public double GetPValue(BitArray input)
{
var pi = 0.0;
foreach (var bit in input)
{
if ((bool)bit)
{
pi++;
}
}
pi /= input.Length;
if (Math.Abs(pi - 0.5) >= 2.0 / Math.Sqrt(input.Length))
{
return(0.0);
}
var V = 1.0;
for (int k = 0; k < input.Length - 1; k++)
{
if (input[k] != input[k + 1])
{
V++;
}
}
var erfcArg = Math.Abs(V - 2 * input.Length * pi * (1 - pi)) / (2 * Math.Sqrt(2 * input.Length) * pi * (1 - pi));
var pValue = Special.Erfc(erfcArg);
return(pValue);
}
/// <summary>
/// Returns the value of the probability distribution function.
/// </summary>
/// <param name="x">Value</param>
/// <returns>float precision floating point number</returns>
public float Distribution(float x)
{
if (x < mu)
{
return(0);
}
return(Special.Erfc((float)Math.Sqrt(scale / (2 * (x - mu)))));
}
/// <summary>
/// Returns the value of the probability distribution function.
/// </summary>
/// <param name="x">Value</param>
/// <returns>float precision floating point number</returns>
public float Distribution(float x)
{
float a = (float)Math.Sqrt(x);
float b = (float)Math.Sqrt(1.0 / x);
float z = (a - b) / gamma;
// Normal cumulative distribution function
return(Special.Erfc(-z / 1.4142135623731f) * 0.5f);
}
/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <remarks>
/// <para>
/// The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.</para>
/// </remarks>
///
public override double DistributionFunction(double x)
{
double a = Math.Sqrt(x);
double b = Math.Sqrt(1.0 / x);
double z = (a - b) / shape;
// Normal cumulative distribution function
return(Special.Erfc(-z / Constants.Sqrt2) * 0.5);
}
/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <remarks>
/// The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.
/// </remarks>
///
/// <example>
/// See <see cref="InverseGaussianDistribution"/>.
/// </example>
///
protected internal override double InnerDistributionFunction(double x)
{
double sqrt = Math.Sqrt(lambda / x);
double a = 0.5 * Special.Erfc(sqrt * (mean - x) / (Constants.Sqrt2 * mean));
double b = 0.5 * Special.Erfc(sqrt * (mean + x) / (Constants.Sqrt2 * mean));
double c = Math.Exp((2.0 * lambda) / mean);
return(a + b * c);
}
/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <remarks>
/// The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.
/// </remarks>
///
public override double DistributionFunction(double x)
{
if (x < location)
{
return(0);
}
double cdf = Special.Erfc(Math.Sqrt(scale / (2 * (x - location))));
return(cdf);
}
/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <remarks>
/// <para>
/// The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.</para>
/// </remarks>
///
protected internal override double InnerDistributionFunction(double x)
{
double c = x - location;
double a = Math.Sqrt(c);
double b = Math.Sqrt(1.0 / c);
double z = (a - b) / shape;
// Normal cumulative distribution function
return(Special.Erfc(-z / Constants.Sqrt2) * 0.5);
}
/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// the this Log-Normal distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">
/// A single point in the distribution range.</param>
/// <remarks>
///
/// <para>
/// The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.</para>
///
/// <para>
/// The calculation is computed through the relationship to the error function
/// as <see cref="Accord.Math.Special.Erfc">erfc</see>(-z/sqrt(2)) / 2. See
/// [Weisstein] for more details.</para>
///
/// <para>
/// References:
/// <list type="bullet">
/// <item><description>
/// Weisstein, Eric W. "Normal Distribution Function." From MathWorld--A Wolfram Web
/// Resource. http://mathworld.wolfram.com/NormalDistributionFunction.html </description></item>
/// </list></para>
/// </remarks>
///
/// <example>
/// See <see cref="LognormalDistribution"/>.
/// </example>
///
public override double DistributionFunction(double x)
{
if (x <= 0)
{
return(0.0);
}
double z = (Math.Log(x) - location) / shape;
return(0.5 * Special.Erfc(-z / Constants.Sqrt2));
}
/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// the this Normal distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">
/// A single point in the distribution range.</param>
///
/// <remarks>
/// <para>
/// The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.</para>
/// <para>
/// The calculation is computed through the relationship to the error function
/// as <see cref="Accord.Math.Special.Erfc">erfc</see>(-z/sqrt(2)) / 2.</para>
///
/// <para>
/// References:
/// <list type="bullet">
/// <item><description>
/// Weisstein, Eric W. "Normal Distribution." From MathWorld--A Wolfram Web Resource.
/// Available on: http://mathworld.wolfram.com/NormalDistribution.html </description></item>
/// <item><description><a href="http://en.wikipedia.org/wiki/Normal_distribution#Cumulative_distribution_function">
/// Wikipedia, The Free Encyclopedia. Normal distribution. Available on:
/// http://en.wikipedia.org/wiki/Normal_distribution#Cumulative_distribution_function </a></description></item>
/// </list></para>
/// </remarks>
///
public override double DistributionFunction(double x)
{
double z = (x - mean) / stdDev;
return(Special.Erfc(-z / Special.Sqrt2) * 0.5);
/*
* // For a normal distribution with zero variance, the cdf is the Heaviside
* // step function (Wipedia, http://en.wikipedia.org/wiki/Normal_distribution)
* return (x >= mean) ? 1.0 : 0.0;
*/
}
/// <summary>
/// Returns the value of the probability density function.
/// </summary>
/// <param name="x">Value</param>
/// <returns>float precision floating point number</returns>
public float Function(float x)
{
float c = x - mu;
float a = (float)Math.Sqrt(c / beta);
float b = (float)Math.Sqrt(beta / c);
float alpha = (a + b) / (2 * gamma * c);
float z = (a - b) / gamma;
// Normal cumulative distribution function
return(alpha * Special.Erfc(-z / 1.4142135623731f) * 0.5f);
}
public double GetPValue(BitArray input)
{
var sum = 0.0;
foreach (var bit in input)
{
sum += (bool)bit ? 1 : -1;
}
var stat = Math.Abs(sum) / Math.Sqrt(input.Length);
var pValue = Special.Erfc(stat / Math.Sqrt(2));
return(pValue);
}
/// <summary>
/// Gets the probability density function (pdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <returns>
/// The probability of <c>x</c> occurring
/// in the current distribution.
/// </returns>
///
/// <remarks>
/// <para>
/// The Probability Density Function (PDF) describes the
/// probability that a given value <c>x</c> will occur.</para>
/// </remarks>
///
protected internal override double InnerProbabilityDensityFunction(double x)
{
double c = x - location;
double a = Math.Sqrt(c / scale);
double b = Math.Sqrt(scale / c);
double alpha = (a + b) / (2 * shape * c);
double z = (a - b) / shape;
// Normal cumulative distribution function
return(alpha * Special.Erfc(-z / Constants.Sqrt2) * 0.5);
}
public void InverseErfcTest()
{
for (int i = 0; i < 100; i++)
{
double expected = i / 100.0;
double erfc = Special.Erfc(expected);
double actual = Special.Ierfc(erfc);
Assert.AreEqual(expected, actual, 1e-15);
Assert.IsFalse(double.IsNaN(expected));
Assert.IsFalse(double.IsNaN(actual));
}
}
/// <summary>
/// Метод, считающий p-value на основе частоты встречаемости 1 и 0
/// </summary>
/// <param name="hash">Псевдослучайная последовательность</param>
/// <returns>p-value</returns>
public double getPValue(BitArray hash)
{
// сумма 1 и -1
double sum = 0;
foreach (bool v in hash)
{
sum += v ? 1 : -1;
}
var absoluteSum = Math.Abs(sum) / Math.Sqrt(hash.Length);
var pValue = Special.Erfc(absoluteSum / _rootOf2); // erfc - Complementary Error Function (дополнительная функция ошибок)
return(pValue);
}
/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <remarks>
/// The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.
/// </remarks>
///
/// <example>
/// See <see cref="InverseGaussianDistribution"/>.
/// </example>
///
public override double DistributionFunction(double x)
{
if (x < 0)
{
return(0);
}
double sqrt = Math.Sqrt(lambda / x);
double a = 0.5 * Special.Erfc(sqrt * (mean - x) / (Constants.Sqrt2 * mean));
double b = 0.5 * Special.Erfc(sqrt * (mean + x) / (Constants.Sqrt2 * mean));
double c = Math.Exp((2.0 * lambda) / mean);
return(a + b * c);
}
// ошибка в описании теста (2-6): (2) написано, что НЕ запускать тест, если
// сумма БОЛЬШЕ, чем значение в частотном тесте
// далее пишут пример, где показывают, что сумма меньше, и они говорят, что тест запускать не надо
/// <summary>
/// Метод, считающий p-value на основе количества непрерывных последовательностей одинаковых бит
/// </summary>
/// <param name="hash">Псевдослучайная последовательность</param>
/// <returns>p-value</returns>
public double getPValue(BitArray hash)
{
var hashLength = hash.Length;
double onesProportion = 0; // доля единиц
foreach (bool v in hash)
{
if (v)
{
onesProportion++;
}
}
onesProportion /= hashLength;
if (onesProportion - 0.5 > 2 / Math.Sqrt(hashLength))
{
return(0);
}
var numberOfHoles = 1;
for (int i = 0; i < hash.Length - 1; i++)
{
if (hash[i] ^ hash[i + 1]) // если биты не совпадают, то
{
numberOfHoles++;
}
}
// erfc - Complementary Error Function (дополнительная функция ошибок)
var pValue = Special.Erfc(Math.Abs(numberOfHoles - 2 * hashLength * onesProportion * (1 - onesProportion)) /
(2 * Math.Sqrt(2 * hashLength) * onesProportion * (1 - onesProportion)));
return(pValue);
}
/// <summary>
/// The Probit mean (activation) function.
/// </summary>
///
/// <param name="x">A transformed value.</param>
///
/// <returns>The reverse transformed value.</returns>
///
public double Inverse(double x)
{
return(Special.Erfc(-x / Constants.Sqrt2) * 0.5);
}
/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// the this Log-Normal distribution evaluated at point <c>x</c>.
/// </summary>
/// <param name="x">
/// A single point in the distribution range.</param>
/// <remarks>
/// <para>
/// The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.</para>
/// <para>
/// The calculation is computed through the relationship to the error function
/// as <see cref="Accord.Math.Special.Erfc">erfc</see>(-z/sqrt(2)) / 2. See
/// [Weisstein] for more details.</para>
///
/// <para>
/// References:
/// <list type="bullet">
/// <item><description>
/// Weisstein, Eric W. "Normal Distribution Function." From MathWorld--A Wolfram Web
/// Resource. http://mathworld.wolfram.com/NormalDistributionFunction.html </description></item>
/// </list></para>
/// </remarks>
///
public override double DistributionFunction(double x)
{
double z = (Math.Log(x) - location) / shape;
return(0.5 * Special.Erfc(-z / Special.Sqrt2));
}
/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// the this distribution evaluated at point <c>x</c>.
/// </summary>
/// <param name="x">
/// A single point in the distribution range.</param>
/// <remarks>
/// <para>
/// The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.</para>
/// <para>
/// The calculation is computed through the relationship to
/// the function as <see cref="GABIZ.Base.Mathematic.Special.Erfc">erfc</see>(-z/sqrt(2)) / 2.</para>
///
/// <para>
/// References:
/// <list type="bullet">
/// <item><description><a href="http://mathworld.wolfram.com/NormalDistributionFunction.html">
/// http://mathworld.wolfram.com/NormalDistributionFunction.html</a></description></item>
/// </list></para>
/// </remarks>
public override double DistributionFunction(double x)
{
double z = (x - mean) / variance;
return(Special.Erfc(-z / Special.Sqrt2) / 2.0);
}
/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <remarks>
/// The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.
/// </remarks>
///
protected internal override double InnerDistributionFunction(double x)
{
double cdf = Special.Erfc(Math.Sqrt(scale / (2 * (x - location))));
return(cdf);
}
/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// the this Log-Normal distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">
/// A single point in the distribution range.</param>
/// <remarks>
///
/// <para>
/// The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.</para>
///
/// <para>
/// The calculation is computed through the relationship to the error function
/// as <see cref="Accord.Math.Special.Erfc">erfc</see>(-z/sqrt(2)) / 2. See
/// [Weisstein] for more details.</para>
///
/// <para>
/// References:
/// <list type="bullet">
/// <item><description>
/// Weisstein, Eric W. "Normal Distribution Function." From MathWorld--A Wolfram Web
/// Resource. http://mathworld.wolfram.com/NormalDistributionFunction.html </description></item>
/// </list></para>
/// </remarks>
///
/// <example>
/// See <see cref="LognormalDistribution"/>.
/// </example>
///
protected internal override double InnerDistributionFunction(double x)
{
double z = (Math.Log(x) - location) / shape;
return(0.5 * Special.Erfc(-z / Constants.Sqrt2));
}
/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// the this distribution evaluated at point <c>x</c>.
/// </summary>
/// <param name="x">
/// A single point in the distribution range.</param>
/// <remarks>
/// <para>
/// The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.</para>
/// <para>
/// The calculation is computed through the relationship to
/// the function as <see cref="Accord.Math.Special.Erfc">erfc</see>(-z/sqrt(2)) / 2.</para>
///
/// <para>
/// References:
/// <list type="bullet">
/// <item><description><a href="http://mathworld.wolfram.com/NormalDistributionFunction.html">
/// http://mathworld.wolfram.com/NormalDistributionFunction.html</a></description></item>
/// </list></para>
/// </remarks>
public override double DistributionFunction(double x)
{
double z = ZScore(x);
return(Special.Erfc(-z / Special.Sqrt2) / 2.0);
}
/// <summary>
/// Complemented cumulative distribution function.
/// </summary>
///
/// <returns>
/// The area under the Gaussian p.d.f. integrated
/// from the given value to positive infinity.
/// </returns>
///
public static double Complemented(double value)
{
return(0.5 * Special.Erfc(value / Constants.Sqrt2));
}