The normdist : Math « Development Class « C# / C Sharp
The normdist
// --------------------------------------------------------------------------------------------------------------------
// <copyright file="Simulator.Utils.cs" company="">
//
// </copyright>
// <summary>
// The simulator.
// </summary>
// --------------------------------------------------------------------------------------------------------------------
#region Latence Algo Trading Solution by Sunix First Ltd
// --------------------------------------------------------------------------
// THIS SOURCE FILE IS A PART OF THE LATENCE TRADING SUITE DEDICATED TO EMPOWER ALGORITHMIC TRADING ACTIVITIES.
// BY USING ALL OR ANY PART OF THE SOFTWARE COMPONENT OR SOURCES, YOU AGREE TO THE TERMS OF THE COMMERCIAL LICENCE ISSUED BY SUNIX FIRST LTD.
// DO NOT USE THE SOFTWARE UNTIL YOU HAVE CAREFULLY READ AND AGREED TO THE TERMS AND CONDITIONS OF THE LICENCE.
// THE MATERIALS ARE PROVIDED "AS IS". SUNIX DISCLAIMS ALL EXPRESS OR IMPLIED WARRANTIES WITH RESPECT TO THEM,
// INCLUDING ANY IMPLIED WARRANTIES OF MERCHANTABILITY, NON-INFRINGEMENT, AND FITNESS FOR ANY PARTICULAR PURPOSE.
// SUNIX SHALL NOT BE LIABLE FOR ANY DAMAGES WHATSOEVER (INCLUDING,WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS PROFITS,
// BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR OTHER LOSS) ARISING OUT OF THE USE OF OR INABILITY TO USE THE SOFTWARE.
// contact@latence.co.uk
// ---------------------------------------------------------------------------
#endregion
#region
using System;
#endregion
namespace Latence.Providers.Simulator
{
/// <summary>The simulator.</summary>
public partial class Simulator
{
#region Methods
/// <summary>The normdist.</summary>
/// <param name="x">The x.</param>
/// <param name="mean">The mean.</param>
/// <param name="std">The std. </param>
/// <param name="cumulative">The cumulative.</param>
/// <returns>The normdist.</returns>
private static double NORMDIST(double x, double mean, double std, bool cumulative)
{
if (cumulative)
{
return Phi(x, mean, std);
}
var tmp = 1/(Math.Sqrt(2*Math.PI)*std);
return tmp*Math.Exp(-.5*Math.Pow((x - mean)/std, 2));
}
// from http://www.cs.princeton.edu/introcs/...Math.java.html
// fractional error less than 1.2 * 10 ^ -7.
// cumulative normal distribution
/// <summary>The phi.</summary>
/// <param name="z">The z.</param>
/// <returns>The phi.</returns>
private static double Phi(double z)
{
return 0.5*(1.0 + erf(z/Math.Sqrt(2.0)));
}
// cumulative normal distribution with mean mu and std deviation sigma
/// <summary>The phi.</summary>
/// <param name="z">The z.</param>
/// <param name="mu">The mu.</param>
/// <param name="sigma">The sigma.</param>
/// <returns>The phi.</returns>
private static double Phi(double z, double mu, double sigma)
{
return Phi((z - mu)/sigma);
}
/// <summary>The erf.</summary>
/// <param name="z">The z.</param>
/// <returns>The erf.</returns>
private static double erf(double z)
{
var t = 1.0/(1.0 + 0.5*Math.Abs(z));
// use Horner's method
var ans = 1 -
t*
Math.Exp(
-z*z - 1.26551223 +
t*
(1.00002368 +
t*
(0.37409196 +
t*
(0.09678418 +
t*
(-0.18628806 +
t*
(0.27886807 +
t*(-1.13520398 + t*(1.48851587 + t*(-0.82215223 + t*0.17087277)))))))));
if (z >= 0)
{
return ans;
}
return -ans;
}
#endregion
}
}
