\(N(\mu,\sigma^2)\)

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 \(N(0,1)\).

\(\chi^2_n\)

Chisquared distribution on \(n\) degrees of freedom.

\(t_n\)

Studentâ€™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.

\(F_{a,b}(\delta)\)

Noncentral \(F\) distribution with numerator and denominator degrees of freedom \(a,b\) and noncentrality parameter \(\delta\).
