# 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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### Poisson Gamma Mixture = Negative Binomially Distributed?

This paper introduces a model called "Beta-Geometric / NBD" which models "repeat-buying behavior in settings where customer “dropout” is unobserved: It assumes that customers buy at a ...
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I want to know the theoretical distribution of a mixture of exponential distributions whose rate parameters are distributed according to a gamma distribution: $$y\sim\text{Exp}(\theta), \quad\text{... 2 votes 0 answers 421 views ### Compound Distributions --- Basic Techniques and Key General Results from First Principles Could someone please point me to a source with notation, terminology, key results and basic techniques to approach compound distributions? Definition Compound probability distribution is the ... 1 vote 0 answers 360 views ### Compound Distribution --- Uniform Distribution with Normally Distributed Parameters Could someone please point me to a source or suggest ways in which we can obtain the Distribution, Density Functions, Expected Value, etc. of a Uniform Distribution whose parameters are distributed ... 4 votes 2 answers 226 views ### What is the distribution of a Poisson variable, where the Poisson rate is Normal (or Binomial)? What is the distribution of X if$$ X \sim \text{Poisson}(\lambda), \quad \text{where }\lambda \sim N(\mu,\sigma^2)$$or$$ X \sim \text{Poisson} (\lambda), \quad \text{where }\lambda \sim ...
I would like to calculate the mean value of a PLN distribution,  f(x;\mu,\sigma)=\frac{1}{x!\sigma\sqrt{2\pi}}\int_{0}^{\infty}\lambda_\ast^{x-1} e^{-\lambda_\ast} e^{-\frac{(log(\lambda_\ast-\mu)^2}...