private static QuantilCharacteristic CalculateKurtosis(ref double[] array)
{
QuantilCharacteristic kurtosisCharacteristic = new QuantilCharacteristic();
double quantilStudent = QuantilCalculator.StudentQuantil((1.0 - (alpha / 2)), (array.Length - 1));
double aver = CalculateAverage(ref array);
double sum = 0;
double sum2 = 0;
double _e, _v;
for (int i = 0; i < array.Length; i++)
{
sum += Math.Pow(array[i] - aver, 4);
sum2 += Math.Pow(array[i], 2) - Math.Pow(aver, 2);
}
_v = sum2 / array.Length;
_e = sum / (array.Length * Math.Pow(_v, 2));
kurtosisCharacteristic.value = ((Math.Pow(array.Length, 2.0) - 1.0) / ((array.Length - 2.0) * (array.Length - 3.0))) * ((_e - 3.0) + (6.0 / (array.Length + 1.0)));
kurtosisCharacteristic.standardDeviation = Math.Sqrt(((24.0 * (double)array.Length) * ((double)array.Length - 2.0) * ((double)array.Length - 3.0)) /
(((double)array.Length + 1.0) * ((double)array.Length + 1.0) * ((double)array.Length + 3.0) * ((double)array.Length + 5.0)));
kurtosisCharacteristic.confidenceInterval.min = kurtosisCharacteristic.value - (quantilStudent * kurtosisCharacteristic.standardDeviation);
kurtosisCharacteristic.confidenceInterval.max = kurtosisCharacteristic.value + (quantilStudent * kurtosisCharacteristic.standardDeviation);
kurtosisCharacteristic.value = Math.Round(kurtosisCharacteristic.value, 4);
kurtosisCharacteristic.standardDeviation = Math.Round(kurtosisCharacteristic.standardDeviation, 4);
kurtosisCharacteristic.confidenceInterval.min = Math.Round(kurtosisCharacteristic.confidenceInterval.min, 4);
kurtosisCharacteristic.confidenceInterval.max = Math.Round(kurtosisCharacteristic.confidenceInterval.max, 4);
return kurtosisCharacteristic;
}
private static QuantilCharacteristic CalculateSkewness(ref double[] array)
{
QuantilCharacteristic skewnessCharacteristic = new QuantilCharacteristic();
double quantilStudent = QuantilCalculator.StudentQuantil((1.0 - (alpha / 2)), (array.Length - 1));
double aver = CalculateAverage(ref array);
double sum = 0;
double sum2 = 0;
double _a, _v;
for (int i = 0; i < array.Length; i++)
{
sum += Math.Pow(array[i] - aver, 3);
sum2 += Math.Pow(array[i], 2) - Math.Pow(aver, 2);
}
_v = sum2 / array.Length;
_a = sum / (array.Length * Math.Pow(_v, 3.0 / 2.0));
skewnessCharacteristic.value = _a * (Math.Sqrt(array.Length * (array.Length - 1)) / (array.Length - 2));
skewnessCharacteristic.standardDeviation = Math.Sqrt((6.0 * ((double)array.Length - 2.0)) / (((double)array.Length + 1.0) * ((double)array.Length + 3.0)));
skewnessCharacteristic.confidenceInterval.min = skewnessCharacteristic.value - (quantilStudent * skewnessCharacteristic.standardDeviation);
skewnessCharacteristic.confidenceInterval.max = skewnessCharacteristic.value + (quantilStudent * skewnessCharacteristic.standardDeviation);
skewnessCharacteristic.value = Math.Round(skewnessCharacteristic.value, 4);
skewnessCharacteristic.standardDeviation = Math.Round(skewnessCharacteristic.standardDeviation, 4);
skewnessCharacteristic.confidenceInterval.min = Math.Round(skewnessCharacteristic.confidenceInterval.min, 4);
skewnessCharacteristic.confidenceInterval.max = Math.Round(skewnessCharacteristic.confidenceInterval.max, 4);
return skewnessCharacteristic;
}
private static QuantilCharacteristic CalculateMedian(ref double[] array)
{
QuantilCharacteristic medianCharacteristic = new QuantilCharacteristic();
if ((array.Length % 2) == 1)
{
medianCharacteristic.value = array[array.Length / 2];
}
else
{
medianCharacteristic.value = (array[array.Length / 2] + array[(array.Length / 2) - 1]) / 2.0;
}
medianCharacteristic.value = Math.Round(medianCharacteristic.value, 4);
return medianCharacteristic;
}
private static QuantilCharacteristic CalculateStandardDeviation(ref double[] array)
{
QuantilCharacteristic standardDeviationCharacteristic = new QuantilCharacteristic();
double sum = 0;
double aver = CalculateAverage(ref array);
double quantilStudent = QuantilCalculator.StudentQuantil((1.0 - (alpha / 2)), (array.Length - 1));
for (int i = 0; i < array.Length; i++)
{
sum += Math.Pow(array[i] - aver, 2);
}
standardDeviationCharacteristic.value = sum / (double)(array.Length - 1);
standardDeviationCharacteristic.standardDeviation = Math.Sqrt(standardDeviationCharacteristic.value / (2.0 * (double)array.Length));
standardDeviationCharacteristic.confidenceInterval.min = Math.Sqrt(standardDeviationCharacteristic.value) - (quantilStudent * standardDeviationCharacteristic.standardDeviation);
standardDeviationCharacteristic.confidenceInterval.max = Math.Sqrt(standardDeviationCharacteristic.value) + (quantilStudent * standardDeviationCharacteristic.standardDeviation);
standardDeviationCharacteristic.value = Math.Round(standardDeviationCharacteristic.value, 4);
standardDeviationCharacteristic.standardDeviation = Math.Round(standardDeviationCharacteristic.standardDeviation, 4);
standardDeviationCharacteristic.confidenceInterval.min = Math.Round(standardDeviationCharacteristic.confidenceInterval.min, 4);
standardDeviationCharacteristic.confidenceInterval.max = Math.Round(standardDeviationCharacteristic.confidenceInterval.max, 4);
return standardDeviationCharacteristic;
}
private static QuantilCharacteristic CalculateAverageWithDeviationAndIntervals(ref double[] array)
{
double quantilStudent = QuantilCalculator.StudentQuantil((1.0 - (alpha / 2)), (array.Length - 1));
QuantilCharacteristic averageCharacteristic = new QuantilCharacteristic();
double sum = 0;
for (int i = 0; i < array.Length; i++)
{
sum += array[i];
}
averageCharacteristic.value = sum / (double)array.Length;
averageCharacteristic.standardDeviation = Math.Sqrt(CalculateStandardDeviation(ref array).value / (double)array.Length);
averageCharacteristic.confidenceInterval.min = averageCharacteristic.value - (quantilStudent * averageCharacteristic.standardDeviation);
averageCharacteristic.confidenceInterval.max = averageCharacteristic.value + (quantilStudent * averageCharacteristic.standardDeviation);
averageCharacteristic.value = Math.Round(averageCharacteristic.value, 4);
averageCharacteristic.standardDeviation = Math.Round(averageCharacteristic.standardDeviation, 4);
averageCharacteristic.confidenceInterval.min = Math.Round(averageCharacteristic.confidenceInterval.min, 4);
averageCharacteristic.confidenceInterval.max = Math.Round(averageCharacteristic.confidenceInterval.max, 4);
return averageCharacteristic;
}
