get me similar results. I think I'm making a mistake but I can't really understand which one.

From this first issue, a second one arises because the plot with nls is similar (maybe not a great fit bust still...) to my original CDF while the plot of fitdistr is basically a straight line of constant value y=1. On the other side, the fitdistr outperforms in the Kolmogorov-Smirnov test, which for nls has values of probability around 0 (not a good score huh?).

allvals.x=array(t(cdf.all[1]))
allvals.y=array(t(cdf.all[2]))
library(MASS)
bestval.exp.nls=bestval.exp.fit=-1
plot(allvals.x, allvals.y)

for(it in 1:100){

#extract random samples

```	random=sort(sample(1:length(allvals.x), 15))
somevals.x=allvals.x[c(random)]
somevals.y=allvals.y[c(random)]

#fit with nls and fitdistr

fit.exp = fitdistr(somevals.y, "exponential")
nls.exp <- nls(somevals.y ~ pexp(somevals.x, rate), start=list(rate=.
0001), model=TRUE)

#plot what you get out of the two fits

lines(allvals.x, pexp(allvals.x, coef(fit.exp)), col=it)
lines(allvals.x, pexp(allvals.x, coef(nls.exp)), col=it)

#perform kolmogorov-smirnov test on your fit

ks.exp.nls = ks.test(somevals.y, "pexp", coef(nls.exp))
ks.exp.fit = ks.test(somevals.y, "pexp", coef(fit.exp))

bestval.exp.fit = max(bestval.exp.fit, ks.exp.fit\$p.value)
bestval.exp.nls = max(bestval.exp.nls, ks.exp.nls\$p.value)
```
}

print(bestval.exp.fit)
print(bestval.exp.nls)

----------END OF

```CODE--------------------------------------------------------------------

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