| \(\theta\) |
parameter(s) that dictate the shape/location of a distribution |
| \(\hat{\theta}\) |
parameter estimate(s) |
|
|
| \(\alpha\) |
the confidence coefficient or hypothesis test Type I error |
| \(\beta_i\) |
the \(i^{\rm th}\) coefficient in a regression model |
| \(\Gamma(x)\) |
the gamma function \((= (x-1)!\) if \(x\) is an integer) |
| \(\epsilon\) |
the error term in a linear regression model |
| \(\mu\) |
the distribution mean (or population mean) \((= E[X])\) |
| \(\mu_k'\) |
the \(k^{\rm th}\) distribution moment \((= E[X^k])\) |
| \(\nu\) |
the number of degrees of freedom |
| \(\sigma\) |
the distribution standard deviation (or population standard deviation) |
| \(\sigma^2\) |
the distribution variance (or population variance) \((= V[X])\) |
| \(\boldsymbol{\Sigma}\) |
the covariance matrix |
| \(\Omega\) |
the sample space corresponding to an experiment |
|
|
| \(A\),\(B\) |
generic symbols for events in a sample space |
| \(B(\alpha,\beta)\) |
the beta function |
| \(B[\hat{\theta}]\) |
the bias of the estimator \(\hat{\theta}\) |
| \(E[X]\) |
the expected value of the random variable \(X\) \((= \mu)\) |
| erf(\(x\)) |
the error function |
| \(f_X(x)\) |
the probability density function for the continuous random variable \(X\) |
| \(F_X(x)\) |
the cumulative distribution function for the random variable \(X\) |
| iid |
independent and identically distributed random variables |
| MSE |
mean-squared error (\(V[\hat{\theta}] + B[\hat{\theta}]^2\)) |
| \(P(a \leq X \leq b)\) |
the probability that \(X \in [a,b]\) |
| \(p_X(x)\) |
the probability mass function for the discrete random variable \(X\) |
| \(S\) |
the standard deviation of \(n\) sampled data |
| \(S^2\) |
the variance of \(n\) sampled data |
| \(T\) |
a datum sampled from a \(t\) distribution |
| \(U\) |
a sufficient statistic, found via likelihood factorization |
| \(V[X]\) |
the variance of the random variable \(X\) \((= \sigma^2)\) |
| \(W\) |
a datum sampled from a chi-square distribution |
| \(X\) |
a single datum (or random variable), sampled from a pmf or pdf |
| \(X_i\) |
the \(i^{\rm th}\) datum of \(n\) sampled data |
| \(X_{(i)}\) |
the \(i^{\rm th}\) smallest datum of \(n\) sampled data |
| \(\bar{X}\) |
the mean of \(n\) sample |
| \(Y\) |
a statistic, a function of the data in a data sample |
|
|
| \(\mathcal{L}(\theta \vert \mathbf{x}\) |
the likelihood of \(\theta\) given data coordinates \(\mathbf{x}\) |
| \(\ell(\theta \vert \mathbf{x}\) |
the log-likelihood \(\log \mathcal{L}(\theta \vert \mathbf{x})\) |
|
|
| \(\cup\) |
“or” in a probability statment |
| \(\cap\) |
“and” in a probability statment |
| \(|\) |
a condition, stated to the right of \(|\), in a probability statement |
| \(\in\) |
“in,” as in \(x \in [a,b]\) or “\(x\) is in the range \(a\) to \(b\)” |
|
|
| \(\prod_{i=1}^n x_i\) |
the product \(x_1 \cdot x_2 \cdot \cdots \cdot x_n\) |
| \(\sum_{i=1}^n x_i\) |
the summation \(x_1 \cdot x_2 \cdot \cdots \cdot x_n\) |