Module_Statistics_Distribution

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Statistics module

Distribution

Vorcyc.Mathematics.Statistics.Distribution is a class that provides methods for computing various probability distributions, including normal, Poisson, exponential, binomial, multinomial, Gamma, and Beta distributions.

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

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📒Contents

• 🔖 NormalPDF method
• 🔖 NormalCDF method
• 🔖 PoissonPMF method
• 🔖 PoissonCDF method
• 🔖 ExponentialPDF method
• 🔖 ExponentialCDF method
• 🔖 BinomialPMF method
• 🔖 BinomialCDF method
• 🔖 MultinomialPMF method
• 🔖 GammaPDF method
• 🔖 GammaCDF method
• 🔖 BetaPDF method
• 🔖 BetaCDF method

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Vorcyc.Mathematics.Statistics.Distribution class

Vorcyc.Mathematics.Statistics.Distribution is a class that provides methods for computing various probability distributions, including normal, Poisson, exponential, binomial, multinomial, Gamma, and Beta distributions.

Methods

1. NormalPDF method

• public static T NormalPDF<T>(T x, T mean, T stdDev) where T : IFloatingPointIeee754<T>
  • Computes the probability density function of the normal distribution.
  • Parameters:
    • x: The variable value.
    • mean: The mean.
    • stdDev: The standard deviation.
  • Returns: The probability density value of the normal distribution.

2. NormalCDF method

• public static T NormalCDF<T>(T x, T mean, T stdDev) where T : IFloatingPointIeee754<T>
  • Computes the cumulative distribution function of the normal distribution.
  • Parameters:
    • x: The variable value.
    • mean: The mean.
    • stdDev: The standard deviation.
  • Returns: The cumulative distribution value of the normal distribution.

3. PoissonPMF method

• public static T PoissonPMF<T>(int k, T lambda) where T : IFloatingPointIeee754<T>
  • Computes the probability mass function of the Poisson distribution.
  • Parameters:
    • k: The number of event occurrences.
    • lambda: The average rate of events per unit time.
  • Returns: The probability mass value of the Poisson distribution.

4. PoissonCDF method

• public static T PoissonCDF<T>(int k, T lambda) where T : IFloatingPointIeee754<T>
  • Computes the cumulative distribution function of the Poisson distribution.
  • Parameters:
    • k: The number of event occurrences.
    • lambda: The average rate of events per unit time.
  • Returns: The cumulative distribution value of the Poisson distribution.

5. ExponentialPDF method

• public static T ExponentialPDF<T>(T x, T lambda) where T : IFloatingPointIeee754<T>
  • Computes the probability density function of the exponential distribution.
  • Parameters:
    • x: The variable value.
    • lambda: The distribution parameter.
  • Returns: The probability density value of the exponential distribution.

6. ExponentialCDF method

• public static T ExponentialCDF<T>(T x, T lambda) where T : IFloatingPointIeee754<T>
  • Computes the cumulative distribution function of the exponential distribution.
  • Parameters:
    • x: The variable value.
    • lambda: The distribution parameter.
  • Returns: The cumulative distribution value of the exponential distribution.

7. BinomialPMF method

• public static T BinomialPMF<T>(int k, int n, T p) where T : IFloatingPointIeee754<T>
  • Computes the probability mass function of the binomial distribution.
  • Parameters:
    • k: The number of successes.
    • n: The total number of trials.
    • p: The probability of success on each trial.
  • Returns: The probability mass value of the binomial distribution.

8. BinomialCDF method

• public static T BinomialCDF<T>(int k, int n, T p) where T : IFloatingPointIeee754<T>
  • Computes the cumulative distribution function of the binomial distribution.
  • Parameters:
    • k: The number of successes.
    • n: The total number of trials.
    • p: The probability of success on each trial.
  • Returns: The cumulative distribution value of the binomial distribution.

9. MultinomialPMF method

• public static T MultinomialPMF<T>(int[] counts, T[] probabilities) where T : IFloatingPointIeee754<T>
  • Computes the probability mass function of the multinomial distribution.
  • Parameters:
    • counts: The count for each category.
    • probabilities: The probability for each category.
  • Returns: The probability mass value of the multinomial distribution.

10. GammaPDF method

• public static T GammaPDF<T>(T x, T shape, T scale) where T : IFloatingPointIeee754<T>
  • Computes the probability density function of the Gamma distribution.
  • Parameters:
    • x: The variable value.
    • shape: The shape parameter.
    • scale: The scale parameter.
  • Returns: The probability density value of the Gamma distribution.

11. GammaCDF method

• public static T GammaCDF<T>(T x, T shape, T scale) where T : IFloatingPointIeee754<T>
  • Computes the cumulative distribution function of the Gamma distribution.
  • Parameters:
    • x: The variable value.
    • shape: The shape parameter.
    • scale: The scale parameter.
  • Returns: The cumulative distribution value of the Gamma distribution.

12. BetaPDF method

• public static T BetaPDF<T>(T x, T alpha, T beta) where T : IFloatingPointIeee754<T>
  • Computes the probability density function of the Beta distribution.
  • Parameters:
    • x: The variable value.
    • alpha: Shape parameter α.
    • beta: Shape parameter β.
  • Returns: The probability density value of the Beta distribution.

13. BetaCDF method

• public static T BetaCDF<T>(T x, T alpha, T beta) where T : IFloatingPointIeee754<T>
  • Computes the cumulative distribution function of the Beta distribution.
  • Parameters:
    • x: The variable value.
    • alpha: Shape parameter α.
    • beta: Shape parameter β.
  • Returns: The cumulative distribution value of the Beta distribution.

Code example

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

using System;
using Vorcyc.Mathematics.Statistics;

public class DistributionExample
{
    public static void Main()
    { 
        // Normal distribution example
        double normalPDF = Distribution.NormalPDF(1.0, 0.0, 1.0); 
        double normalCDF = Distribution.NormalCDF(1.0, 0.0, 1.0); 
        Console.WriteLine($"Normal PDF: {normalPDF}, Normal CDF: {normalCDF}");

      // Poisson distribution example
        double poissonPMF = Distribution.PoissonPMF(3, 2.0);
        double poissonCDF = Distribution.PoissonCDF(3, 2.0);
        Console.WriteLine($"Poisson PMF: {poissonPMF}, Poisson CDF: {poissonCDF}");

        // Exponential distribution example
        double exponentialPDF = Distribution.ExponentialPDF(1.0, 1.0);
        double exponentialCDF = Distribution.ExponentialCDF(1.0, 1.0);
        Console.WriteLine($"Exponential PDF: {exponentialPDF}, Exponential CDF: {exponentialCDF}");

        // Binomial distribution example
        double binomialPMF = Distribution.BinomialPMF(2, 5, 0.5);
        double binomialCDF = Distribution.BinomialCDF(2, 5, 0.5);
        Console.WriteLine($"Binomial PMF: {binomialPMF}, Binomial CDF: {binomialCDF}");

        // Multinomial distribution example
        int[] counts = { 2, 3, 1 };
        double[] probabilities = { 0.2, 0.5, 0.3 };
        double multinomialPMF = Distribution.MultinomialPMF(counts, probabilities);
        Console.WriteLine($"Multinomial PMF: {multinomialPMF}");

        // Gamma distribution example
        double gammaPDF = Distribution.GammaPDF(2.0, 2.0, 2.0);
        double gammaCDF = Distribution.GammaCDF(2.0, 2.0, 2.0);
        Console.WriteLine($"Gamma PDF: {gammaPDF}, Gamma CDF: {gammaCDF}");

        // Beta distribution example
        double betaPDF = Distribution.BetaPDF(0.5, 2.0, 2.0);
        double betaCDF = Distribution.BetaCDF(0.5, 2.0, 2.0);
        Console.WriteLine($"Beta PDF: {betaPDF}, Beta CDF: {betaCDF}");
    }
}