Good Morning.
I have recently been faced with modeling a quantity that is best modeled via a Gamma distribution. I have noticed that, in the characterization of the distribution via the parameters $k$ and $θ$, the mean of the distribution is $kθ$, whereas the "top" of the distribution, representing the point that is sampled with the highest probability, is found at point $θ( k - 1)$.
This contradicts my intuition. If the mean represents the expected value of the distribution, then why is it not placed at the "top" of the distribution, much like in the normal distribution?
Thanks,
Jason