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
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 $\lambda$
How to interpret coefficients in a Poisson regression? Q2: In that case, in a poisson regression, are the exponentiated coefficients also referred to as "odds ratios"? – oort A2: No If it were logistic regression they would be but in Poisson regression, where the LHS is number of events and the implicit denominator is the number at risk, then the exponentiated coefficients are "rate ratios" or
What advantages does Poisson regression have over linear regression in . . . The Poisson regression then relates this parameter to the explanatory variables, rather than the count The reason this is better than normal linear regression is to do with the errors If our model is correct, and each student has their own $\lambda$, then for a given $\lambda$ we would expect a poisson distribution of counts around it - i e