Statistics How To

Statistics Definitions > Concordant Pairs and Discordant Pairs What are Concordant Pairs and Discordant Pairs? Concordant pairs and discordant pairs refer to comparing two pairs of data points to see if they “match.” The meaning is slightly different depending on if you are finding these pairs from various coefficients (such as Kendall’s Tau) or if … Read more

Regression Analysis > Mallows’ Cp Mallows’ Cp Criterionis a way to assess the fit of a multiple regression model. The metric is used to pick a “best” regression model from a set of smaller models. The Mallows’ Cp procedure involves comparing a full model to a subset model with p parameters (explanatory variables) and quantifying the … Read more

List of Statistical Distributions > Copula distributions What are copula distributions? Copulas (from the Latin link) are invaluable tools for understanding complex variables and their interrelationships. Copula distributions allow us to better identify dependencies between random variables in multivariate settings by combining independently specified marginal probability functions with copula densities. In other words, a copula helps … Read more

Probability Distributions > Categorical Distribution What is a Categorical Distribution? The term “categorical distribution” has come to mean two separate things: Informally, it’s any distribution with categories; Alternatively (and more precisely), it’s a generalization of the Bernoulli distribution for a categorical random variable. While a random variable in a Bernoulli distribution has two possible outcomes, … Read more

Statistics Definitions > Statistical Noise What is statistical noise? Statistical noise refers to the random irregularity present in real-life data. Noisy data lacks a discernible pattern, causing readings to fluctuate between being too small or too large. These errors are typically unpredictable and inevitable. The existence of noise implies that the outcomes of sampling may … Read more

Probability Distributions > Bivariate normal distribution Contents: Bivariate Normal Multivariate Normal Bravais distribution Variance ratio distribution 1. Bivariate normal distribution A bivariate normal distribution is made up of two independent random variables instead of the single one found with the “regular” normal distribution. The two variables in a bivariate normal are both normally distributed and … Read more

Probability Distributions > Von Mises Distribution What is the Von Mises Distribution? The Von Mises distribution (also called the circular normal or Tikhonov distribution) is a continuous probability distribution with a range from 0 to 2π. It is similar to the normal distribution, except coordinates are placed on a circular plane. The von Mises distribution … Read more

Probability Distribution: List of Statistical Distributions > Hansmann’s distributions What are Hansmann’s distributions? Hansmann’s distributions [1] are a Pearson type symmetric family obtained from a generalized Pearson differential equation [2]. These distributions are symmetric about zero and flexible in shape; Hansmann gave explicit solutions for seven different forms. Outside of a mention in the usual … Read more

Probability Distributions List  > Johnson’s SB Distribution What is Johnson’s SB distribution? Johnson’s SB distribution (or “special bounded” distribution) is a four-parameter bounded distribution used to model different types of data in a wide variety of fields, including finance, quality control, and reliability engineering. Johnson’s SB distribution is part of Johnson’s system, which contains three other distributions: the … Read more

< List of probability distributions < Cosine distribution The cosine distribution is an approximation to the normal distribution. Using a cosine distribution instead of a normal can simplify algebraic manipulations. For example, expressions with products or powers of the normal probability density function (PDF) and its integral are difficult to evaluate but the cosine distribution … Read more