public static void MonteCarlo_Variation()
{
int n = 20000; //n is the number of simulations
double l_three_d = 0; //length of a line
double[] distancesThreeD = new double[n]; // here the distance is stored in an array for each iteration of n
BoxMullerNormal b = new BoxMullerNormal();
//repeat the experiment n (20k) times
for (int i = 0; i < n; i++)
{
//get a point (x1,x2,y1,y2) at random
double x1 = b.GetRandom();
double x2 = b.GetRandom();
double y1 = b.GetRandom();
double y2 = b.GetRandom();
double z1 = b.GetRandom();
double z2 = b.GetRandom();
//3D
double result2 = ThreeD(x1, x2, y1, y2, z1, z2);
l_three_d = result2; //get length of a 3d line
distancesThreeD[i] = l_three_d;
}
#region average
double averageOfLineThreeD = Queryable.Average(distancesThreeD.AsQueryable());
#endregion
#region standard dev
double sum = distancesThreeD.Sum(d => Math.Pow(d - averageOfLineThreeD, 2));
double sd_3d = Math.Sqrt((sum) / (distancesThreeD.Count() - 1));
#endregion
#region confidence interval
double marginOfError_3d = 2.58 * (sd_3d / Math.Sqrt(n));
double lowerEndOfInterval_3d = averageOfLineThreeD - marginOfError_3d; //lower end of the interval is average - margin of error
double UpperEndOfInterval_3d = averageOfLineThreeD + marginOfError_3d; //and upper end is average + margin of error
#endregion
#region display results
Console.WriteLine("3D Results: \n");
Console.WriteLine("Average of 3d: " + averageOfLineThreeD);
Console.WriteLine("Standard Deviation 3d: " + sd_3d);
Console.WriteLine("μ: " + averageOfLineThreeD + " ± " + marginOfError_3d);
Console.WriteLine("lower end of interval = " + lowerEndOfInterval_3d);
Console.WriteLine("upper end of interval = " + UpperEndOfInterval_3d);
Console.WriteLine("You can be 99% confident that the population mean (μ) falls between " + lowerEndOfInterval_3d + " and " + UpperEndOfInterval_3d);
#endregion
Console.WriteLine("\nPress any key to continue..... \n");
}
public static string FindMaxError(double e, double alpha, int n = 100, int repeats = 1)
{
Console.WriteLine("Default problem size = " + n);
double l_three_d = 0; //length of a line
double[] distancesThreeD = new double[n]; // here the distance is stored in an array for each iteration of n
double c = 0;
int k = 0;
BoxMullerNormal b = new BoxMullerNormal();
//repeat the experiment n times
for (int i = 0; i < n; i++)
{
//get a point (x1,x2,y1,y2,z1,z2) at random
double x1 = b.GetRandom();
double x2 = b.GetRandom();
double y1 = b.GetRandom();
double y2 = b.GetRandom();
double z1 = b.GetRandom();
double z2 = b.GetRandom();
//3D
double result2 = ThreeD(x1, x2, y1, y2, z1, z2);
l_three_d = result2; //get length of a 3d line
distancesThreeD[i] = l_three_d;
}
double averageOfLineThreeD = Queryable.Average(distancesThreeD.AsQueryable());
double sum = distancesThreeD.Sum(d => Math.Pow(d - averageOfLineThreeD, 2));
double sd_3d = Math.Sqrt((sum) / (distancesThreeD.Count() - 1));
//double sd_3d = Math.Sqrt(distancesThreeD.Average(v => Math.Pow(v - averageOfLineThreeD, 2)));
c = alpha * (sd_3d / Math.Sqrt(n));
if (c > e)
{
Console.WriteLine("c is less than e, so try again...");
k = 1;
n = (int)Math.Ceiling(Math.Pow((alpha * sd_3d / e), 2) + k);
repeats++;
return(FindMaxError(e, alpha, n, repeats));
}
else
{
Console.WriteLine("c is greater than e, Done!");
#region confidence interval
//3D
double marginOfError_3d = alpha * (sd_3d / Math.Sqrt(n));
double lowerEndOfInterval_3d = averageOfLineThreeD - marginOfError_3d; //lower end of the interval is average - margin of error
double UpperEndOfInterval_3d = averageOfLineThreeD + marginOfError_3d; //and upper end is average + margin of error
Console.WriteLine("μ: " + averageOfLineThreeD + " ± " + marginOfError_3d);
Console.WriteLine("lower end of interval = " + lowerEndOfInterval_3d);
Console.WriteLine("upper end of interval = " + UpperEndOfInterval_3d);
Console.WriteLine($"You can be {alpha}% confident that the population mean (μ) falls between" + lowerEndOfInterval_3d + " and " + UpperEndOfInterval_3d);
#endregion
Console.WriteLine("Repeats: " + repeats);
return("Max error: " + c + " , Ideal n = " + n);
}
}