Class Complex128BiGaussian

java.lang.Object
org.flag4j.rng.distributions.Distribution<Complex128,RandomComplex>
org.flag4j.rng.distributions.Complex128BiGaussian
public class Complex128BiGaussian extends Distribution<Complex128,RandomComplex>
A 2D bivariate Gaussian distribution on the complex plane.

The covariance matrix, \( \mathbf{\Sigma } \), of such a distribution is expressed as: \[ \mathbf{\Sigma} = \begin{bmatrix} \sigma_x^2 & \rho\sigma_x\sigma_y \\ \rho\sigma_x\sigma_y & \sigma_y^2 \end{bmatrix} \] where \( \rho \) is the correlation coefficient, \( \sigma _{x} \) is the standard deviation along the real axis, and \( \sigma _{y} \) is the standard deviation along the imaginary axis. Let \( \pmb{\mu} = \begin{bmatrix} x_0 & y_0 \end{bmatrix}^T \) be the mean column vector and \( \mathbf{z} = \begin{bmatrix} x & y \end{bmatrix}^T \) also be a column vector. Then, the PDF of the bivariate Gaussian distribution may be expressed as: \[ f(\mathbf{z}) = \frac{1}{2\pi \sqrt{\det(\mathbf{\Sigma})}} \exp\left[ -\frac{1}{2} (\mathbf{z} - \pmb{\mu})^T \mathbf{\Sigma}^{-1}(\mathbf{z} - \pmb{\mu})\right] \]

See Also:

  • Field Summary

    Fields inherited from class org.flag4j.rng.distributions.Distribution

    rng

  • Constructor Summary

    Constructors
    Constructor
    Description
    Complex128BiGaussian(RandomComplex rng, double meanRe, double stdRe, double meanIm, double stdIm)
    Constructs 2D bivariate Gaussian distribution on the complex plane with a correlation coefficient of zero.
    Complex128BiGaussian(RandomComplex rng, double meanRe, double stdRe, double meanIm, double stdIm, double corrCoeff)
    Constructs 2D bivariate Gaussian distribution on the complex plane with a specified correlation coefficient.

  • Method Summary

    Modifier and Type
    Method
    Description
    Complex128
    sample()
    Randomly samples this distribution.

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • Complex128BiGaussian

      public Complex128BiGaussian(RandomComplex rng, double meanRe, double stdRe, double meanIm, double stdIm)
      Constructs 2D bivariate Gaussian distribution on the complex plane with a correlation coefficient of zero. To specify a correlation coefficient use Complex128BiGaussian(RandomComplex, double, double, double, double, double).
      Parameters:
      rng - Pseudorandom number generator to use when randomly sampling from this distribution.
      meanRe - Mean along real axis of complex plane for the distribution.
      stdRe - Standard deviation along real axis of complex plane for the distribution.
      meanIm - Mean along imaginary axis of complex plane for the distribution.
      stdIm - Standard deviation along imaginary axis of complex plane for the distribution.

    • Complex128BiGaussian

      public Complex128BiGaussian(RandomComplex rng, double meanRe, double stdRe, double meanIm, double stdIm, double corrCoeff)
      Constructs 2D bivariate Gaussian distribution on the complex plane with a specified correlation coefficient.
      Parameters:
      rng - Pseudorandom number generator to use when randomly sampling from this distribution.
      meanRe - Mean along real axis of complex plane for the distribution.
      stdRe - Standard deviation along real axis of complex plane for the distribution.
      meanIm - Mean along imaginary axis of complex plane for the distribution.
      stdIm - Standard deviation along imaginary axis of complex plane for the distribution.
      corrCoeff - Correlation coefficient of the bivariate distribution.

  • Method Details