Contents

# Discrete Distribution

#### What is a Discrete Distribution?

A discrete distribution is a probability distribution of data that shows the probabilities of discrete outcomes. Discrete values are can be represented by countable positive integers such as 1, 2, 10, 50, etc.

There are many types of discrete distributions. The most common ones include binomial, Poisson, Bernoulli, Rademacher, and multinomial. They can also be of part distributions that are partly discrete and partly continuous.

Discrete distributions also result from samples of larger populations, where each sample point has a discrete probability value. Similarly, they arise from certain modeling techniques such as Monte Carlo simulation.

#### Why are Discrete Distributions Important?

Discrete distributions are widely used in many areas of science and technology as they have good practical value. For example, they are used by businesses to manage inventories and model sales, by researchers to obtain results from data samples, by economists to analyze the state of an economy from sample-based studies, and more.

In science, one well-known example is the Boltzman distribution, which is used to describe the probabilities of the energy levels of a system in thermal equilibrium. This distribution also has a continuous version and is the base of other distributions, such as the Gibbs distribution and the Maxwell-Boltzmann distribution.

In machine learning, discrete distributions find many applications, such as in the modeling of binary and multi-class classification problems.

#### Discrete Distribution + LogicPlum

Discrete distributions are a central tool in statistics and machine learning. Thus, knowledge about them is something that every specialist must have. However, there are many areas – such as business – where interested parties usually lack the necessary statistical and mathematical knowledge.

LogicPlum’s platform provides a practical tool for those who are interested in modeling but don’t have the necessary background. This system handles all calculations automatically, requiring minimal or no human intervention, and selecting the best alternative among hundreds of possible solutions. Additionally, it provides users with an automatically generated report and a blueprint that together describe in detail the main aspects of the obtained model.

LogicPlum’s platform, thus, empowers people and organizations to take advantage of the latest modeling techniques, and use their professional knowledge to interpret the obtained results.

##### Guide to further reading

Brownlee, J. (2020). *Discrete Probability Distributions for Machine Learning*. Available at https://machinelearningmastery.com/discrete-probability-distributions-for-machine-learning/