I have a dataset that represents the difference, in milliseconds, between an input event (a key pressed in a keyboard) and the next one.
I have grouped the data in sets of 25ms, e.g. (0, 25], (25, 50]. When plotted as an histogram this is the result:
- It ranges from 0ms to 2150ms.
- Some of the values of the long tail could be ignored.
- The most frequent set is [75, 100).
Due to its shape, and the nature of the dataset, I am assuming this is an Erlang distribution (which may not be the case).
Questions:
- Is this an Erlang distribution?
- In layman's terms, how could I obtain the k and λ of this Erlang distribution?
This is the first time I learn about this distribution but, if the probability density function is given by $$\frac{\lambda ^k x^{k-1} e^{-\lambda x}}{(k-1)!}$$ it goes through a maximum for $$x_*=\frac{k-1}{\lambda }$$ and, for this value, the value of the probability density function is given by $$\frac{(k-1)^{k-1}}{\lambda~ e^{k-1}~(k-1)! }$$ So, if we guess $x_*$, you have a guess of $\lambda$ as a function of $k$ and you have to solve for $k$ the equation which gives the maximum value.
I hope and wish this could help you for the generation of reasonable and consitent estimates of the parameters.