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Verify distribution uniformity/Chi-squared test: Difference between revisions
Verify distribution uniformity/Chi-squared test (view source)
Revision as of 19:37, 29 April 2021
, 3 years ago→{{header|Nim}}
(Add Rust implementation) |
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Line 781:
<lang Mathematica>{discreteUniformDistributionQ[uniformData],discreteUniformDistributionQ[nonUniformData]}</lang>
{{out}}<pre>{True,False}</pre>
=={{header|Nim}}==
{{trans|Go}}
We use the gamma function from the “math” module. To simplify the code, we use also the “lenientops” module which provides mixed operations between floats ane integers.
<lang Nim>import lenientops, math, stats, strformat, sugar
func simpson38(f: (float) -> float; a, b: float; n: int): float =
let h = (b - a) / n
let h1 = h / 3
var sum = f(a) + f(b)
for i in countdown(3 * n - 1, 1):
if i mod 3 == 0:
sum += 2 * f(a + h1 * i)
else:
sum += 3 * f(a + h1 * i)
result = h * sum / 8
func gammaIncQ(a, x: float): float =
let aa1 = a - 1
func f(t: float): float = pow(t, aa1) * exp(-t)
var y = aa1
let h = 1.5e-2
while f(y) * (x - y) > 2e-8 and y < x:
y += 0.4
if y > x: y = x
result = 1 - simpson38(f, 0, y, (y / h / gamma(a)).toInt)
func chi2ud(ds: openArray[int]): float =
let expected = mean(ds)
var s = 0.0
for d in ds:
let x = d.toFloat - expected
s += x * x
result = s / expected
func chi2p(dof: int; distance: float): float =
gammaIncQ(0.5 * dof, 0.5 * distance)
const SigLevel = 0.05
proc utest(dset: openArray[int]) =
echo "Uniform distribution test"
let s = sum(dset)
echo " dataset:", dset
echo " samples: ", s
echo " categories: ", dset.len
let dof = dset.len - 1
echo " degrees of freedom: ", dof
let dist = chi2ud(dset)
echo " chi square test statistic: ", dist
let p = chi2p(dof, dist)
echo " p-value of test statistic: ", p
let sig = p < SigLevel
echo &" significant at {int(SigLevel * 100)}% level? {sig}"
echo &" uniform? {not sig}\n"
for dset in [[199809, 200665, 199607, 200270, 199649],
[522573, 244456, 139979, 71531, 21461]]:
utest(dset)</lang>
{{out}}
<pre>Uniform distribution test
dataset:[199809, 200665, 199607, 200270, 199649]
samples: 1000000
categories: 5
degrees of freedom: 4
chi square test statistic: 4.14628
p-value of test statistic: 0.3865708330827673
significant at 5% level? false
uniform? true
Uniform distribution test
dataset:[522573, 244456, 139979, 71531, 21461]
samples: 1000000
categories: 5
degrees of freedom: 4
chi square test statistic: 790063.27594
p-value of test statistic: 2.34864350190378e-11
significant at 5% level? true
uniform? false</pre>
=={{header|OCaml}}==
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