What distributions exist and where are they applied?

In statistics and machine learning, there are many distributions, each describing the probabilistic behavior of data or random variables. Here are the main ones and their applications:

• Normal distribution (Gaussian) — describes many natural and social phenomena (growth of people, measurement errors). Often used in regression, least squares methods.
• Bernoulli distribution — for binary outcomes (success/failure). Used in classification, modeling binary events.
• Binomial distribution — number of successes in independent trials. Used in discrete event problems.
• Poisson distribution — number of events in a fixed interval of time or space. Used in rare event modeling.
• Exponential distribution — waiting time between events in a Poisson process. Used in modeling waiting times.
• Student's t-distribution — used for small samples to estimate the mean.
• Chi-square distribution — used in hypothesis testing and variance estimation.

In machine learning, the choice of distribution is important for building probabilistic models, estimating parameters, and data generation.