DISTRIBUTIONS

This distribution assigns equal probability to a finite set of outcomes. It is used for scenarios where each outcome is equally likely, such as rolling a fair die

This distribution represents a single trial with two possible outcomes: success (1) or failure (0). It is used to model binary outcomes, like flipping a coin.

This distribution represents the number of successes in a fixed number of independent Bernoulli trials. It is used for modeling the number of successes in a series of yes/no experiments.

This distribution represents the number of events occurring within a fixed interval of time or space. It is used for modeling the number of events in a given time period, such as the number of phone calls received by a call center.

This distribution represents the number of failures before a specified number of successes in a series of Bernoulli trials. It is used for modeling over-dispersed count data or the number of attempts until a target number of successes is achieved

This distribution represents the number of trials needed to get the first success in a series of independent Bernoulli trials

This distribution represents the number of successes in a sample drawn without replacement from a finite population. It is used for scenarios where sampling is without replacement, like drawing cards from a deck

This distribution assigns equal probability to all values in a continuous range. It is used for scenarios where all outcomes in a range are equally likely, such as random number generation

This distribution is symmetric and bell-shaped, characterized by its mean and standard deviation. It is used for modeling natural phenomena and measurement errors, as it describes many real-world variables

The t distribution is used for inference about means when the population variance is unknown and the sample size is small

The chi-squared distribution is fundamental in hypothesis testing, goodness-of-fit tests, and confidence intervals for variance

The F distribution is used to compare variances and is fundamental in ANOVA and regression analysis

This distribution represents the time between events in a Poisson process. It is used for modeling time to failure or the time between events, such as the lifespan of an electronic component

This distribution generalizes the exponential distribution with an additional shape parameter. It is used for modeling waiting times and life data analysis, such as the time until multiple events occur

This distribution is flexible with scale and shape parameters, often used to model life data. It is used for reliability analysis and failure time analysis in engineering and survival studies

The beta distribution models random variables constrained to the interval [0,1], making it ideal for probabilities, proportions, and Bayesian priors

This distribution represents a variable whose logarithm is normally distributed. It is used for modeling positively skewed data, such as incomes and stock prices

This distribution represents a power-law probability distribution used to describe phenomena with heavy tails. It is used for modeling the distribution of wealth, natural phenomena, and insurance claims.