Math 3020 lesson 8

Beta Distribution

A family of continuous probability distributions defined on the interval \([0, 1]\), parameterized by two positive shape parameters that control its density shape.

Chi-Squared Distribution

A continuous probability distribution of the sum of the squares of independent, standard normal random variables, commonly used in hypothesis testing.

Erlang Distribution

A specific case of the gamma distribution with an integer shape parameter, often used to model waiting times in queuing systems.

Exponential Distribution

A continuous probability distribution that models the time or distance between independent events occurring at a constant average rate.

Gamma Distribution

A continuous probability distribution used to model waiting times for multiple independent events to occur, generalizing the exponential and Erlang distributions.

Gamma Function

An extension of the factorial function to complex and real numbers, defined by an integral and denoted by \(\Gamma(n) = (n-1)!\) for positive integers.

Lognormal Distribution

A continuous probability distribution of a random variable whose logarithm is normally distributed, typically used for positively skewed data.

QQ-plot

A Quantile-Quantile scatterplot that compares the quantiles of two probability distributions to visually assess if a dataset follows a specific distribution.

Weibull Distribution

A versatile continuous probability distribution frequently used in reliability engineering to model failure rates and the lifespans of components.