List of Symbols
Lowercase Greek letters
| Letter | Symbol | Uses |
|---|---|---|
| alpha | \(\alpha\) | A generic constant, or a significance threshold |
| beta | \(\beta\) | An intercept, slope, or other model coefficient |
| gamma | \(\gamma\) | A step size |
| delta | \(\delta\) | A partial derivative, or a tiny amount |
| epsilon | \(\varepsilon\) | An error term, or a tolerance factor |
| eta | \(\eta\) | The linear predictor for a GLM |
| theta | \(\theta\) | A generic parameter or set of parameters |
| lambda | \(\beta\) | The rate of a Poisson or exponential distribution |
| mu | \(\mu\) | The mean of a random variable |
| nu | \(\nu\) | The t-test df when using a pooled variance |
| pi | \(\pi\) | The constant 3.14159…, or a probability |
| rho | \(\rho\) | Correlation |
| sigma | \(\sigma\) | The standard deviation of a random variable |
| \(\sigma^2\) | The variance of a random variable | |
| phi | \(\phi\) | Dispersion parameter for quasi-likelihood models |
| chi | \(\chi\) | Symbol used to name the chi-squared distribution |
Uppercase Greek letters
| Letter | Symbol | Uses |
|---|---|---|
| Delta | \(\Delta\) | Change |
| Pi | \(\Pi\) | Product |
| Sigma | \(\Sigma\) | Sum |
| Phi | \(\Phi\) | CDF of the standard normal distribution |
| Omega | \(\Omega\) | Universal set (all possible outcomes) |
Set theory
| Name | Symbol | Meaning |
|---|---|---|
| \(\in\) | Is an element of | |
| \(\subseteq\) | Is a subset of (and can be equal to) | |
| \(\cup\) | Union (“or”) | |
| \(\cap\) | Intersection (“and”) | |
| \(\mathcal{A}^c\) | A-complement (“everything but A”) | |
| null | \(\emptyset\) | The empty set (or null set) |
| Omega | \(\Omega\) | Universal set (all possible outcomes) |
| \(\mathbb{R}\) | The real numbers | |
| \(\mathbb{Z}\) | The integers | |
| \(\mathbb{Z}^+,\mathbb{Z}^-\) | The positive or negative integers | |
| \(\mathbb{N}\) | The natural numbers incl. zero (0, 1, 2, …) |
Other mathematical symbols
| Name | Symbol | Meaning |
|---|---|---|
| nabla | \(\nabla\) | Gradient (vector of first derivatives) |
| factorial | \(!\) | Factorial operator, e.g. 5! = 5 x 4 x 3 x 2 x 1 = 120 |
| \(\lfloor\;\rfloor\) | Floor operator, e.g. \(\lfloor3.14159\rfloor=3\) | |
| \(\sim\) | Is distributed according to, or depends upon | |
| \(\approx\) | Is approximately equal to | |
| \(\ll,\gg\) | Is much less than, is much greater than | |
| \(\perp\) | Perpendicular or orthogonal to, independent of | |
| dot | \(\circ\) | Dot product (a vector operator) |
| \(|x|\) | Absolute value of a scalar x | |
| \(||\boldsymbol{x}||\) | Magnitude (length) of a vector x | |
| \(F^{-1},\mathbf{A}^{-1}\) | Inverse of a function F or matrix A | |
| \(\boldsymbol{x}^T,\mathbf{A}^T\) | Transpose of a vector x or matrix A | |
| \(1\!\!1\) | Indicator function, or a vector of ones | |
| \(\mathcal{L}\) | Likelihood | |
| \(\mathcal{l}\) | Log-likelihood |