Statistics How To

Probability Distributions > Pareto distribution What is the Pareto Distribution? The Pareto distribution is a skewed distribution with heavy, or “slowly decaying” tails (i.e. much of the data is in the tails).   The Pareto distribution is defined by a shape parameter, α (also called a slope parameter or Pareto Index) and a location parameter, … Read more

Probability and Statistics > Non normal Distributions > Gamma Distribution The gamma distribution is a family of right-skewed, continuous probability distributions. These distributions are useful in real-life where something has a natural minimum of 0. For example, it is commonly used in finance, for elapsed times, or during Poisson processes. Gamma Distribution PDF If X … Read more

Probability Distributions > Dirichlet Distribution Contents: What is a Dirichlet Distribution? What are Random PMFs? The Dirichlet Process. PDF/Mean/Variance. Similarity to Other Distributions. 1. What is a Dirichlet Distribution? A Dirichlet distribution (pronounced Deer-eesh-lay) is a way to model random probability mass functions (PMFs) for finite sets. The distribution creates n positive numbers (a set … Read more

Probability Distributions > What is a Parabolic Distribution? A parabolic distribution is any distribution that has the shape of a parabola. Many different probability distributions from a wide variety of families can be parabolic in shape.   A parabolic relationship arises when two variables interact in such a way that their representation on a graph … Read more

Statistics Definitions > Nonlinearity A nonlinearity is a relation between data points that can’t be condensed into a neat linear graph. Models of systems such as biochemical reactions in living organisms, combustion and fluid turbulence all show examples of nonlinearities. Nonlinearity vs. Linearity To understand nonlinearity we first need to define what it means for … Read more

Probability Distributions > Waring Distribution What is the Waring distribution? The Waring distribution is a generalization of the Simon-Yule distribution, allowing for more flexibility and greater accuracy when modeling data. To put that another way, the Simon-Yule is a special case of the Waring distribution when the parameters take on certain limiting values. It is … Read more

Probability Distribution > Pólya distribution Contents: Pólya distribution Rutherford distribution Arfwedson distribution What is a Pólya Distribution? The Pólya distribution (also called the Pólya-Eggenberger distribution), named after George Pólya, is a discrete probability distribution related to Pólya’s urn (also called the Pólya-Eggenberger urn scheme) [1]. It describes the number of red balls drawn in the … Read more

Statistics Blog > Same Birthday Odds   It stands to reason that same birthday odds for one person meeting another are 1/365 (365 days in the year and your birthday is on one of them). But it may surprise you to know that with a class of 23 people, there is a 50% chance that … Read more

Binomial Theorem > Negative Binomial Experiment Contents: Negative Binomial Experiment Negative Binomial Distribution   1. Negative Binomial Experiment   A negative binomial experiment is a series of Bernoulli trials with constant success probability that continues until a specified number of successes is reached.     The negative binomial experiment is similar to a binomial experiment … Read more

< Regression Analysis < Bivariate Correlation and Regression What is Bivariate Correlation? Bivariate correlation analyzes the relationship between two variables — usually two types of related data such as caloric intake and weight, income and house expenditures, or daily temperature and ice cream sales [1]. It tests whether the two variables have a linear relationship, … Read more