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In reality, almost nothing is well modelled by the Poisson distribution The Poisson distribution has only one parameter, so it can fit mean behaviour of a process but it cannot model the variance of a …

The Poisson distribution keeps track of counts of things, and it has support $n = 0,1,2,...$, so you wouldn't use it to measure a binary event (e.g., whether it will rain tomorrow). You would use it …

Without observing actual data from those sports, what you are talking about are essentially just prior beliefs about what the processes might plausibly look like. Ultimately you will need to test the …

Let $T_1$ and $T_2$ be the waiting times for each car. You are trying to find $T \equiv \max (T_1, T_2)$. For this type of problem it is fairly simple to obtain the result by working with the CDFs. …

This is a hyperparameter arising in a mixture representation of the prior For hierarchical Bayesian models of this kind, the parameter $\beta$ is what we usually call a hyperparameter. A hyperparamet …

You should incorporate your estimate of the shift into your analysis As others have pointed out, no, this is not a Poisson distribution (it is actually a shifted Poisson distribution). The bigger iss …

Quantile function: If you already have the CDF $F$ available, you can write the quantile function for the Poisson distributon as: $$\begin{align} Q(p) &\equiv \inf \Big\{ x = 0,1,2,... \Big| \ p \leq …