AddedDistribution

Model a weighted mixture of component distributions.

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Declaration

classdef AddedDistribution < Distribution

Overview

AddedDistribution implements a mixture distribution by combining component densities \(p_i(z)\) with nonnegative weights \(\alpha_i\) that sum to one. The resulting density and cumulative distribution are \(p(z) = \sum_{i=1}^{N} \alpha_i p_i(z),\) \(F(z) = \sum_{i=1}^{N} \alpha_i F_i(z),\) and the stored total variance is the weighted sum \(\mathrm{variance} = \sum_{i=1}^{N} \alpha_i \, \mathrm{variance}_i.\) When scalings is supplied as a scalar, the constructor interprets it as the first weight in a two-component mixture and expands it to \([\alpha, 1-\alpha].\)

distribution = AddedDistribution(scalings=[0.2 0.8], distributions=[NormalDistribution(sigma=2.0); StudentTDistribution(nu=4.5, sigma=1.0)]);

Topics

• Compose distributions
  • AddedDistribution Create a weighted mixture from two or more distributions.
  • distributions Component distributions used in the mixture model.
  • scalings Mixture weights \(\alpha_i\) for the component distributions.

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