/// <summary>
/// Computes the two-tail probability using the Wilson-Sterne rule,
/// which defines the tail of the distribution based on a ordering
/// of the null probabilities of X. (Smirnoff, 2003)
/// </summary>
///
/// <remarks>
/// References: Jeffrey S. Simonoff, Analyzing
/// Categorical Data, Springer, 2003 (pg 64).
/// </remarks>
///
private double wilsonSterne(double x)
{
double mean = StatisticDistribution.Mean;
if (x == mean)
{
return(1);
}
int trials = StatisticDistribution.NumberOfTrials;
// Construct a map of values and point probabilities
double[] probabilities = new double[trials];
for (int i = 0; i < probabilities.Length; i++)
{
probabilities[i] = StatisticDistribution.ProbabilityMassFunction(i);
}
int[] values;
// Build the ordered Wilson-Sterne table
probabilities.Sort(out values);
// Now, compute the cumulative probability
double[] cumulative = new double[trials];
cumulative[0] = probabilities[0];
for (int i = 1; i < cumulative.Length; i++)
{
cumulative[i] += cumulative[i - 1] + probabilities[i];
}
int v = 0;
for (int i = 0; i < values.Length; i++)
{
if (values[i] == (int)x)
{
v = i;
while (v < probabilities.Length && probabilities[i] == probabilities[v])
{
v++;
}
}
}
return(cumulative[v - 1]);
}
/// <summary>
/// Computes the two-tail probability using the Wilson-Sterne rule,
/// which defines the tail of the distribution based on a ordering
/// of the null probabilities of X. (Smirnoff, 2003)
/// </summary>
///
/// <remarks>
/// References: Jeffrey S. Simonoff, Analyzing
/// Categorical Data, Springer, 2003 (pg 64).
/// </remarks>
///
private double wilsonSterne(double x)
{
int trials = StatisticDistribution.NumberOfTrials;
// Construct a map of values and point probabilities
int[] values = new int[trials];
for (int i = 0; i < values.Length; i++)
{
values[i] = i;
}
double[] probabilities = new double[trials];
for (int i = 0; i < probabilities.Length; i++)
{
probabilities[i] = StatisticDistribution.ProbabilityMassFunction(i);
}
// Build the ordered Wilson-Sterne table
Array.Sort(probabilities, values);
// Now, compute the cumulative distribution
double[] cumulative = new double[trials];
cumulative[0] = probabilities[0];
for (int i = 1; i < cumulative.Length; i++)
{
cumulative[i] += cumulative[i - 1] + probabilities[i];
}
int v = 0; // Locate the desired value
for (int i = 0; i < values.Length; i++)
{
if (values[i] == (int)x)
{
v = i;
}
}
// Report the p-value
return(cumulative[v]);
}