// My original:
//public static double VWithinMargin(double teamPerformanceDifference, double drawMargin)
//{
// var teamPerformanceDifferenceAbsoluteValue = Math.Abs(teamPerformanceDifference);
// return (GaussianDistribution.At(-drawMargin - teamPerformanceDifferenceAbsoluteValue) - GaussianDistribution.At(drawMargin - teamPerformanceDifferenceAbsoluteValue))
// /
// (GaussianDistribution.CumulativeTo(drawMargin - teamPerformanceDifferenceAbsoluteValue) - GaussianDistribution.CumulativeTo(-drawMargin - teamPerformanceDifferenceAbsoluteValue));
//}
// from F#:
public static double VWithinMargin(double teamPerformanceDifference, double drawMargin)
{
double teamPerformanceDifferenceAbsoluteValue = Math.Abs(teamPerformanceDifference);
double denominator =
GaussianDistribution.CumulativeTo(drawMargin - teamPerformanceDifferenceAbsoluteValue) -
GaussianDistribution.CumulativeTo(-drawMargin - teamPerformanceDifferenceAbsoluteValue);
if (denominator < 2.222758749e-162)
{
if (teamPerformanceDifference < 0.0)
{
return(-teamPerformanceDifference - drawMargin);
}
return(-teamPerformanceDifference + drawMargin);
}
double numerator = GaussianDistribution.At(-drawMargin - teamPerformanceDifferenceAbsoluteValue) -
GaussianDistribution.At(drawMargin - teamPerformanceDifferenceAbsoluteValue);
if (teamPerformanceDifference < 0.0)
{
return(-numerator / denominator);
}
return(numerator / denominator);
}
public void TestGaussianInt()
{
Statistics.Frequencies(
new[]
{
// 0
(float)GaussianDistribution.At(0, 5, 3) + (float)GaussianDistribution.At(-1, 5, 3) + (float)GaussianDistribution.At(-2, 5, 3),
// 1
(float)GaussianDistribution.At(1, 5, 3),
// 2
(float)GaussianDistribution.At(2, 5, 3),
// 3
(float)GaussianDistribution.At(3, 5, 3),
// 4
(float)GaussianDistribution.At(4, 5, 3),
// 5
(float)GaussianDistribution.At(5, 5, 3),
// 6
(float)GaussianDistribution.At(6, 5, 3),
// 7
(float)GaussianDistribution.At(7, 5, 3),
// 8
(float)GaussianDistribution.At(8, 5, 3),
// 9
(float)GaussianDistribution.At(9, 5, 3),
// 10
(float)GaussianDistribution.At(10, 5, 3) + (float)GaussianDistribution.At(11, 5, 3) + (float)GaussianDistribution.At(12, 5, 3)
},
() => Rng.GaussianInt(5, 5, 3));
Statistics.Frequencies(
new[]
{
0,
(float)GaussianDistribution.At(1, 10, 3),
(float)GaussianDistribution.At(2, 10, 3),
(float)GaussianDistribution.At(3, 10, 3),
(float)GaussianDistribution.At(4, 10, 3),
(float)GaussianDistribution.At(5, 10, 3),
(float)GaussianDistribution.At(6, 10, 3),
(float)GaussianDistribution.At(7, 10, 3),
(float)GaussianDistribution.At(8, 10, 3),
(float)GaussianDistribution.At(9, 10, 3),
(float)GaussianDistribution.At(10, 10, 3),
(float)GaussianDistribution.At(11, 10, 3),
(float)GaussianDistribution.At(12, 10, 3),
(float)GaussianDistribution.At(13, 10, 3),
(float)GaussianDistribution.At(14, 10, 3),
(float)GaussianDistribution.At(15, 10, 3),
(float)GaussianDistribution.At(16, 10, 3),
(float)GaussianDistribution.At(17, 10, 3),
(float)GaussianDistribution.At(18, 10, 3),
(float)GaussianDistribution.At(19, 10, 3)
},
() => Rng.GaussianInt(10, 9, 3));
}
private double VExceedsMargin(double drawMargin, double performanceDiff)
{
var denominator = GaussianDistribution.CumulativeTo(performanceDiff - drawMargin);
if (denominator < 2.222758749e-162)
{
return(-performanceDiff + drawMargin);
}
return(GaussianDistribution.At(performanceDiff - drawMargin) / denominator);
}
public static double VExceedsMargin(double teamPerformanceDifference, double drawMargin)
{
double denominator = GaussianDistribution.CumulativeTo(teamPerformanceDifference - drawMargin);
if (denominator < 2.222758749e-162)
{
return(-teamPerformanceDifference + drawMargin);
}
return(GaussianDistribution.At(teamPerformanceDifference - drawMargin) / denominator);
}
private double VWithinMargin(double drawMargin, double performanceDiff)
{
var performanceDiffAbsoluteValue = Math.Abs(performanceDiff);
var denominator = GaussianDistribution.CumulativeTo(drawMargin - performanceDiffAbsoluteValue) - GaussianDistribution.CumulativeTo(-drawMargin - performanceDiffAbsoluteValue);
if (denominator < 2.222758749e-162)
{
return(performanceDiff < 0 ? -performanceDiff - drawMargin : -performanceDiff + drawMargin);
}
var numerator = GaussianDistribution.At(-drawMargin - performanceDiffAbsoluteValue) - GaussianDistribution.At(drawMargin - performanceDiffAbsoluteValue);
return(performanceDiff < 0 ? -numerator / denominator : numerator / denominator);
}
private double WWithinMargin(double drawMargin, double performanceDiff)
{
var performanceDiffAbsoluteValue = Math.Abs(performanceDiff);
var denominator = GaussianDistribution.CumulativeTo(drawMargin - performanceDiffAbsoluteValue) - GaussianDistribution.CumulativeTo(-drawMargin - performanceDiffAbsoluteValue);
if (denominator < 2.222758749e-162)
{
return(1);
}
var vt = VWithinMargin(drawMargin, performanceDiff);
// Separating large return math shown in original work for readability
var factor1 = drawMargin - performanceDiffAbsoluteValue;
var factor2 = GaussianDistribution.At(drawMargin - performanceDiffAbsoluteValue);
var factor3 = -drawMargin - performanceDiffAbsoluteValue;
var factor4 = GaussianDistribution.At(-drawMargin - performanceDiffAbsoluteValue);
var numerator = (factor1 * factor2) - (factor3 * factor4);
return((vt * vt) + (numerator / denominator));
}
// My original:
//public static double WWithinMargin(double teamPerformanceDifference, double drawMargin)
//{
// var teamPerformanceDifferenceAbsoluteValue = Math.Abs(teamPerformanceDifference);
// var vDraw = VWithinMargin(teamPerformanceDifferenceAbsoluteValue, drawMargin);
// return (vDraw * vDraw)
// +
// (
// ((drawMargin - teamPerformanceDifferenceAbsoluteValue) * GaussianDistribution.At(drawMargin - teamPerformanceDifferenceAbsoluteValue) + (drawMargin + teamPerformanceDifferenceAbsoluteValue) * GaussianDistribution.At(drawMargin + teamPerformanceDifferenceAbsoluteValue))
// /
// (GaussianDistribution.CumulativeTo(drawMargin - teamPerformanceDifferenceAbsoluteValue) - GaussianDistribution.CumulativeTo(-drawMargin - teamPerformanceDifferenceAbsoluteValue))
// );
//}
// From F#:
public static double WWithinMargin(double teamPerformanceDifference, double drawMargin)
{
double teamPerformanceDifferenceAbsoluteValue = Math.Abs(teamPerformanceDifference);
double denominator = GaussianDistribution.CumulativeTo(drawMargin - teamPerformanceDifferenceAbsoluteValue)
-
GaussianDistribution.CumulativeTo(-drawMargin - teamPerformanceDifferenceAbsoluteValue);
if (denominator < 2.222758749e-162)
{
return(1.0);
}
double vt = VWithinMargin(teamPerformanceDifferenceAbsoluteValue, drawMargin);
return(vt * vt +
(
(drawMargin - teamPerformanceDifferenceAbsoluteValue)
*
GaussianDistribution.At(
drawMargin - teamPerformanceDifferenceAbsoluteValue)
- (-drawMargin - teamPerformanceDifferenceAbsoluteValue)
*
GaussianDistribution.At(-drawMargin - teamPerformanceDifferenceAbsoluteValue)) / denominator);
}
public void AtTests()
{
// Verified with WolframAlpha
// (e.g. http://www.wolframalpha.com/input/?i=PDF%5BNormalDistribution%5B0%2C1%5D%2C+0.5%5D )
Assert.AreEqual(0.352065, GaussianDistribution.At(0.5), ErrorTolerance);
}
public void AtTests()
{
Assert.AreEqual(0.352065, GaussianDistribution.At(0.5), ErrorTolerance);
}