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Verify distribution uniformity/Chi-squared test: Difference between revisions
Verify distribution uniformity/Chi-squared test (view source)
Revision as of 16:49, 14 April 2016
, 8 years agoAdded Elixir
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More information about the <math>\chi^2</math> distribution may be found at
[http://mathworld.wolfram.com/Chi-SquaredDistribution.html mathworld].
=={{header|Ada}}==
First, we specifay a simple package to compute the Chi-Square Distance from the uniform distribution:
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$ ./Test_Chi_Square 522573 244456 139979 71531 21461
Degrees of Freedom: 4, Distance: 790063.28; (deviates significantly from uniform)</pre>
=={{header|C}}==
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4 4.146 0.38657083 YES [199809, 200665, 199607, 200270, 199649]
4 790063.276 0.00000000 NO [522573, 244456, 139979, 71531, 21461]</pre>
=={{header|Elixir}}==
{{trans|Ruby}}
<lang elixir>defmodule Verify do
defp gammaInc_Q(a, x) do
a1 = a-1
f0 = fn t -> :math.pow(t, a1) * :math.exp(-t) end
df0 = fn t -> (a1-t) * :math.pow(t, a-2) * :math.exp(-t) end
y = while_loop(f0, x, a1)
n = trunc(y / 3.0e-4)
h = y / n
hh = 0.5 * h
sum = Enum.reduce(n-1 .. 0, 0, fn j,sum ->
t = h * j
sum + f0.(t) + hh * df0.(t)
end)
h * sum / gamma_spounge(a, make_coef)
end
defp while_loop(f, x, y) do
if f.(y)*(x-y) > 2.0e-8 and y < x, do: while_loop(f, x, y+0.3), else: min(x, y)
end
@a 12
defp make_coef do
coef0 = [:math.sqrt(2.0 * :math.pi)]
{_, coef} = Enum.reduce(1..@a-1, {1.0, coef0}, fn k,{k1_factrl,c} ->
h = :math.exp(@a-k) * :math.pow(@a-k, k-0.5) / k1_factrl
{-k1_factrl*k, [h | c]}
end)
Enum.reverse(coef) |> List.to_tuple
end
defp gamma_spounge(z, coef) do
accm = Enum.reduce(1..@a-1, elem(coef,0), fn k,res -> res + elem(coef,k) / (z+k) end)
accm * :math.exp(-(z+@a)) * :math.pow(z+@a, z+0.5) / z
end
def chi2UniformDistance(dataSet) do
expected = Enum.sum(dataSet) / length(dataSet)
Enum.reduce(dataSet, 0, fn d,sum -> sum + (d-expected)*(d-expected) end) / expected
end
def chi2Probability(dof, distance) do
1.0 - gammaInc_Q(0.5*dof, 0.5*distance)
end
def chi2IsUniform(dataSet, significance\\0.05) do
dof = length(dataSet) - 1
dist = chi2UniformDistance(dataSet)
chi2Probability(dof, dist) > significance
end
end
dsets = [ [ 199809, 200665, 199607, 200270, 199649 ],
[ 522573, 244456, 139979, 71531, 21461 ] ]
Enum.each(dsets, fn ds ->
IO.puts "Data set:#{inspect ds}"
dof = length(ds) - 1
IO.puts " degrees of freedom: #{dof}"
distance = Verify.chi2UniformDistance(ds)
:io.fwrite " distance: ~.4f~n", [distance]
:io.fwrite " probability: ~.4f~n", [Verify.chi2Probability(dof, distance)]
:io.fwrite " uniform? ~s~n", [(if Verify.chi2IsUniform(ds), do: "Yes", else: "No")]
end)</lang>
{{out}}
<pre>
Data set:[199809, 200665, 199607, 200270, 199649]
degrees of freedom: 4
distance: 4.1463
probability: 0.3866
uniform? Yes
Data set:[522573, 244456, 139979, 71531, 21461]
degrees of freedom: 4
distance: 790063.2759
probability: -0.0000
uniform? No
</pre>
=={{header|Fortran}}==
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end program ChiTest</lang>
=={{header|Go}}==
{{trans|C}}
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4 isUniform 4 4 4 5 5 5 5 5 5 5 NB. not uniform if 4 categories possible
0</lang>
=={{header|Java}}==
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