This distribution is one of the most used distributions. It is preferred over other distributions because it is a relation between exponential and normal distribution. This is a two-parameter distribution, and exponential, erlang distribution and chi-square are special cases of this distribution. This distribution is based on gamma function, which is an extension of the factorial, it is denoted by,
And its graph looks like this,
This is the gamma functions graph for real values plotted on both axes.
The gamma distribution is defined as the continuous random variable x is said to be gamma distribution with parameters α > 0 and λ > 0, shown as x ≈ gamma (α, λ).
Now, let’s have a look at some properties of gamma function,
- Γ (α) = ∫0∞ xα-1e-xdx
- Γ(α+1) = αΓ(α)
- Γ(1/2) = √π.
These are some of the properties that we should know while using or handling the gamma function. This distribution has some applications which are written below,
- The amount of water gathered in the tank.
- The size of loan defaulters.
- The flow of manufacturing of items in the factory.
- The load on the web servers.
