Gamma Distribution
=
Tap a term to see what it means, or .
Calculate
Example: on average, 3 customers an hour arrive at a shop. How long until the day's 5th customer, and what is the chance they arrive within 2 hours? Change the values to work out your own case.
Step by step
What each term means
- Density (f(x))
- The height of the curve at x, for x ≥ 0. As in any continuous distribution, probabilities are areas under it.
- Rate to the Power k (λᵏ)
- The rate of events per unit of time, raised to the number of events awaited. Together with Γ(k), it makes the total area equal 1.
- Power of x (xᵏ⁻¹)
- Makes the curve start near zero and rise: it is unlikely that k events all happen in a very short time. With k = 1 it vanishes, leaving the exponential.
- Decay (e^(−λx))
- Makes the curve fall for long times, as in the exponential.
- Gamma Function (Γ(k))
- The generalization of the factorial: Γ(k) = (k − 1)! for integer k. It lets the shape k be any positive number.