Common Probability Distributions

Standard distributions include discrete examples (Bernoulli, Binomial, Poisson) and continuous examples (Normal, Exponential, Gamma, Beta, Uniform). Each distribution has mathematical properties that make it suitable for modeling different types of random phenomena in the real world.

In machine learning applications:

• Normal distributions underlie linear regression, many neural network outputs, and regularization techniques.
• Bernoulli and Binomial distributions form the basis for logistic regression and binary classification.
• Poisson distributions model count data in applications like customer arrival prediction.
• Exponential and Weibull distributions help with survival analysis and reliability modeling.
• Dirichlet distributions provide priors for topic models and multinomial processes.

Selecting the appropriate probability distribution for your data is a critical step in building accurate and well-calibrated machine learning models.