Probability Distributions

A continuous distribution for probabilities or proportions bounded between 0 and 1.

Discrete probability of k successes in n independent Bernoulli trials with probability p.

A heavy-tailed distribution where mean and variance are undefined. Educational for understanding pathological distributions.

Used to test if data fits a model (goodness of fit) or if variables are independent.

Models the time between independent events that happen at a constant average rate.

Used in ANOVA and regression analysis to compare variances between groups.

A flexible distribution for positive continuous data, often used to model waiting times and rainfall.

The number of failures before the first success in independent Bernoulli trials.

A distribution of a random variable whose logarithm is normally distributed. Common in finance and biology.

Models the number of failures before achieving a fixed number of successes. Common for overdispersed count data.

A bell-shaped, symmetric distribution for real‑valued variables. The mean sets the center and the standard deviation controls the spread.

A power-law distribution modeling wealth, city sizes, and the famous 80-20 rule.

Discrete probability of a given number of events occurring in a fixed interval.

Similar to the normal distribution but with heavier tails; used for estimating means of small samples.

A continuous distribution where all intervals of the same length are equally probable.

A versatile distribution for reliability engineering, modeling time-to-failure and survival analysis.