private void ListOfBinomCdf()
{
Console.WriteLine("|||\n" +
"|| List of cumulative likelyhoods of AT MOST rate [r] success': X~b( n , p ) P( X <= r ) [r = 0,..,n]\n" +
"|| given the probability [p] of a success among [n] elements: X~b(n,p) P(X=r)\n||");
CheckValuesForBadness();
bool longList = DecideListLength();
for (int i = 0; i <= xVar.number; i++)
{
double binomCdf = BinomialStochasticVariables.binomCdf(xVar, i);
if (binomCdf > 0.0025 && binomCdf < 0.98 | longList)
{
//Console.ForegroundColor = ConsoleColor.Green;
//if ((binomCdf <= 0.05)) { Console.ForegroundColor = ConsoleColor.DarkRed; }
//if ((binomCdf >= 0.95)) { Console.ForegroundColor = ConsoleColor.DarkYellow; }
ColorCodeIntervals(binomCdf);
Console.WriteLine("||| Chance of {0} or less success' = {1}%:\t X~b( {2} , {3} ) P(X <= {0}) = {4} \t\t {5}",
i, 100 * Math.Round(binomCdf, 4), xVar.number, xVar.probability,
Math.Round(binomCdf, 5), Access.Dash(binomCdf /*, 4*/));
if (binomCdf > 0.9999)
{
break;
}
}
}
Console.ResetColor();
Console.ReadLine();
}
private void ListOfBinomICdf()
{
Console.WriteLine("|||\n|| X~b( n , p ) P( X >= r ) [r = 0,..,n]\n|| List of cumulative likelyhoods of AT LEAST rate [r] success':\n" +
"|| given the probability of a success [p] among [n] elements: X~b(n,p) P(X=r)\n||");
CheckValuesForBadness();
bool longList = DecideListLength();
int iterationsOfBinomCdf = (int)xVar.number; // number of times the binomCdf() will run; changed if only a non-longList is demanded by user
int iterationStartingPoint = 0; // will be 0 if traversing all values; set to xVars My value if going for short list
//Here is implemented a way of cutting off the list that uses the actual numbers of the
// xVar - doesn't make much difference... which is cool.
DetermineIterationDetails(longList, ref iterationsOfBinomCdf, ref iterationStartingPoint);
for (int i = iterationStartingPoint; i <= iterationsOfBinomCdf; i++)
{
double binomICdf = BinomialStochasticVariables.binomICdf(xVar, i);
//if (binomICdf > 0.0025 && binomICdf < 0.951 | longList)
//{
ColorCodeIntervals(binomICdf);
Console.WriteLine("||| Chance of {0} or more success' = {1}%:\t X~b( {2} , {3} ) P(X >= {0}) = {4} \t\t {5}",
i, 100 * Math.Round(binomICdf, 4), xVar.number, xVar.probability,
Math.Round(binomICdf, 7), Access.Dash(binomICdf /*, 3*/));
//}
}
Console.ResetColor();
Console.ReadLine();
}
private void ListChanceOfAllSingleRatesSuccess()
{
Console.WriteLine("|||\n|| List of the chances of all specific rates [r] of success\n" +
"|| given the probability of a success [p] among [n] elements: X~b(n,p) P(X=r)\n||");
CheckValuesForBadness();
bool longList = DecideListLength();
for (int i = 0; i <= xVar.number; i++)
{
double binomPdf = BinomialStochasticVariables.binomPdf(xVar, i);
if (binomPdf > 0.0002 | longList)
{
ColorCodeIntervals(binomPdf);
Console.WriteLine("||| Chance of {0} success = {1}% :\tX~b( {2} , {3} ) P(X = {0}) = {4}\t\t {5}",
i, 100 * Math.Round(binomPdf, 4), xVar.number, xVar.probability,
Math.Round(binomPdf, 5), Access.Dash(binomPdf));
}
}
Console.ResetColor();
Console.ReadLine();
}
void CalculateChanceOfNoLessThanRateSuccess()
{
Console.WriteLine("|||Calculate the chance of EQUAL TO OR MORE than rate [r] of success: X~b( n , p ) P( X >= r )\n" +
"|| given the probability of a success [p] among [n] elements: X~b(n,p) P(X=r)\n||");
CheckValuesForBadness();
Rate = FetchRate();
Console.WriteLine("||\n||| Chance of {0} or more success' = {1}% : X~b( {2} , {3} ) P(X >= {0}) = {4}\n||",
Rate, 100 * Math.Round(BinomialStochasticVariables.binomICdf(xVar, Rate), 5), xVar.number, xVar.probability,
Math.Round(BinomialStochasticVariables.binomICdf(xVar, Rate), 7));
Console.WriteLine("|| Enter to continue.");
Console.ReadLine();
}
void CalculateChanceOfAtLeastRateSuccess()
{
Console.WriteLine("|||Calculate the probability of EQUAL OR LESS than rate [r] of success: X~b( n , p ) P( X <= r )\n" +
"|| given the probability [p] of a success among [n] elements: X~b(n,p) P(X=r)\n||");
CheckValuesForBadness();
Rate = FetchRate();
Console.WriteLine("||\n||| Chance of no more than {0} success' = {1}% : X~b( {2} , {3} ) P(X <= {0}) = {4}\n||",
Rate, 100 * Math.Round(BinomialStochasticVariables.binomCdf(xVar, Rate), 5), xVar.number, xVar.probability,
Math.Round(BinomialStochasticVariables.binomCdf(xVar, Rate), 5));
Console.WriteLine("|| Enter to continue.");
Console.ReadLine();
}
private void ChanceOfSingleRateSuccess()
{
Console.WriteLine("|||Calculate the chance of a specific rate [r] of success\n" +
"|| given the probability of a success [p] among [n] elements:\t X~b(n,p) P(X=r)\n||");
CheckValuesForBadness();
Rate = FetchRate();
Console.WriteLine("||\n||| The likelyhood of {0} success' = {1}% : X~b( {2} , {3} ) P(X = {0}) = {4}\n||",
Rate, 100 * Math.Round(BinomialStochasticVariables.binomPdf(xVar, Rate), 3), xVar.number, xVar.probability,
Math.Round(BinomialStochasticVariables.binomPdf(xVar, Rate), 5));
Console.WriteLine("|| Enter to continue.");
Console.ReadLine();
}
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();
}
