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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!
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
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 receive k k call per unit of time ? But also to the question : what is the probability to receive a call between t t and t + h t + h ?
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] - \\
probability - What is the connection between binomial and poisson . . . Poisson is also for counting events happening What is the connection between them? I know is that when sample size is large both can be approximated with normal But how are they similar or different? I learned in class their PMF are different but not really understand where does such PMF comes from and intuitive way of explaining them
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