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.
2
questions
4
votes
2answers
166 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
$$ X \sim \text{Poisson} (\lambda), \quad \text{where }\lambda \sim ...
3
votes
1answer
115 views
Mean of a Poisson-Lognormal Distribution (PLN)
I would like to calculate the mean value of a PLN distribution,
$$
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}...
