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Relationship between poisson and exponential distribution The waiting times for poisson distribution is an exponential distribution with parameter lambda But I don't understand it Poisson models the number of arrivals per unit of time for example How i
probability - When to use Binomial Distribution vs. Poisson . . . Poisson distribution a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and or space if these events occur with a known average rate and independently of the time since the last event
Why is Poisson regression used for count data? I understand that for certain datasets such as voting it performs better Why is Poisson regression used over ordinary linear regression or logistic regression? What is the mathematical motivation
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
r - Rule of thumb for deciding between Poisson and negative binomal . . . The Poisson distribution implies z ∼ N(0, 1) z ∼ N (0, 1) so a one-sample t t test can provide a P -value for testing Poisson vs negative binomial Another test for equidispersion is the Lagrange Multiplier (∑(μ2 i) − ny¯)2 (2 ∑μ2 i) (∑ (μ i 2) n y) 2 (2 ∑ μ i 2) which follows a one-degree χ2 χ 2 distribution under the null
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
What is the relationship between poisson, gamma, and exponential . . . Poisson and exponential distributions are very strongly related but they're fundamentally different because the Poisson is discrete (a count variable) and the exponential is continuous (a waiting time) So how are they related? If the time between a certain type of event is exponentially distributed with rate λ λ, then the number of events in a given time period of length t t follows a