Common Probability Distributions in Finance › Summary

The normal distribution provides a tractable baseline, while the lognormal distribution connects normal log changes to positive modeled prices. Binomial and Poisson distributions address different discrete questions: a fixed number of trials versus event counts over an interval. Student's t and power-law models make slower tail decay explicit, but their parameters and moment conditions must be checked rather than assumed.

No distribution is selected by its name alone. The relevant variable, horizon, dependence structure, evidence, and decision determine whether its assumptions are useful.