private void DetermineIterationDetails(bool longList, ref int iterationsOfBinomCdf, ref int iterationStartingPoint)
{
if (!longList)
{
double mean = BinomialStochasticVariables.My(xVar);
double dev = BinomialStochasticVariables.Deviation(xVar);
iterationStartingPoint = (int)(mean - 3 * dev);
if (iterationStartingPoint <= 0)
{
iterationStartingPoint = 0;
}
iterationsOfBinomCdf = (int)(6 * dev + mean);
if (iterationsOfBinomCdf > xVar.number)
{
iterationsOfBinomCdf = (int)xVar.number;
}
}
}
void WorkWithPropertiesOfXVar()
{
Console.WriteLine("||\n||| Working out useful properties of supplied XVar.");
CheckValuesForBadness();
double tempMy = BinomialStochasticVariables.My(xVar);
Console.WriteLine("||\n|| > Expected value E(X) or my: X~b( n , p ) E(X) = n * p");
Console.ForegroundColor = ConsoleColor.Green;
Console.WriteLine("||| Expected value E(X) or my:\n||| > X~b( {0} , {1} ) E(X) = {0} * {1} = {2}",
xVar.number, xVar.probability, tempMy);
Console.ResetColor();
double tempVariance = BinomialStochasticVariables.Variance(xVar);
Console.Write("||\n|| > Binomial Variance Var(X): X~b( n , p ) Var(X) = n * p * (1 - p)");
Console.ForegroundColor = ConsoleColor.DarkBlue;
Console.Write("\t\tI made this up, but the values it produces make sense; \n");
Console.ForegroundColor = ConsoleColor.Green;
Console.Write("|| Variance Var(X):");
Console.ForegroundColor = ConsoleColor.DarkBlue;
Console.Write("\t\t\t\t\t\t\t\tand the sense of the formula is parallel to variance proper, Var(X).\n");
Console.ForegroundColor = ConsoleColor.Green;
Console.Write("||| > X~b( {0} , {1} ) Var(X) = {0} * {1} * (1 - {1}) = {2}\n",
xVar.number, xVar.probability, Math.Round(tempVariance, 7));
Console.ResetColor();
double tempDeviation = BinomialStochasticVariables.Deviation(xVar);
Console.WriteLine("||\n|| > Mean Deviance / sigma(X): X~b( n , p ) sigma(X) = squareroot of Var(x) \n" +
"|| So sigma(X) = squareroot of (n * p * (1 - p))");
Console.ForegroundColor = ConsoleColor.Green;
Console.WriteLine("|| Deviation sigma(X):" +
"\n||| > X~b( {0} , {1} ) Var(X) = sqr({2}) = squareroot of ( {0} * {1} * (1 - {1} )) = {3}",
xVar.number, xVar.probability, Math.Round(tempVariance, 3), Math.Round(tempDeviation, 7));
Console.ResetColor();
//Console.WriteLine("||");
double negStandardDeviation = Math.Round(tempMy - tempDeviation, 2);
double neg2ndDeviation = Math.Round(tempMy - tempDeviation * 2, 2);
double neg3rdDeviation = Math.Round(tempMy - tempDeviation * 3, 2);
double posStandardDeviation = Math.Round(tempMy + tempDeviation, 2);
double pos2ndDeviation = Math.Round(tempMy + tempDeviation * 2, 2);
double pos3rdDeviation = Math.Round(tempMy + tempDeviation * 3, 2);
Console.WriteLine("" +
"||\n|| > Normal Distribution for X ~b( {0} , {1} ):\n" +
"|| Case: ", xVar.number, xVar.probability);
Console.ForegroundColor = ConsoleColor.DarkGreen;
Console.WriteLine(
"|| \tLow --- \tLow -- \tLow - \t\tMean \t\tHigh + \t\tHigh ++ \tHigh +++ ");
Console.ForegroundColor = ConsoleColor.Green;
if (neg3rdDeviation <= 0)
{
Console.ForegroundColor = ConsoleColor.DarkMagenta;
} // to represent the impossibility of a negative deviation, go dark magenta
Console.Write("|||\t{0}", neg3rdDeviation);
if (neg2ndDeviation <= 0)
{
Console.ForegroundColor = ConsoleColor.DarkMagenta;
} // to represent the impossibility of a negative deviation, go dark magenta
Console.Write("\t\t{0}", neg2ndDeviation);
Console.ForegroundColor = ConsoleColor.Green;
Console.Write("\t\t{0}\t\t{1}\t\t{2}\t\t{3}\t\t{4}\n",
negStandardDeviation, tempMy, posStandardDeviation, pos2ndDeviation, pos3rdDeviation);
Console.ResetColor();
double confidenceCoefficient = Math.Sqrt(xVar.probability * (1 - xVar.probability)) / Math.Sqrt(xVar.number);
double confidenceIntervalLowPoint = xVar.probability - 2 * confidenceCoefficient;
double confidenceIntervalHighPoint = xVar.probability + 2 * confidenceCoefficient;
//double confidenceIntLow = 0;
Console.WriteLine("" +
"||\n||| > 95% Confidence Interval 'using' XVar ~b( n = {0} , p = {1} );\n" +
"|| where {0} is 'interpreted' as sample size \t\t[n] = {0} \t[ Number of cases included in experiment. ]\n" +
"|| and {1} is 'treated' as estimated likelyhood\t[p] = {1}\n" +
"|| [ [p] of your XVar is treated as if:\t\t\t[p] = rate of queried quality found in sample / sample size ]", Math.Round(xVar.number, 2), Math.Round(xVar.probability, 2));
//Console.ForegroundColor = ConsoleColor.Green;
Console.Write("" +
"|| Assuming that the sample size {0} is representative of the total population in question,\n" +
"|| it might be concluded with confidence that the actual percentage in that total population is\n||| " +
"\t\t\t\t\tbetween\t", xVar.number);
Console.ForegroundColor = ConsoleColor.DarkGreen;
Console.Write("\t\t{0}%\t", Math.Round(confidenceIntervalLowPoint * 100, 2));
Console.ResetColor();
Console.Write(" and\t");
Console.ForegroundColor = ConsoleColor.DarkGreen;
Console.Write("{0}%.\n", Math.Round(confidenceIntervalHighPoint * 100, 2));
Console.ResetColor();
Console.Write("||\n");
Console.ForegroundColor = ConsoleColor.DarkBlue;
Console.Write("|| End of list. Press enter to continue.\n");
Console.ReadLine();
Console.ResetColor();
MethodExit();
}
