Benford's law: Difference between revisions
Add MATLAB implementation
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8 0.053 0.0511525
9 0.045 0.0457575</pre>
=={{header|MATLAB}}==
{{trans|Julia}}
<syntaxhighlight lang="MATLAB">
benfords_law();
function benfords_law
% Benford's Law
P = @(d) log10(1 + 1./d);
% Benford function
function counts = benford(numbers)
firstdigit = @(n) floor(mod(n / 10^floor(log10(n)), 10));
counts = zeros(1, 9);
for i = 1:length(numbers)
digit = firstdigit(numbers(i));
if digit ~= 0
counts(digit) = counts(digit) + 1;
end
end
counts = counts ./ sum(counts);
end
% Generate Fibonacci numbers
function fibNums = fibonacci(n)
fibNums = zeros(1, n);
a = 0;
b = 1;
for i = 1:n
c = b;
b = a + b;
a = c;
fibNums(i) = b;
end
end
% Sample
sample = fibonacci(1000);
% Observed and expected frequencies
observed = benford(sample) * 100;
expected = arrayfun(P, 1:9) * 100;
% Table
mytable = [1:9; observed; expected]';
% Plotting
bar(1:9, observed);
hold on;
plot(1:9, expected, 'LineWidth', 2);
hold off;
title("Benford's Law");
xlabel("First Digit");
ylabel("Frequency %");
legend("1000 Fibonacci Numbers", "P(d) = log10(1 + 1/d)");
xticks(1:9);
% Displaying the results
fprintf("Benford's Law\nFrequency of first digit\nin 1000 Fibonacci numbers\n");
disp(table(mytable(:,1),mytable(:,2),mytable(:,3),'VariableNames',{'digit', 'observed(%)', 'expected(%)'}))
end
</syntaxhighlight>
{{out}}
<pre>
Benford's Law
Frequency of first digit
in 1000 Fibonacci numbers
digit observed(%) expected(%)
_____ ___________ ___________
1 30 30.103
2 17.7 17.609
3 12.5 12.494
4 9.6 9.691
5 8 7.9181
6 6.7 6.6947
7 5.7 5.7992
8 5.3 5.1153
9 4.5 4.5757
</pre>
=={{header|NetRexx}}==
<syntaxhighlight lang="netrexx">/* NetRexx */
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