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08.03.2008 at 05:36PM PDT, ID: 23617810
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8.0

Calculating skewness and kurtosis

Asked by mjcoyne in Perl Programming Language, Math & Science, Probability & Statistics

The attached code produces the following output:

   Excel results:

   Standard Deviation  11.03035112
   Skewness             0.363338937
   Kurtosis            -0.070497874

   My results:

   Standard Deviation  11.0303511188038
   Skewness             0.314893745627018
   Kurtosis            -0.595823617828494

As you can see, my results for skewness and kurtosis are off from those produced by Excel (or SPSS 16 for Windows, for that matter) given the same data.

I've taken the equations for skewness and kurtosis from http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm, and I *think* I've reproduced them faithfully in Perl.

Can anyone spot the problem?Start Free Trial 
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#!/usr/bin/perl -w
use strict;
 
my @data = qw(
    91.3698
    76.3382
    74.5692
    85.2957
    99.0112
    86.9900
    70.7837
    72.8340
    78.1644
    77.7472
    66.0627
    59.7810
    68.4793
    78.6103
    59.8621
);
 
my $excel = <<END;
   Excel results:
 
   Standard Deviation  11.03035112
   Skewness             0.363338937
   Kurtosis            -0.070497874
 
END
 
my $std_dev = sample_sd(\@data);
my $skewness = skewness(\@data);
my $kurtosis = kurtosis(\@data);
 
my $results = <<END;
   My results:
 
   Standard Deviation  $std_dev
   Skewness             $skewness
   Kurtosis            $kurtosis
 
END
 
print $excel, $results;
 
sub sample_sd {
    my $arrayref = shift;
    my ($sum, $sum_sq);
    foreach (@$arrayref) {
        $sum += $_;
    }
    my $mean = $sum/@$arrayref;
    foreach (@$arrayref) {
        $sum_sq += ($_ - $mean) ** 2;
    }
    return sqrt($sum_sq / $#{$arrayref}); # (N-1)
}
 
sub skewness {
    my $arrayref = shift;
    my ($sum, $sum_cubes);
    foreach (@$arrayref) {
        $sum += $_;
    }
    my $mean = $sum/@$arrayref;
    my $std_dev = sample_sd($arrayref);
    foreach (@$arrayref) {
        $sum_cubes += ($_ - $mean) ** 3;
    }
    return $sum_cubes / ($#{$arrayref} * ($std_dev ** 3));
}
 
sub kurtosis {
    my $arrayref = shift;
    my ($sum, $sum_fourth);
    foreach (@$arrayref) {
        $sum += $_;
    }
    my $mean = $sum/@$arrayref;
    my $sd = sample_sd($arrayref);
    foreach (@$arrayref) {
        $sum_fourth += ($_ - $mean) ** 4;
    }
    return $sum_fourth / ($#{$arrayref} * ($sd ** 4)) - 3;
}
[+][-]08.03.2008 at 07:07PM PDT, ID: 22149544

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Zones: Perl Programming Language, Math & Science, Probability & Statistics
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Solution Provided By: Adam314
Participating Experts: 1
Solution Grade: A
 
 
[+][-]08.03.2008 at 08:03PM PDT, ID: 22149694

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[+][-]08.03.2008 at 08:16PM PDT, ID: 22149737

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