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Vorcyc.Mathematics.Statistics.Advanced is a class that provides advanced statistical functions, including methods for percentiles, quartiles, skewness, kurtosis, confidence intervals, hypothesis tests, analysis of variance, chi-square tests, and nonparametric tests.

All methods below are located in class: Vorcyc.Mathematics.Statistics.Advanced

📒Contents

• 🔖 Percentile method
• 🔖 Quartiles method
• 🔖 Skewness method
• 🔖 Kurtosis method
• 🔖 ConfidenceInterval method
• 🔖 TTest method
• 🔖 Anova method
• 🔖 ChiSquaredTest method
• 🔖 MannWhitneyUTest method

Vorcyc.Mathematics.Statistics.Advanced is a class that provides advanced statistical functions, including methods for percentiles, quartiles, skewness, kurtosis, confidence intervals, hypothesis tests, analysis of variance, chi-square tests, and nonparametric tests.

• public static T Percentile<T>(this Span<T> sequence, double percentile) where T : IFloatingPointIeee754<T>
  • Computes the specified percentile of a dataset.
  • Parameters:
    • sequence: The dataset.
    • percentile: The percentile (between 0 and 1).
  • Returns: The value at the specified percentile.

• public static (T Q1, T Q2, T Q3) Quartiles<T>(this Span<T> sequence) where T : IFloatingPointIeee754<T>
  • Computes the quartiles of a dataset.
  • Parameters:
    • sequence: The dataset.
  • Returns: A tuple containing the first, second, and third quartiles.

• public static T Skewness<T>(this Span<T> sequence) where T : IFloatingPointIeee754<T>
  • Computes the skewness of a dataset, measuring the symmetry of the distribution.
  • Parameters:
    • sequence: The dataset.
  • Returns: The skewness value of the dataset.

• public static T Kurtosis<T>(this Span<T> sequence) where T : IFloatingPointIeee754<T>
  • Computes the kurtosis of a dataset, measuring the peakedness of the distribution.
  • Parameters:
    • sequence: The dataset.
  • Returns: The kurtosis value of the dataset.

• public static (T Lower, T Upper) ConfidenceInterval<T>(this Span<T> sequence, double confidenceLevel) where T : IFloatingPointIeee754<T>
  • Computes a confidence interval for the mean or proportion.
  • Parameters:
    • sequence: The dataset.
    • confidenceLevel: The confidence level (for example, 0.95 for 95%).
  • Returns: A tuple containing the lower and upper bounds of the confidence interval.

• public static T TTest<T>(this Span<T> sample, T populationMean) where T : IFloatingPointIeee754<T>
  • Implements hypothesis tests such as z-test, t-test, chi-square test, and others.
  • Parameters:
    • sample: The sample dataset.
    • populationMean: The population mean.
  • Returns: The t-test statistic.

• public static T Anova<T>(this IEnumerable<ArraySegment<T>> groups) where T : IFloatingPointIeee754<T>
  • Implements one-way and multi-way analysis of variance.
  • Parameters:
    • groups: A collection of data groups.
  • Returns: The F-value from analysis of variance.

• public static T ChiSquaredTest<T>(this Span<T> observed, Span<T> expected) where T : IFloatingPointIeee754<T>
  • Implements chi-square tests of independence and goodness of fit.
  • Parameters:
    • observed: The observed data.
    • expected: The expected data.
  • Returns: The chi-square test statistic.

• public static T MannWhitneyUTest<T>(this Span<T> sample1, Span<T> sample2) where T : IFloatingPointIeee754<T>
  • Implements nonparametric tests such as the Mann–Whitney U test and Kruskal–Wallis test.
  • Parameters:
    • sample1: The first sample dataset.
    • sample2: The second sample dataset.
  • Returns: The Mann–Whitney U test statistic.

The following example uses several methods from the Advanced class, with comments in the sample:

using System;
using System.Collections.Generic;
using Vorcyc.Mathematics.Statistics;
using static System.Runtime.InteropServices.JavaScript.JSType;

public class AdvancedStatisticsExample
{
    public static void Main()
    {
        // Define dataset
        Span<double> data = new double[] { 1.0, 2.0, 3.0, 4.0, 5.0 };

        // Compute percentile
        double percentile = data.Percentile(0.9);
        Console.WriteLine("90th Percentile: " + percentile);

        // Compute quartiles
        var (Q1, Q2, Q3) = data.Quartiles();
        Console.WriteLine($"Q1: {Q1}, Q2: {Q2}, Q3: {Q3}");

        // Compute skewness
        double skewness = data.Skewness();
        Console.WriteLine("Skewness: " + skewness);

        // Compute kurtosis
        double kurtosis = data.Kurtosis();
        Console.WriteLine("Kurtosis: " + kurtosis);

        // Compute confidence interval
        var (lower, upper) = data.ConfidenceInterval(0.95);
        Console.WriteLine($"95% Confidence Interval: ({lower}, {upper})");

        // Perform t-test
        double tTest = data.TTest(3.0);
        Console.WriteLine("T-Test: " + tTest);

        // Perform analysis of variance
        var groups = new List<ArraySegment<double>>
    {
        new ArraySegment<double>(new double[] { 1.0, 2.0, 3.0 }),
        new ArraySegment<double>(new double[] { 4.0, 5.0, 6.0 }),
        new ArraySegment<double>(new double[] { 7.0, 8.0, 9.0 })
    };
        double anova = groups.Anova();
        Console.WriteLine("ANOVA: " + anova);

        // Perform chi-square test
        Span<double> observed = new double[] { 10, 20, 30 };
        Span<double> expected = new double[] { 15, 25, 35 };
        double chiSquared = observed.ChiSquaredTest(expected);
        Console.WriteLine("Chi-Squared Test: " + chiSquared);

        // Perform Mann–Whitney U test
        Span<double> sample1 = new double[] { 1.0, 2.0, 3.0 };
        Span<double> sample2 = new double[] { 4.0, 5.0, 6.0 };
        double mannWhitneyU = sample1.MannWhitneyUTest(sample2);
        Console.WriteLine("Mann-Whitney U Test: " + mannWhitneyU);
    }
}

Outlier-resistant descriptive helpers (Robust static methods on Span<T> / ReadOnlySpan<T>):

Welford single-pass mean/variance accumulator: