Module_Statistics_Basic

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Statistics module

Basic statistics functions

Vorcyc.Mathematics.Statistics.Basic is a class that provides basic statistical functions, including methods for mean, median, mode, variance, standard deviation, and coefficient of variation.

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

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📒Contents

• 🔖 Sum method
• 🔖 Average method
• 🔖 Median method
• 🔖 Mode method
• 🔖 Variance method
• 🔖 StandardDeviation method
• 🔖 CoefficientOfVariation method
• 🔖 CalculateAllStatistics method

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Vorcyc.Mathematics.Statistics.Basic class

Vorcyc.Mathematics.Statistics.Basic is a class that provides basic statistical functions, including methods for mean, median, mode, variance, standard deviation, and coefficient of variation.

Methods

1. Sum method

• public static T Sum<T>(this Span<T> values) where T : INumber<T>

  • Computes the sum of elements in a set of values, optimized with SIMD.
  • Parameters:
    • values: The set of values to sum.
  • Returns: The sum of elements in the set of values.
  • Exceptions:
    • ArgumentException: Thrown when values is empty.

• public static T Sum<T>(this Span<T> values, Func<T, T> selector) where T : INumber<T>

  • Computes the sum of elements in a set of values using the specified selector function.
  • Parameters:
    • values: The set of values to sum.
    • selector: A function used to select values.
  • Returns: The sum of elements in the set of values.
  • Exceptions:
    • ArgumentException: Thrown when values is empty.

2. Average method

• public static T Average<T>(this Span<T> values) where T : INumber<T>
  • Computes the average of elements in a set of values.
  • Parameters:
    • values: The set of values to average.
  • Returns: The average of elements in the set of values.
  • Exceptions:
    • ArgumentException: Thrown when values is empty.

3. Median method

• public static T Median<T>(this Span<T> values) where T : INumber<T>
  • Computes the median of elements in a set of values.
  • Parameters:
    • values: The set of values for which to compute the median.
  • Returns: The median of elements in the set of values.
  • Exceptions:
    • ArgumentException: Thrown when values is empty.

4. Mode method

• public static T Mode<T>(this Span<T> values) where T : INumber<T>
  • Computes the mode of elements in a set of values.
  • Parameters:
    • values: The set of values for which to compute the mode.
  • Returns: The element with the highest frequency in the set of values.
  • Exceptions:
    • ArgumentException: Thrown when values is empty.

5. Variance method

• public static (T average, T variance) Variance<T>(this Span<T> values) where T : INumber<T>
  • Computes the average and variance of elements in a set of values.
  • Parameters:
    • values: The set of values for which to compute average and variance.
  • Returns: A tuple containing the average and variance of elements in the set of values.
  • Exceptions:
    • ArgumentException: Thrown when values is empty.

6. StandardDeviation method

• public static T StandardDeviation<T>(this Span<T> values) where T : IFloatingPointIeee754<T>
  • Computes the standard deviation of elements in a set of values.
  • Parameters:
    • values: The set of values for which to compute standard deviation.
  • Returns: The standard deviation of elements in the set of values.
  • Exceptions:
    • ArgumentException: Thrown when values is empty.

7. CoefficientOfVariation method

• public static T CoefficientOfVariation<T>(this Span<T> values) where T : IFloatingPointIeee754<T>
  • Computes the coefficient of variation of elements in a set of values.
  • Parameters:
    • values: The set of values for which to compute the coefficient of variation.
  • Returns: The coefficient of variation of elements in the set of values.
  • Exceptions:
    • ArgumentException: Thrown when values is empty.

8. CalculateAllStatistics method

• public static (T Mean, T Median, T Mode, T Variance, T StandardDeviation, T CoefficientOfVariation) CalculateAllStatistics<T>(this Span<T> values) where T : IFloatingPointIeee754<T>
  • Computes all statistics for a set of values, including mean, median, mode, variance, standard deviation, and coefficient of variation.
  • Parameters:
    • values: The set of values for which to compute statistics.
  • Returns: A tuple containing mean, median, mode, variance, standard deviation, and coefficient of variation.
  • Exceptions:
    • ArgumentException: Thrown when values is empty.

Code example

The following example uses several methods from the Basic 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 BasicStatisticsExample
{
    public static void Main()
    {
        // Define dataset
        Span<double> data = new double[] { 1.0, 2.0, 2.0, 3.0, 4.0, 5.0 };

        // Compute sum
        double sum = data.Sum();
        Console.WriteLine("Sum: " + sum);

        // Compute average
        double average = data.Average();
        Console.WriteLine("Average: " + average);

        // Compute median
        double median = data.Median();
        Console.WriteLine("Median: " + median);

        // Compute mode
        double mode = data.Mode();
        Console.WriteLine("Mode: " + mode);

        // Compute variance
        var (mean, variance) = data.Variance();
        Console.WriteLine("Variance: " + variance);

        // Compute standard deviation
        double standardDeviation = data.StandardDeviation();
        Console.WriteLine("Standard Deviation: " + standardDeviation);

        // Compute coefficient of variation
        double coefficientOfVariation = data.CoefficientOfVariation();
        Console.WriteLine("Coefficient of Variation: " + coefficientOfVariation);

        // Compute all statistics
        var (meanAll, medianAll, modeAll, varianceAll, standardDeviationAll, coefficientOfVariationAll) = data.CalculateAllStatistics();

        Console.WriteLine($"Mean: {meanAll}, Median: {medianAll}, Mode: {modeAll}, Variance: {varianceAll}, Standard Deviation: {standardDeviationAll}, Coefficient of Variation: {coefficientOfVariationAll}");
    }
}