Index: The Book of Statistical Proofs ▷ Statistical Models ▷ Count data ▷ Poisson distribution with exposure values ▷ Definition

Definition: A Poisson distribution with exposure values is defined as a set of observed counts $y = \left\lbrace y_1, \ldots, y_n \right\rbrace$, independently distributed according to a Poisson distribution with common rate $\lambda$ and a set of concurrent exposures $x = \left\lbrace x_1, \ldots, x_n \right\rbrace$:

\[\label{eq:Poiss-exp} y_i \sim \mathrm{Poiss}(\lambda x_i), \quad i = 1, \ldots, n \; .\]
 
Sources:
  • Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB (2014): "Other standard single-parameter models"; in: Bayesian Data Analysis, 3rd edition, ch. 2.6, p. 45, eq. 2.14; URL: http://www.stat.columbia.edu/~gelman/book/.

Metadata: ID: D42 | shortcut: poissexp | author: JoramSoch | date: 2020-03-22, 22:57.