What is gamma distribution?

The gamma distribution is a continuous probability distribution that models the waiting time for a certain number of events to occur.

The gamma distribution is often used in reliability analysis, queuing theory, and finance. It is a two-parameter distribution, with the shape parameter (α) and the rate parameter (β). The probability density function (PDF) of the gamma distribution is given by:

f(x) = (β^α / Γ(α)) * x^(α-1) * e^(-βx)

where x ≥ 0, β > 0, and Γ(α) is the gamma function.

The mean and variance of the gamma distribution are given by:

μ = α/β
σ^2 = α/β^2

The gamma distribution can be used to model the waiting time for a certain number of events to occur. For example, if we are waiting for a certain number of customers to arrive at a store, we can use the gamma distribution to model the waiting time until the desired number of customers arrive.

The gamma distribution is also related to the exponential distribution. If α = 1, then the gamma distribution reduces to the exponential distribution. The exponential distribution models the waiting time for a single event to occur, while the gamma distribution models the waiting time for multiple events to occur.