public static double TestImpl(double[][] data, out double statistic, double s0, out double pvalS0, out double[] gmeans)
{
List <int> v = new List <int>();
for (int i = 0; i < data.Length; i++)
{
if (data[i].Length > 1)
{
v.Add(i);
}
}
data = ArrayUtils.SubArray(data, v.ToArray());
int g = data.Length;
if (g < 2)
{
statistic = 0;
pvalS0 = 1;
gmeans = null;
return(1);
}
gmeans = new double[g];
double totMean = 0;
int n = 0;
for (int i = 0; i < g; i++)
{
gmeans[i] = ArrayUtils.Mean(data[i]);
totMean += gmeans[i] * data[i].Length;
n += data[i].Length;
}
totMean /= n;
double ssw = 0;
double ssb = 0;
for (int i = 0; i < g; i++)
{
ssb += data[i].Length * (gmeans[i] - totMean) * (gmeans[i] - totMean);
for (int j = 0; j < data[i].Length; j++)
{
ssw += (data[i][j] - gmeans[i]) * (data[i][j] - gmeans[i]);
}
}
if (ssw <= 0.0)
{
statistic = 0;
pvalS0 = 1;
return(1);
}
double dw = n - g;
double db = g - 1;
statistic = ssb * dw / db / ssw;
double gms = GetGeomMeanSquared(data);
double denom = n * db * ssw / dw / gms;
double statisticS0 = n * ssb / gms / (Math.Sqrt(denom) + s0) / (Math.Sqrt(denom) + s0);
pvalS0 = IncompleteBeta.Value(dw * 0.5, db * 0.5, dw / (dw + db * statisticS0));
return(IncompleteBeta.Value(dw * 0.5, db * 0.5, dw / (dw + db * statistic)));
}
public static double StudentDistributionInversed(int k, double p)
{
double z;
double rk = k;
if (p is > .25 and < .75)
{
if (Math.Abs(p - .5) < Eps)
{
return(0);
}
z = IncompleteBeta.IncompleteBetaInversed(.5, .5 * rk, Math.Abs(1 - 2 * p));
var t = Math.Sqrt(rk * z / (1 - z));
return(p < 0 ? -t : t);
}
var r_flg = -1;
if (p >= .5)
{
p = 1 - p;
r_flg = 1;
}
z = IncompleteBeta.IncompleteBetaInversed(.5 * rk, .5, 2 * p);
return(__MaxRealNumber * z < rk ? r_flg * __MaxRealNumber : r_flg *Math.Sqrt(rk / z - rk));
}
public static double StudentDistribution(int k, double t)
{
if (Math.Abs(t - 0) < Eps)
{
return(.5);
}
if (t < -2)
{
return(.5 * IncompleteBeta.IncompleteBetaValue(.5 * k, .5, k / (k + t * t)));
}
var x = t < 0 ? -t : t;
double rk = k;
var z = 1 + x * x / rk;
double tz;
double f;
double p;
int j;
if (k % 2 != 0)
{
var x_sqk = x / Math.Sqrt(rk);
p = Math.Atan(x_sqk);
if (k > 1)
{
f = 1;
tz = 1;
j = 3;
while (j <= k - 2 & tz / f > Eps)
{
tz *= (j - 1) / (z * j);
f += tz;
j += 2;
}
p += f * x_sqk / z;
}
p *= 2 / Consts.pi;
}
else
{
f = tz = 1;
j = 2;
while (j <= k - 2 & tz / f > Eps)
{
tz *= (j - 1) / (z * j);
f += tz;
j += 2;
}
p = f * x / Math.Sqrt(z * rk);
}
return(.5 + .5 * (t < 0 ? -p : p));
}
/*************************************************************************
* Student's t distribution
*
* Computes the integral from minus infinity to t of the Student
* t distribution with integer k > 0 degrees of freedom:
*
* t
* -
| |
| - | 2 -(k+1)/2
| ( (k+1)/2 ) | ( x )
| ---------------------- | ( 1 + --- ) dx
| - | ( k )
| sqrt( k pi ) | ( k/2 ) |
| |
| -
| -inf.
|
| Relation to incomplete beta integral:
|
| 1 - stdtr(k,t) = 0.5 * incbet( k/2, 1/2, z )
| where
| z = k/(k + t**2).
|
| For t < -2, this is the method of computation. For higher t,
| a direct method is derived from integration by parts.
| Since the function is symmetric about t=0, the area under the
| right tail of the density is found by calling the function
| with -t instead of t.
|
| ACCURACY:
|
| Tested at random 1 <= k <= 25. The "domain" refers to t.
| Relative error:
| arithmetic domain # trials peak rms
| IEEE -100,-2 50000 5.9e-15 1.4e-15
| IEEE -2,100 500000 2.7e-15 4.9e-17
|
| Cephes Math Library Release 2.8: June, 2000
| Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
*************************************************************************/
public static double Cumulative(int k, double t)
{
if (k <= 0)
{
throw new Exception("Negative value for k in Student's distribution");
}
if (t == 0)
{
return(0.5);
}
double rk;
double z;
if (t < -2.0)
{
rk = k;
z = rk / (rk + t * t);
return(0.5 * IncompleteBeta.Value(0.5 * rk, 0.5, z));
}
double x;
if (t < 0)
{
x = -t;
}
else
{
x = t;
}
rk = k;
z = 1.0 + x * x / rk;
double p;
if (k % 2 != 0)
{
double xsqk = x / Math.Sqrt(rk);
p = Math.Atan(xsqk);
if (k > 1)
{
double f = 1.0;
double tz = 1.0;
int j = 3;
while (j <= k - 2 & tz / f > epsilon)
{
tz = tz * ((j - 1) / (z * j));
f = f + tz;
j = j + 2;
}
p = p + f * xsqk / z;
}
p = p * 2.0 / Math.PI;
}
else
{
double f = 1.0;
double tz = 1.0;
int j = 2;
while (j <= k - 2 & tz / f > epsilon)
{
tz = tz * ((j - 1) / (z * j));
f = f + tz;
j = j + 2;
}
p = f * x / Math.Sqrt(z * rk);
}
if (t < 0)
{
p = -p;
}
return(0.5 + 0.5 * p);
}