June 2018 Update

2018-06-22 20:57:24 +00:00 · 2018-06-22 20:57:24 +00:00 · 22f33d4004
commit 22f33d4004
parent ba8067c3b7
5278 changed files with 84726 additions and 14379 deletions
--- a/Task/Verify-distribution-uniformity-Chi-squared-test/Kotlin/verify-distribution-uniformity-chi-squared-test.kotlin
+++ b/Task/Verify-distribution-uniformity-Chi-squared-test/Kotlin/verify-distribution-uniformity-chi-squared-test.kotlin
@ -0,0 +1,77 @@
+// version 1.1.51
+
+typealias Func = (Double) -> Double
+
+fun gammaLanczos(x: Double): Double {
+    var xx = x
+    val p = doubleArrayOf(
+        0.99999999999980993,
+      676.5203681218851,
+    -1259.1392167224028,
+      771.32342877765313,
+     -176.61502916214059,
+       12.507343278686905,
+       -0.13857109526572012,
+        9.9843695780195716e-6,
+        1.5056327351493116e-7
+    )
+    val g = 7
+    if (xx < 0.5) return Math.PI / (Math.sin(Math.PI * xx) * gammaLanczos(1.0 - xx))
+    xx--
+    var a = p[0]
+    val t = xx + g + 0.5
+    for (i in 1 until p.size) a += p[i] / (xx + i)
+    return Math.sqrt(2.0 * Math.PI) * Math.pow(t, xx + 0.5) * Math.exp(-t) * a
+}
+
+fun integrate(a: Double, b: Double, n: Int, f: Func): Double {
+    val h = (b - a) / n
+    var sum = 0.0
+    for (i in 0 until n) {
+        val x = a + i * h
+        sum += (f(x) + 4.0 * f(x + h / 2.0) + f(x + h)) / 6.0
+    }
+    return sum * h
+}
+
+fun gammaIncompleteQ(a: Double, x: Double): Double {
+    val aa1 = a - 1.0
+    fun f0(t: Double) = Math.pow(t, aa1) * Math.exp(-t)
+    val h = 1.5e-2
+    var y = aa1
+    while ((f0(y) * (x - y) > 2.0e-8) && y < x) y += 0.4
+    if (y > x) y = x
+    return 1.0 - integrate(0.0, y, (y / h).toInt(), ::f0) / gammaLanczos(a)
+}
+
+fun chi2UniformDistance(ds: DoubleArray): Double {
+    val expected = ds.average()
+    val sum = ds.map { val x = it - expected; x * x }.sum()
+    return sum / expected
+}
+
+fun chi2Probability(dof: Int, distance: Double) =
+    gammaIncompleteQ(0.5 * dof, 0.5 * distance)
+
+fun chiIsUniform(ds: DoubleArray, significance: Double):Boolean {
+    val dof = ds.size - 1
+    val dist = chi2UniformDistance(ds)
+    return chi2Probability(dof, dist) > significance
+}
+
+fun main(args: Array<String>) {
+    val dsets = listOf(
+        doubleArrayOf(199809.0, 200665.0, 199607.0, 200270.0, 199649.0),
+        doubleArrayOf(522573.0, 244456.0, 139979.0,  71531.0,  21461.0)
+    )
+    for (ds in dsets) {
+        println("Dataset: ${ds.asList()}")
+        val dist = chi2UniformDistance(ds)
+        val dof = ds.size - 1
+        print("DOF: $dof  Distance: ${"%.4f".format(dist)}")
+        val prob = chi2Probability(dof, dist)
+        print("  Probability: ${"%.6f".format(prob)}")
+        val uniform = if (chiIsUniform(ds, 0.05)) "Yes" else "No"
+        println("  Uniform? $uniform\n")
+    }
+}