Probability Distribution: Probability Distribution can be described as a statistical function which describes all the possible values and likelihoods than a random variable can take within given range. This range lies between the minimum and maximum statistical possible values.
Probability distribution can be classified into two categories parametric and nonparametric.
Parametric Distribution: Distributions, such as a normal distribution which can be described by using a mathematical function and makes assumptions about the parameters of data from which sample can be drawn. These types of distributions make it easier to draw conclusions about the data however; they also make restrictive assumptions which are not necessarily supported by real-world patterns.
Nonparametric distributions: Distributions such as a historical distribution cannot be described by using a mathematical function. Instead of making restrictive assumptions, these types of distributions fit the data perfectly however, without generalizing the data, it can be difficult for a researcher to draw any conclusions.
In the following Sections we will study several Parametric Distributions like:
- Uniform Distribution
- Exponential Distribution
- Log Distribution
- Normal Distribution
- Log-Normal Distribution
- Binomial /Bernoulli Distribution
- Poisson Distribution
We would also look into the application of distribution in finance: Credit Risk or Market Risk.