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This graph shows the data as a ''time series'':
This graph shows the data as a ''time series'':
[[File:Barrie time series.jpg|border|700 px]]
[[File:Barrie time series.jpg|border|600 px]]
The number of times each depth of storm occured can be counted and grouped like this:
The number of times each depth of storm occured can be counted and grouped like this:
[[File:Picture1.jpg|border|700 px]]
[[File:Picture1.jpg|border|600 px]]
These same data can be fitted to a single equation which would then allow predictions to be made. In this example an exponential distribution function has been selected and an [https://www.wessa.net/rwasp_fitdistrexp.wasp online tool] used to find the fitting parameter 'λ'.
These same data can be fitted to a single equation which would then allow predictions to be made. In this example an exponential distribution function has been selected and an [https://www.wessa.net/rwasp_fitdistrexp.wasp online tool] used to find the fitting parameter 'λ'.
<math>f\left(x,\lambda\right)=\lambda e^{-\lambda x}</math>
<math>f\left(x,\lambda\right)=\lambda e^{-\lambda x}</math>
The fitting found λ to be 0.11. When the equation is plotted, the graph looks like this:
[[File:Barrie prob.jpg|border|600 px]]
But the patterns aren't very easy to understand like this. The cumulative distribution function uses the same λ and is often a more useful way to understand the data.
<math>F\left(x,\lambda\right)=1- e^{-\lambda x}</math>
Plotted, it looks like this: