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- probability - What is the difference between a Poisson and an . . .
As A S 's comment indicates, both distributions relate to the same kind of process (a Poisson process), but they govern different aspects: The Poisson distribution governs how many events happen in a given period of time, and the exponential distribution governs how much time elapses between consecutive events
- probability - Cumulative Distribution function of a Poisson . . .
Hence, by the Fundamental Theorem of Calculus, $$ P(X \leq n) = P(X \leq n)(\lambda=0) - \int_0^{\lambda} p_n(x) \, dx $$ The first term is $1$ since a Poisson distribution with parameter $0$ takes the value $0$ with probability $1$, the second is the integral given in the answer
- Relationship between poisson and exponential distribution
Exponential pdf can be used to model waiting times between any two successive poisson hits while poisson models the probability of number of hits Poisson is discrete while exponential is continuous distribution It would be interesting to see a real life example where the two come into play at the same time $\endgroup$ –
- Why is Poisson regression used for count data?
Poisson distributed data is intrinsically integer-valued, which makes sense for count data Ordinary Least Squares (OLS, which you call "linear regression") assumes that true values are normally distributed around the expected value and can take any real value, positive or negative, integer or fractional, whatever
- Difference between Poisson processes and Poisson distribution
A Poisson process can do much better since indeed it answer to the question : What is the probability to
- probability - What is the connection between binomial and poisson . . .
So Poisson distribution is a limiting binomial distribution with $\lambda$ being the average rate (that is
- Poisson or quasi poisson in a regression with count data and . . .
So now, I'm trying a regression with Poisson Errors With a model with all significant variables, I get: Null deviance: 12593 2 on 53 degrees of freedom Residual deviance: 1161 3 on 37 degrees of freedom AIC: 1573 7 Number of Fisher Scoring iterations: 5 Residual deviance is larger than residual degrees of freedom: I have overdispersion
- Derivation of the variance of the Poisson distribution
Finding the Mean, Variance, and Probability of a Poisson Model 3 For a Poisson model, show that the sample mean $\overline X$ is an unbiased estimator of $\lambda$
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