Statistics/Chi-squared distribution: Difference between revisions

=={{header|Perl}}==

{{trans|Raku}}

<syntaxhighlight lang="perl" line>use v5.36;

use Math::MPFR;

use List::Util 'sum';

sub Gamma ($z) {

my $g = Math::MPFR->new();

Math::MPFR::Rmpfr_gamma($g, Math::MPFR->new($z), 0);

$g;

}

sub chi2($x,$k) { $x>0 && $k>0 ? ($x**($k/2 - 1) * exp(-$x/2)/(2**($k/2)*Gamma($k / 2))) : 0 }

sub gamma_cdf($k,$x) { $x**$k * exp(-$x) * sum map { $x** $_ / Gamma($k+$_+1) } 0..100 }

sub cdf_chi2($x,$k) { ($x <= 0 or $k <= 0) ? 0.0 : gamma_cdf($k / 2, $x / 2) }

print 'x χ² ';

print "k = $_" . ' 'x13 for 1..5;

say "\n" . '-' x (my $width = 93);

for my $x (0..10) {

printf '%2d', $x;

printf ' %.' . (int(($width-2)/5)-4) . 'f', chi2($x, $_) for 1..5;

say '';

}

say "\nχ² x cdf for χ² P value (df=3)\n" . '-' x 36;

for my $p (map { 2**$_ } 0..5) {

my $cdf = cdf_chi2($p, 3);

printf "%2d %-.10f %-.10f\n", $p, $cdf, 1-$cdf;

}

my @airport = <77 23 88 12 79 21 81 19>;

my @expected = split ' ', '81.25 18.75 ' x 4;

my $dtotal;

$dtotal += ($airport[$_] - $expected[$_])**2 / $expected[$_] for 0..$#airport;

printf "\nFor the airport data, diff total is %.5f, χ² is %.5f, p value %.5f\n", $dtotal, chi2($dtotal, 3), cdf_chi2($dtotal, 3);</syntaxhighlight>

{{out}}

<pre>x χ² k = 1 k = 2 k = 3 k = 4 k = 5

---------------------------------------------------------------------------------------------

0 0.00000000000000 0.00000000000000 0.00000000000000 0.00000000000000 0.00000000000000

1 0.24197072451914 0.30326532985632 0.24197072451914 0.15163266492816 0.08065690817305

2 0.10377687435515 0.18393972058572 0.20755374871030 0.18393972058572 0.13836916580686

3 0.05139344326792 0.11156508007421 0.15418032980377 0.16734762011132 0.15418032980377

4 0.02699548325659 0.06766764161831 0.10798193302638 0.13533528323661 0.14397591070183

5 0.01464498256193 0.04104249931195 0.07322491280963 0.10260624827987 0.12204152134939

6 0.00810869555494 0.02489353418393 0.04865217332964 0.07468060255180 0.09730434665928

7 0.00455334292164 0.01509869171116 0.03187340045148 0.05284542098906 0.07437126772012

8 0.00258337316926 0.00915781944437 0.02066698535409 0.03663127777747 0.05511196094425

9 0.00147728280398 0.00555449826912 0.01329554523581 0.02499524221105 0.03988663570744

10 0.00085003666025 0.00336897349954 0.00850036660252 0.01684486749771 0.02833455534173

χ² x cdf for χ² P value (df=3)

------------------------------------

1 0.1987480431 0.8012519569

2 0.4275932955 0.5724067045

4 0.7385358701 0.2614641299

8 0.9539882943 0.0460117057

16 0.9988660157 0.0011339843

32 0.9999994767 0.0000005233

For the airport data, diff total is 4.51282, χ² is 0.08875, p value 0.78885</pre>