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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Joint Models - compound poisson

Let's say I have a longitudinal process that I can dicotomize as 0/1 depending on a literature established cutoff. I would be interested in modelling the number of events occurring for each individual ...
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Compounding Gamma with Gamma to yield F-distribution?

I am working through some problems from my Bayesian Statistics course and am having trouble understanding a step in the solution to a question. For reference this is the question: And here is the ...
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How does posterior predictive mean depend on parameters of the likelihood and prior distribution?

I have come across a problem in my research which deals with the mean of the posterior predictive distribution, i.e. $$p(x'|x)=\int d\theta p(x'|\theta)p(\theta|x)$$ where $x$ is an observed sample ...
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Which compound distributions of common discrete random variables have closed-form solutions?

I'm interested in modeling a number of processes that are chains of compounded distributions, i.e. $x \sim F(x|y)$, $y \sim G(z)$ etc., where the distributions $F$, $G$, etc. are common exponential ...
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How to specify a parameters for Gamma distribution?

I have a task: A frequency claim distribution, $K$ is a compound Poisson-Gamma distribution. The mean of the Poisson distribution is gamma distributed with mean equal to 1 and variation equal 2. Find ...
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Monte Carlo for Dirichlet Multinomial Model

Problem I am trying to implement Markov Chain Monte Carlo for the Dirichlet Multinomial mixture, described in this reference (where one used the expectation maximization algorithm). The model is as ...
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1 vote
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1 vote
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Compound Poisson process for demand

I have a demand pattern for a service part. Demand event rate of this part is Poisson distributed. Demand of the part is 3 times in a year. So the demand event rate is 0.25/Month. Each demand ...
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228 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 ...
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Compound Poisson random variable

A compound Poisson random variable $S$ is defined as: $S=\displaystyle\sum^N_{i=1}X_i,$ where $N$ is a random draw from a Poisson distribution with intensity parameter $\lambda$, and $X_i$ are ...
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Characteristic Function of a Compound Poisson Process

The definition of a compound Poisson process and its characteristic function I have are the following: Let $\lambda>0$ and $N\sim\text{Poisson}(\lambda T)$. Also, $\{X_i\}_{i=1}^N$ are i.i.d. ...
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 ...
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1 vote
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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 ...
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PMF of compound Poisson process?

Can I obtain an analytic expression for PMF of compound Poisson process? $Y_t = \sum \limits_{i=1}^{X_t} D_i$, where $X_t \sim \mathcal{Poisson}(\lambda)$ and $D \sim \mathcal{Geometric}(\rho)$.
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Can I estimate Variance of Gamma from Negative Binomial distribution distributed data, given NB is Gamma-Poisson compound

I believe the data I have follows Negative Binomial distribution (over-dispersed Poisson). We know Negative Binomial is a Gamma-Poisson compound distribution. The variance of this Gamma distribution ...
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