Composite Probability Distributions

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Abstractions about probability distributions built by combining or decomposing simpler ones — sums of uniforms in the Bates distribution, convolutions of components in the Delaporte and mixture distributions, copula-based joint construction via Sklar's theorem, and distributions that resist such decomposition entirely.

5 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Bates Distribution — The probability distribution of the arithmetic mean of n independent identically distributed uniform random variables, a scaled Irwin–Hall sum.
• Delaporte Distribution — A discrete count distribution formed as the convolution of independent Poisson and negative-binomial components, equivalently a Poisson count with a mean containing fixed and gamma-random parts.
• Indecomposable distribution — An indecomposable probability distribution cannot be represented as the convolution of two non-degenerate probability distributions, making it irreducible with respect to addition of independent random variables.
• Mixture Distribution — A probability law generated by first selecting a latent component according to normalized weights and then sampling from that component.
• Sklar's theorem — Sklar's theorem states that every multivariate distribution can be represented by a copula joining its univariate marginal distributions, with the copula unique when the marginals are continuous.