Verify distribution uniformity/Chi-squared test: Difference between revisions
Verify distribution uniformity/Chi-squared test (view source)
Revision as of 17:19, 10 September 2019
, 4 years agoAdded Sidef
(Scala contribution added.) |
(Added Sidef) |
||
Line 1,409:
}
}</lang>
=={{header|Sidef}}==
<lang ruby># Confluent hypergeometric function of the first kind F_1(a;b;z)
func F1(a, b, z, limit=100) {
sum(0..limit, {|k|
rising_factorial(a, k) / rising_factorial(b, k) * z**k / k!
})
}
func γ(a,x) { # lower incomplete gamma function γ(a,x)
#a**(-1) * x**a * F1(a, a+1, -x) # simpler formula
a**(-1) * x**a * exp(-x) * F1(1, a+1, x) # slightly better convergence
}
func P(a,z) { # regularized gamma function P(a,z)
γ(a,z) / Γ(a)
}
func chi_squared_cdf (k, x) {
var f = (k<20 ? 20 : 10)
given(x) {
when (0) { 0 }
case (. < (k + f*sqrt(k))) { P(k/2, x/2) }
else { 1 }
}
}
func chi_squared_test(arr, significance = 0.05) {
var n = arr.len
var N = arr.sum
var expected = N/n
var χ_squared = arr.sum_by {|v| (v-expected)**2 / expected }
var p_value = (1 - chi_squared_cdf(n-1, χ_squared))
[χ_squared, p_value, p_value > significance]
}
[
%n< 199809 200665 199607 200270 199649 >,
%n< 522573 244456 139979 71531 21461 >,
].each {|dataset|
var r = chi_squared_test(dataset)
say "data: #{dataset}"
say "χ² = #{r[0]}, p-value = #{r[1].round(-4)}, uniform = #{r[2]}\n"
}</lang>
{{out}}
<pre>
data: [199809, 200665, 199607, 200270, 199649]
χ² = 4.14628, p-value = 0.3866, uniform = true
data: [522573, 244456, 139979, 71531, 21461]
χ² = 790063.27594, p-value = 0, uniform = false
</pre>
=={{header|Tcl}}==
{{works with|Tcl|8.5}}
| |||