# Questions tagged [compound-distributions]

When a random variable is distributed according to some parameterized distribution, where the parameter itself is a random variable. Also known as a "mixture" distribution, but the term "mixture" also has other senses in statistics.

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### Maximum likelihood estimate for multivariate sum of normal distributions

For each $j = 1,\dots,N$, let $\mu_j \in \mathbb{R}^N$ denote a known column vector, $\Sigma_j \in \mathbb{R}^{N\times N}$ a known covariance matrix, and $\theta_j \in \mathbb{R}$ an unknown parameter,...
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### Compendium or catalog of compound distributions?

Does anyone know of a good compendium or catalog of compound distributions, or finite mixture representations of those distributions? I am trying to find out to what extent the common multi-...
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### Compounding a gamma distribution with another distribution to yield a gamma

I have a gamma distributed random variable $X$, with its mean $\mu$ distributed as some other function $$X \sim \text{Gamma}(\mu,k)\\ \mu \sim P(\theta)$$ What is the distribution $P(\theta)$ such ...
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### When can a finite mixture of distributions drawn from a distributional family be well-described by a distribution from the same family?

This question is motivated by a situation that we frequently encounter in economic variables. We believe that the overall distribution of some variable is well approximated by a particular ...
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### Compound Distributions --- Basic Techniques and Key General Results from First Principles

Could someone please point me to a source with notation, terminology, key results and basic techniques to approach compound distributions? Definition Compound probability distribution is the ...
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### Sampling Variance of Sample Proportion with a Discarded Outcome

Question: A random experiment with three exhaustive and mutually exclusive outcomes $A, B, C$ is performed $n$ times, resulting in a sample of outcomes $X_1, X_2, \ldots, X_n$. The following statistic ...