Class Distributions

java.lang.Object

org.episteme.core.mathematics.statistics.Distributions

public class Distributions
extends Object

Common probability distributions for statistical analysis.

Provides PDF, CDF, and parameter calculations for various distributions

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Method Summary

Modifier and Type	Method	Description
static Real	binomialCdf(int k, int n, Real p)	Binomial distribution CDF.
static Real	binomialCoefficient(int n, int k)	Binomial coefficient C(n, k).
static Real	binomialPmf(int k, int n, Real p)	Binomial distribution PMF.
static Real	chiSquaredPdf(Real x, int k)	Chi-squared distribution PDF. f(x) = (x^(k/2-1) * e^(-x/2)) / (2^(k/2) * Γ(k/2))
static double	correlation(double[] x, double[] y)	Pearson correlation coefficient for double arrays.
static Real	correlation(Real[] x, Real[] y)	Pearson correlation coefficient.
static double	covariance(double[] x, double[] y)	Covariance for double arrays.
static Real	covariance(Real[] x, Real[] y)	Covariance.
static Real	exponentialCdf(Real x, Real lambda)	Exponential distribution CDF.
static Real	exponentialPdf(Real x, Real lambda)	Exponential distribution PDF. f(x) = λ * e^(-λx) for x ≥ 0
static Real	exponentialQuantile(Real p, Real lambda)	Exponential quantile function.
static double	mean(double[] data)	Sample mean for double array.
static Real	mean(Real[] data)	Sample mean.
static Real	normalCdf(Real x, Real mean, Real stdDev)	Normal distribution CDF (approximation using error function).
static Real	normalPdf(Real x, Real mean, Real stdDev)	Normal distribution PDF. f(x) = (1/σ√2π) * e^(-(x-μ)²/(2σ²))
static Real	poissonCdf(int k, Real lambda)	Poisson distribution CDF.
static Real	poissonPmf(int k, Real lambda)	Poisson distribution PMF.
static Real	standardNormalCdf(Real z)	Standard normal CDF.
static Real	standardNormalPdf(Real z)	Standard normal PDF (μ=0, σ=1).
static Real	standardNormalQuantile(Real p)	Inverse standard normal (quantile function).
static double	stdDev(double[] data)	Sample standard deviation for double array.
static Real	stdDev(Real[] data)	Sample standard deviation.
static double	variance(double[] data)	Sample variance for double array.
static Real	variance(Real[] data)	Sample variance (unbiased).

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

normalPdf

public static Real normalPdf(Real x,
 Real mean,
 Real stdDev)

Normal distribution PDF. f(x) = (1/σ√2π) * e^(-(x-μ)²/(2σ²))

standardNormalPdf

public static Real standardNormalPdf(Real z)

Standard normal PDF (μ=0, σ=1).

normalCdf

public static Real normalCdf(Real x,
 Real mean,
 Real stdDev)

Normal distribution CDF (approximation using error function).

standardNormalCdf

public static Real standardNormalCdf(Real z)

Standard normal CDF.

standardNormalQuantile

public static Real standardNormalQuantile(Real p)

Inverse standard normal (quantile function).

poissonPmf

public static Real poissonPmf(int k,
 Real lambda)

Poisson distribution PMF. P(X=k) = (λ^k * e^(-λ)) / k!

poissonCdf

public static Real poissonCdf(int k,
 Real lambda)

Poisson distribution CDF.

exponentialPdf

public static Real exponentialPdf(Real x,
 Real lambda)

Exponential distribution PDF. f(x) = λ * e^(-λx) for x ≥ 0

exponentialCdf

public static Real exponentialCdf(Real x,
 Real lambda)

Exponential distribution CDF. F(x) = 1 - e^(-λx)

exponentialQuantile

public static Real exponentialQuantile(Real p,
 Real lambda)

Exponential quantile function.

binomialPmf

public static Real binomialPmf(int k,
 int n,
 Real p)

Binomial distribution PMF. P(X=k) = C(n,k) * p^k * (1-p)^(n-k)

binomialCoefficient

public static Real binomialCoefficient(int n,
 int k)

Binomial coefficient C(n, k).

binomialCdf

public static Real binomialCdf(int k,
 int n,
 Real p)

Binomial distribution CDF.

chiSquaredPdf

public static Real chiSquaredPdf(Real x,
 int k)

Chi-squared distribution PDF. f(x) = (x^(k/2-1) * e^(-x/2)) / (2^(k/2) * Γ(k/2))

mean

public static Real mean(Real[] data)

Sample mean.

mean

public static double mean(double[] data)

Sample mean for double array.

variance

public static Real variance(Real[] data)

Sample variance (unbiased).

variance

public static double variance(double[] data)

Sample variance for double array.

stdDev

public static Real stdDev(Real[] data)

Sample standard deviation.

stdDev

public static double stdDev(double[] data)

Sample standard deviation for double array.

covariance

public static Real covariance(Real[] x,
 Real[] y)

Covariance.

covariance

public static double covariance(double[] x,
 double[] y)

Covariance for double arrays.

correlation

public static Real correlation(Real[] x,
 Real[] y)

Pearson correlation coefficient.

correlation

public static double correlation(double[] x,
 double[] y)

Pearson correlation coefficient for double arrays.