public static ContinuousDistribution ConvolutionOfUniformAndUniform(ContinuousDistribution pdfX, ContinuousDistribution pdfY)
{
var unif1 = (UniformContinuousDistribution)pdfX.BaseDistribution;
var unif2 = (UniformContinuousDistribution)pdfY.BaseDistribution;
double a1 = (unif1.Support.Min * pdfX.Coefficient) + pdfX.Offset;
double b1 = (unif1.Support.Max * pdfX.Coefficient) + pdfX.Offset;
if (a1 > b1)
{
double t = a1;
a1 = b1;
b1 = t;
}
double a2 = (unif2.Support.Min * pdfY.Coefficient) + pdfY.Offset;
double b2 = (unif2.Support.Max * pdfY.Coefficient) + pdfY.Offset;
if (a2 > b2)
{
double t = a2;
a2 = b2;
b2 = t;
}
double a = a1 + a2;
double b = b1 + b2;
double l1 = Math.Abs((b1 - a1) - (b2 - a2)) / 2d;
double l2 = (b - a) / 2d;
return(new ContinuousDistribution(new IsoscelesTrapezoidalDistribution(a, b, l2 - l1), pdfX.Samples));
}
public BivariateTDistribution(double mean1, double mean2, double sigma1, double sigma2, double rho, double degreesOfFreedom, int samples)
: base(mean1, mean2, sigma1, sigma2, rho, samples)
{
if (degreesOfFreedom < 1)
{
throw new DistributionsArgumentException(DistributionsArgumentExceptionType.DegreesOfFreedomMustNotBeLessThenOne);
}
DegressOfFreedom = degreesOfFreedom;
ContinuousDistribution left = new ContinuousDistribution(new StudentGeneralizedDistribution(mean1, sigma1, degreesOfFreedom), samples);
ContinuousDistribution right = new ContinuousDistribution(new StudentGeneralizedDistribution(mean2, sigma2, degreesOfFreedom), samples);
supportMinLeft = left.MinX;
supportMaxLeft = left.MaxX;
supportMinRight = right.MinX;
supportMaxRight = right.MaxX;
k = 1d / (2d * Math.PI * sigma1 * sigma2 * Math.Sqrt(1 - Math.Pow(rho, 2)));
d = degreesOfFreedom * (1d - Math.Pow(rho, 2));
p = -(degreesOfFreedom + 2d) / 2d;
vInv1 = 1d / Variance1;
vInv2 = 1d / Variance2;
sProdInv = 1d / (Sigma1 * Sigma2);
}
private static PrivateCoordinates DiscretizeContinious(ContinuousDistribution continiousDistribution, int samples)
{
if (samples < 2)
{
throw new DistributionsArgumentException(DistributionsArgumentExceptionType.SamplesNumberMustBeGreaterThenTwo);
}
if (continiousDistribution == null)
{
throw new ArgumentNullException(nameof(continiousDistribution));
}
double[] xAxis = CommonRandomMath.GenerateXAxis(continiousDistribution.InnerMinX, continiousDistribution.InnerMaxX, samples, out _);
double[] pdf = new double[samples];
for (int i = 0; i < samples; i++)
{
double x = xAxis[i];
pdf[i] = continiousDistribution.InnerGetPDFYbyX(x);
}
return(new PrivateCoordinates {
XCoordinates = xAxis, PDFCoordinates = pdf, FromContinuous = true
});
}
public static ContinuousDistribution ConvolutionOfStudentAndUniform(ContinuousDistribution pdfX, ContinuousDistribution pdfY)
{
var student = (StudentGeneralizedDistribution)pdfX.BaseDistribution;
var unif = (UniformContinuousDistribution)pdfY.BaseDistribution;
double a = (unif.Support.Min * pdfY.Coefficient) + pdfY.Offset;
double b = (unif.Support.Max * pdfY.Coefficient) + pdfY.Offset;
var s = Math.Abs(student.ScaleCoefficient * pdfX.Coefficient);
var m = (student.Mean * pdfX.Coefficient) + pdfX.Offset;
return(new ContinuousDistribution(new StudentUniformDistribution(a, b, m, s, student.DegreesOfFreedom), pdfX.Samples));
}
public static ContinuousDistribution ConvolutionOfNormalAndUniform(ContinuousDistribution pdfX, ContinuousDistribution pdfY)
{
var norm = (NormalDistribution)pdfX.BaseDistribution;
var unif = (UniformContinuousDistribution)pdfY.BaseDistribution;
double a = (unif.Support.Min * pdfY.Coefficient) + pdfY.Offset;
double b = (unif.Support.Max * pdfY.Coefficient) + pdfY.Offset;
var s = Math.Abs(norm.StandardDeviation * pdfX.Coefficient);
var m = (norm.Mean * pdfX.Coefficient) + pdfX.Offset;
return(new ContinuousDistribution(new BhattacharjeeDistribution(a, b, m, s), pdfX.Samples));
}
public static ContinuousDistribution ConvolutionOfNormalAndNormal(ContinuousDistribution pdfX, ContinuousDistribution pdfY)
{
var norm1 = (NormalDistribution)pdfX.BaseDistribution;
var norm2 = (NormalDistribution)pdfY.BaseDistribution;
var v1 = norm1.Variance * Math.Pow(pdfX.Coefficient, 2);
var m1 = (norm1.Mean * pdfX.Coefficient) + pdfX.Offset;
var v2 = norm2.Variance * Math.Pow(pdfY.Coefficient, 2);
var m2 = (norm2.Mean * pdfY.Coefficient) + pdfY.Offset;
var newDistribution = new ContinuousDistribution(new NormalDistribution(m1 + m2, Math.Sqrt(v1 + v2)), pdfX.Samples);
return(newDistribution);
}
public BivariateNormalDistribution(double mean1, double mean2, double sigma1, double sigma2, double rho, int samples)
: base(mean1, mean2, sigma1, sigma2, rho, samples)
{
ContinuousDistribution left = new ContinuousDistribution(new NormalDistribution(Mean1, Sigma1), samples);
ContinuousDistribution right = new ContinuousDistribution(new NormalDistribution(Mean2, Sigma2), samples);
supportMinLeft = left.MinX;
supportMaxLeft = left.MaxX;
supportMinRight = right.MinX;
supportMaxRight = right.MaxX;
k = 1d / (2d * Math.PI * sigma1 * sigma2 * Math.Sqrt(1 - Math.Pow(rho, 2)));
e = -1d / (2d * (1 - Math.Pow(rho, 2)));
vInv1 = 1d / Variance1;
vInv2 = 1d / Variance2;
sProdInv = 1d / (Sigma1 * Sigma2);
}
public static ContinuousDistribution ConvolutionOfNormalAndBhattacharjee(ContinuousDistribution pdfX, ContinuousDistribution pdfY)
{
var norm = (NormalDistribution)pdfX.BaseDistribution;
var bhat = (BhattacharjeeDistribution)pdfY.BaseDistribution;
var v1 = norm.Variance * Math.Pow(pdfX.Coefficient, 2);
var m1 = (norm.Mean * pdfX.Coefficient) + pdfX.Offset;
var v2 = Math.Pow(bhat.NormalSigma * pdfY.Coefficient, 2);
var m2 = (bhat.NormalMean * pdfY.Coefficient) + pdfY.Offset;
var a = bhat.UniformMin * pdfY.Coefficient;
var b = bhat.UniformMax * pdfY.Coefficient;
var s = Math.Sqrt(v1 + v2);
var m = m1 + m2;
return(new ContinuousDistribution(new BhattacharjeeDistribution(a, b, m, s), pdfX.Samples));
}
/// <summary>
/// Initializes a new instance of the <see cref="DiscreteDistribution"/> class
/// by <paramref name="continiousDistribution"/> by sampling with <paramref name="samples"/> count.
/// </summary>
/// <param name="continiousDistribution">Sampled <see cref="ContinuousDistribution"/>.</param>
/// <param name="samples">Samples count.</param>
public DiscreteDistribution(ContinuousDistribution continiousDistribution, int samples)
: this(DiscretizeContinious(continiousDistribution, samples))
{
}
/// <summary>
/// Initializes a new instance of the <see cref="DiscreteDistribution"/> class
/// by <paramref name="continiousDistribution"/> by sampling.
/// </summary>
/// <param name="continiousDistribution">Sampled <see cref="ContinuousDistribution"/>.</param>
public DiscreteDistribution(ContinuousDistribution continiousDistribution)
: this(continiousDistribution, continiousDistribution.InnerSamples)
{
}
public static ContinuousDistribution Negate(ContinuousDistribution value)
{
return(Multiply(value, -1));
}
public static ContinuousDistribution Divide(ContinuousDistribution pdf, double value)
{
return(new ContinuousDistribution(pdf.BaseDistribution, pdf.Samples, pdf.Coefficient / value, pdf.Offset / value));
}
public static ContinuousDistribution Sub(double value, ContinuousDistribution pdf)
{
return(new ContinuousDistribution(pdf.BaseDistribution, pdf.Samples, -pdf.Coefficient, pdf.Offset + value));
}
