# [R] ecdf() to nls() - how to transform data?

Jochen1980 info at jochen-bauer.net
Mon Jul 18 02:13:39 CEST 2011

```Hi David,

my first attempt to work through your code was successful, my predicted line
is pretty close to the ecdf-function. I have no idea why you inverted the
gumbel-function and what the advantage of this strategy is?

I interpret your (1:100/100)-trick like this: you build a sequence of 100
Tics. In addition to this 100 is identical to the number of created points.

In my real world situation, ecdf() will produce ties, same values, and this
results that I do not know what number knot() will return, then this will
result in a non-symmetric-data.frame()-error.

R-Code:
############### Tutorial 3, Gamma-Distribution-Points to Gumbel
################
# --- create Points --- #
http://r.789695.n4.nabble.com/ecdf-to-nls-how-to-transform-data-td3671754.html
print( "Tutorial 3" )
p <- rgamma( 100, 2)
print( p )
ep <- ecdf( p )
x <- knots(ep)
hist( p, main="Tutorial 3" )
ypre <- seq( from=1, to=100, by=1 )
y <- ypre / 100
df <- data.frame( x=x, y=y )
plot( df )
res <- nls( y ~ exp( - exp( - ( x - mue ) / beta )), start=list(mue=2,
beta=2), data=df, trace=TRUE )
print( summary(res) )
#print( str(res))
lines( x, predict( res, list( x=x )), lty = 1, col = "blue" ) # predicted
vals

Console-Output:
[1] "Tutorial 3"
[1] 4.75748951 5.36642043 2.03025702 1.80216440 1.40745277 0.91393251
[7] 1.30575505 2.07451301 1.18500815 0.24972503 1.36604865 2.36786796
[13] 1.37386798 1.72390843 1.93700139 0.78722468 2.92828385 1.51165415
[19] 4.17000960 2.98356424 1.20195996 1.85899533 0.94863757 1.50438053
[25] 0.50854274 3.32760075 2.21334316 0.58463817 2.26985676 2.88033389
[31] 2.00718903 1.19043470 1.62945752 0.32010478 0.54837755 1.32965131
[37] 3.32024573 0.53825226 3.30077557 0.46426513 1.00681720 0.59276030
[43] 1.31431609 2.27822419 2.56404713 0.52459218 1.05228996 2.23799673
[49] 1.14438962 2.41311612 1.40254244 1.20379073 0.44195457 0.95880408
[55] 1.45254027 4.49645001 2.18826796 1.07161515 1.62617544 3.15506003
[61] 2.15611491 2.43261017 1.40293461 2.79977886 3.44503201 3.25282551
[67] 0.91570531 0.70243512 5.67971774 3.55532192 1.71515046 2.97718949
[73] 0.47145131 0.32879089 0.60735231 0.92388638 4.29277857 1.73681839
[79] 0.09387383 2.81281295 1.84419058 2.63070353 1.52298124 2.89761263
[85] 1.05251987 1.24258703 3.09130229 2.66738574 3.17035060 2.15287327
[91] 2.63042751 1.69736779 3.21126033 1.56920999 2.68985477 0.82952068
[97] 3.62230865 1.65286592 2.76798783 2.08091935

Formula: y ~ exp(-exp(-(x - mue)/beta))

Parameters:
Estimate Std. Error t value Pr(>|t|)
mue  1.382744   0.005926   233.3   <2e-16 ***
beta 0.984836   0.008816   111.7   <2e-16 ***

--
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```