Class BetaDistribution

java.lang.Object
cloud.opencode.base.math.distribution.BetaDistribution
public final class BetaDistribution extends Object
Immutable Beta distribution. 不可变 Beta 分布

Provides PDF, CDF, inverse CDF (quantile function), mean, and variance. Thread-safe: instances are immutable.

提供概率密度函数、累积分布函数、逆累积分布函数（分位函数）、均值和方差。 线程安全：实例不可变。

Since:
JDK 25, opencode-base-math V1.0.3
Author:
Leon Soo www.LeonSoo.com
See Also:

  • Method Summary

    Modifier and Type
    Method
    Description
    double
    alpha()
    Returns the alpha (first shape) parameter.
    double
    beta()
    Returns the beta (second shape) parameter.
    double
    cdf(double x)
    Computes the cumulative distribution function (CDF) at x.
    double
    inverseCdf(double p)
    Computes the inverse CDF (quantile function).
    double
    mean()
    Returns the mean of this distribution: alpha / (alpha + beta).
    static BetaDistribution
    of(double alpha, double beta)
    Creates a Beta distribution with the specified parameters.
    double
    pdf(double x)
    Computes the probability density function (PDF) at x.
    String
    toString()
     
    double
    variance()
    Returns the variance of this distribution: alpha*beta / ((alpha+beta)^2 * (alpha+beta+1)).

    Methods inherited from class Object

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

  • Method Details

    • of

      public static BetaDistribution of(double alpha, double beta)
      Creates a Beta distribution with the specified parameters. 创建具有指定参数的 Beta 分布
      Parameters:
      alpha - the first shape parameter, must be > 0 / 第一形状参数，必须 > 0
      beta - the second shape parameter, must be > 0 / 第二形状参数，必须 > 0
      Returns:
      a new BetaDistribution instance / 新的 Beta 分布实例
      Throws:
      IllegalArgumentException - if alpha or beta ≤ 0 or not finite

    • alpha

      public double alpha()
      Returns the alpha (first shape) parameter. 返回 alpha（第一形状）参数
      Returns:
      the alpha parameter / alpha 参数

    • beta

      public double beta()
      Returns the beta (second shape) parameter. 返回 beta（第二形状）参数
      Returns:
      the beta parameter / beta 参数

    • mean

      public double mean()
      Returns the mean of this distribution: alpha / (alpha + beta). 返回此分布的均值：alpha / (alpha + beta)
      Returns:
      the mean / 均值

    • variance

      public double variance()
      Returns the variance of this distribution: alpha*beta / ((alpha+beta)^2 * (alpha+beta+1)). 返回此分布的方差：alpha*beta / ((alpha+beta)^2 * (alpha+beta+1))
      Returns:
      the variance / 方差

    • pdf

      public double pdf(double x)
      Computes the probability density function (PDF) at x. 计算在 x 处的概率密度函数值

      f(x) = x^(alpha-1) * (1-x)^(beta-1) / B(alpha, beta)

      Parameters:
      x - the point at which to evaluate the PDF, should be in [0, 1] / 计算 PDF 的点
      Returns:
      the density at x / x 处的密度值

    • cdf

      public double cdf(double x)
      Computes the cumulative distribution function (CDF) at x. 计算在 x 处的累积分布函数值

      F(x) = I_x(alpha, beta) where I is the regularized incomplete beta function.

      Parameters:
      x - the point at which to evaluate the CDF / 计算 CDF 的点
      Returns:
      the cumulative probability P(X ≤ x) / 累积概率

    • inverseCdf

      public double inverseCdf(double p)
      Computes the inverse CDF (quantile function). 计算逆累积分布函数（分位函数）
      Parameters:
      p - the cumulative probability, must be in (0, 1) / 累积概率，必须在 (0, 1) 内
      Returns:
      the quantile x such that P(X ≤ x) = p / 使得 P(X ≤ x) = p 的分位数
      Throws:
      MathException - if p is not in (0, 1)

    • toString

      public String toString()
      Overrides:
      toString in class Object