## Sum of Squares: Residual Sum, Total Sum, Explained Sum, Within

Statistics Definitions > Residual Sum of Squares, Total and Explained   Contents: Sum of Squares. Total Sum of Sq. Explained Sum of Sq. Residual Sum of Sq. Sum of Squares Within Error Mean Sum of Squares. Extra Sum of Squares Uses. 1. What is sum of squares? Sum of squares is a measure of dispersion, … Read more

## Normalizing Constant: Definition

Statistics Definitions > Normalizing Constant What is a Normalization Constant? A normalizing constant ensures that a probability density function (pdf) has a probability of 1. The constant can take on various guises: it could be a scalar value, an equation, or even a function. As such, there isn’t a “one size fits all” constant; every … Read more

## Concordant Pairs and Discordant Pairs

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

## Mallows’ Cp: Definition, Example

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

## Copula Distributions

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

## Categorical Distribution: Definition & Examples

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

## Statistical Noise: Simple Definition

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

## Bivariate Normal Distribution / Multivariate Normal (Overview)

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

## Von Mises Distribution: Simple Definition & Examples

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