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Jachym.Barvinek committed Nov 29, 2024
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8 changes: 4 additions & 4 deletions _posts/2024-10-17-counting-events.md
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Expand Up @@ -174,10 +174,10 @@ for example when we want to count events per day and an event may be recorded at

We can now summarize these analogies into the following table:

| Time model | Waiting time for next event<br>$Y_i$ | Waiting time for $k$-th event<br>$S_k$ | Count of events<br>$N(T)$ |
|---------------------------------|--------------------------------------|----------------------------------------|------------------------------------------------|
| Continuous $T \in \mathbb{R}^+$ | $\mathrm{Exponential}(\lambda)$ | $\mathrm{Erlang}(k, \lambda)$ | $\mathrm{Poisson}(T \lambda)$ |
| Discrete $T \in \mathbb{N}$ | $\mathrm{Geometric}(\lambda)$ | $\mathrm{NegBin}(k, \lambda)$ | $\mathrm{Bin}(T, \lambda)$ |
| Time model | Waiting time for next event<br>$Y_i$ | Waiting time for $k$-th event<br>$S_k$ | Count of events<br>$N(T)$ |
|---------------------------------|--------------------------------------|----------------------------------------|--------------------------------|
| Continuous $T \in \mathbb{R}^+$ | $\mathrm{Exponential}(\lambda)$ | $\mathrm{Erlang}(k, \lambda)$ | $\mathrm{Poisson}(T \lambda)$ |
| Discrete $T \in \mathbb{N}$ | $\mathrm{Geometric}(\theta)$ | $\mathrm{NegBinomial}(k, \theta)$ | $\mathrm{Binomial}(T, \theta)$ |


### Takeaway
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