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How to Choose Poisson Time Interval - Cross Validated A Poisson process is one where mean = var = λ How do you decide what time interval fulfills these criteria when fitting the Poisson distribution to a process? Can all processes be modeled as Poisson
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? - Cross Validated 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
r - Rule of thumb for deciding between Poisson and negative binomal . . . The Poisson distribution implies so a one-sample test can provide a P -value for testing Poisson vs negative binomial Another test for equidispersion is the Lagrange Multiplier which follows a one-degree distribution under the null
Estimating $\lambda$ in a Poisson Distribution from a set of data Since the mean of the Poisson distribution is $\lambda$, you can use this to estimate $\lambda$ The "theoretical" values in the table are then obtained using the formula for the Poisson distribution, $$\mathbb P (X=x) = e^ {-\lambda} \frac {\lambda^x} {x!}$$ Note that $\lambda^x$ is in the numerator, not denominator
Why Specifically Use Poisson Regression For Count Data? Why should Poisson Regression be used for Count Data instead of a "vanilla linear regression"? I understand the basic argument : Count Data is by definition discrete and you would rather use a model in which predictions are always discrete (i e Poisson Regression) but to me, this seems like a formality