fitting double lognormal distribution on a dataset

sdani has asked for the wisdom of the Perl Monks concerning the following question:

Hi Monks,

My script generates a tons of histograms like this: http://kepfeltoltes.hu/130518/pAKT-tAKT_www.kepfeltoltes.hu_.png

As you can see there are two lognormal distribution on top of each other and I need the parameters of those distribution. To get that, I was trying to use Algorithm::CurveFit function, but the the Math::Symbolic package falis to parse my equation. (That I got from the wikipedia page: http://en.wikipedia.org/wiki/Log-normal_distribution#Probability_density_function)

I think I am making some mistakes when I phrasing the equation (I was trying the single lognormal first).

my $equation = '(exp(-1 * (log(x) - m)**2 / (2 * r ** 2)))/(x * r * 2.
+5066)';
# x - independent variable
# m - mean
# r - standard dev.
[download]

Here is a sample dataset:

0.0643566964735115    1
0.078213413896854    2
0.0862233698701667    2
0.0950536377503222    5
0.104788226940961    12
0.115519750377919    35
0.127350305630187    52
0.140392446235774    116
0.154770252513572    160
0.17062051203871    187
0.188094021012202    250
0.207357018905863    240
0.228592770031414    258
0.252003307080518    252
0.277811353223423    251
0.306262441052688    246
0.337627248531191    197
0.372204174168167    182
0.410322175922981    184
0.4523439008454    167
0.498669135227145    130
0.549738608088756    159
0.606038184187406    130
0.668103486437085    102
0.736524991717946    123
0.811953648555319    118
0.895107070113873    114
0.986776361425825    111
1.0878336458061    111
1.19924036205923    102
1.32205641141595    76
1.4574502412217    98
1.60670996131109    81
1.7712555988274    84
1.95265260807701    68
2.15262676394876    47
2.37308058059129    42
2.61611141155243    45
2.88403140358156    29
3.17938949393169    33
3.50499566043902    19
3.86394765509039    19
4.25966047541651    10
4.69589885409594    8
5.17681307586923    7
5.70697846251846    3
6.29143890156414    6
7.64605614922042    2
8.42910051556786    1
[download]

Was there some error with the equation? Should I use other package to do it? What would be the best way to go? I really need wisdom here! :) Thanks for your help!

Daniel

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Re: fitting double lognormal distribution on a dataset by hdb (Monsignor) on May 18, 2013 at 11:14 UTC
I have not used that package but the documentation of `Algorithm::CurveFit` seems to specify that powers need to be written as `x^n` and not `x**n`.	[reply] [d/l] [select]
Re^2: fitting double lognormal distribution on a dataset by kcott (Archbishop) on May 18, 2013 at 18:11 UTC
G'day hdb, ... the documentation of `Algorithm::CurveFit` seems to specify that powers need to be written as `x^n` and not `xn`. Firstly, I will say that the first line of code in the Algorithm::CurveFit SYNOPSIS: `my $formula = 'c + a * x^2';` [download] is written in a way that suggests this intent `$ perl -MO=Deparse,-p -e 'my $formula = $c + $a * $x*2;' (my $formula = ($c + ($a ($x ** 2)))); -e syntax OK` [download] more than it does this one `$ perl -MO=Deparse,-p -e 'my $formula = $c + $a * $x^2;' (my $formula = (($c + ($a * $x)) ^ 2)); -e syntax OK` [download] However, further down they have The formula should be a string that can be parsed by Math::Symbolic. The doco for that module has Warning: The operator to use for exponentiation is the normal Perl operator for exponentiation `*`, NOT the caret `^` which denotes exponentiation in the notation that is recognized by the Math::Symbolic parsers! The `^` operator will be interpreted as the normal binary xor. [Update (cosmetic): 2 instances of quoting my own code — `<blockquote>`s removed.]* -- Ken	[reply] [d/l] [select]
Re^3: fitting double lognormal distribution on a dataset by hdb (Monsignor) on May 18, 2013 at 19:04 UTC
Thanks for the clarification. I find this documentation very confusing. If I see an example like `'1/2 * m * v^2'` I believe that the caret is the operator for exponentiation and I do not see any need to even continue reading. Obviously wrong here. A fully working example would be useful here to test such presumptions...	[reply] [d/l]
Re^4: fitting double lognormal distribution on a dataset by sdani (Novice) on May 19, 2013 at 03:48 UTC
Re^2: fitting double lognormal distribution on a dataset by sdani (Novice) on May 18, 2013 at 15:51 UTC
That's funny. I was looking for the documentation of Math::Symbolic and they were writing that the regular ** is for the power not ^, that is the xor logical gate. Now I'll definitely try. Thanks.	[reply]