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Relationship between poisson and exponential distribution Note, that a poisson distribution does not automatically imply an exponential pdf for waiting times between events This only accounts for situations in which you know that a poisson process is at work But you'd need to prove the existence of the poisson distribution AND the existence of an exponential pdf to show that a poisson process is a suitable model!
Derivation of the variance of the Poisson distribution Is this derivation of the Poisson variance correct? I mainly want to make sure I'm applying the Law of the Unconscious Statistician (LOTUS) correctly $ Var[X] = E[X^2] - E[X]^2 $ $ = E[X^2] - \\
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 Finally, logistic regression only works for data that is 0-1-valued (TRUE-FALSE
What advantages does Poisson regression have over linear regression in . . . Poisson regression would be more suitible in this case because your response is the count of something Putting things simply, we model that the distribution of number of awards for an individual student comes from a poisson distribution, and that each student has their own λ λ poisson parameter The Poisson regression then relates this parameter to the explanatory variables, rather than the
How to interpret coefficients in a Poisson regression? This was in discussions of interpreting logistic regression coefficients, but Poisson regression is similar if you use an offset of time at risk to get rates You add first all the coefficients (including the intercept term) times eachcovariate values and then exponentiate the resulting sum
Difference-in-difference with Poisson regression - Cross Validated You can do DiD with Poisson regression, so long as you calculate the difference in means with marginal effects Now, DiD has a very rich literature, so I will focus only on the simplest case -- two periods, two groups
probability - Distribution of Event Times in a Poisson Process . . . I am trying to learn how to prove the following: if we know k events occurred in a Poisson process between times t1 and t2, the exact times of these events are uniformly distributed Normally, everyone talks about the distribution of interarrival times in a Poisson Process are Exponential but what about the distribution of the actual event times? I tried to show this below In a Poisson