Gamma Distribution is a probability distribution used in statistics, mathematical distributions, probability theory, data analysis, and machine learning. It is a continuous distribution that is used to model the waiting time between events. Many real-world phenomena are modeled using Gamma Distribution; therefore, understanding this distribution is crucial.
Gamma Distribution is a continuous distribution that is used to model the waiting time between two events. It is a two-parameter family of curves where the first parameter is known as shape parameter and the second parameter as scale parameter. The shape parameter determines the shape of the curve, while the scale parameter determines its location and variability.
Gamma Distribution has several uses in real-world applications such as:
The probability density function (PDF) of Gamma Distribution is defined as:
$$ f(x|\alpha,\beta) = \frac{x^{\alpha-1}e^{-x/\beta}}{\beta^\alpha\Gamma(\alpha)} $$
where x > 0, $\alpha$ > 0, $\beta$ > 0 and $\Gamma(\cdot)$ denotes the gamma function.
The cumulative distribution function (CDF) can be calculated by integrating PDF from 0 to x.
Some of the properties of Gamma Distribution are:
There are two types of Gamma Distribution:
Standard Gamma Distribution: When $\beta$ = 1, it is known as Standard Gamma Distribution.
Non-standard Gamma Distribution: When $\beta$ $\neq$ 1, it is known as Non-standard Gamma Distribution.
To fit Gamma Distribution to a dataset, we need to estimate the values of shape and scale parameters. These can be estimated using Maximum Likelihood Estimation (MLE) or Method of Moments (MOM). Once the parameters are estimated, we can plot the PDF and CDF of the fitted distribution and compare it with the actual data.
