# Symbols and Abbreviations

Symbol Description
$$N(\mu,\sigma^2)$$ Normal distribution with mean $$\mu$$ and variance $$\sigma^2$$.
p.d.f. Probability density function.
CDF Cumulative distribution function.
$$z_p$$ $$p^{th}$$ quantile of the $$N(0,1)$$ distribution.
$$\Phi(\cdot)$$ The CDF of the $$N(0,1)$$.
$$\phi(\cdot)$$ The density function of the $$N(0,1)$$.
$$\chi^2_n$$ Chi-squared distribution on $$n$$ degrees of freedom.
$$t_n$$ Student’s t distribution on $$n$$ degrees of freedom.
$$F_{m,n}$$ F distribution with numerator degrees of freedom $$m$$ and denominator degrees of freedom $$n$$.
i.i.d. Independent and identically distributed.
$$E(X)$$ Expected value of $$X$$.
$$Var(X)$$ Variance of $$X$$.
$$se(\hat \beta)$$ Standard error of $$\hat \beta$$
$$(m_1,m_2)^{\prime}$$ Transpose of $$(m_1,m_2)$$.
$$S_x$$ Sample standard deviation of $$x=(x_1,\ldots,x_n)$$.
FWER Family wise error rate.
$$F_{a,b}(\delta)$$ Non-central $$F$$ distribution with numerator and denominator degrees of freedom $$a,b$$ and non-centrality parameter $$\delta$$.