Characteristics of Distribution

$f(x)$ density of $X$  
$f(x,y)$ joint density of $X$ and $Y$  
$f_{X}(x), f_{Y}(y)$ marginal densities of $X$ and $Y$  
$f_{X_{1}}(x_{1}), \ldots, f_{X_{p}}(x_{2})$ marginal densities of $X_{1},\ldots, X_{p}$  
$\hat{f}_{h}(x)$ histogram or kernel estimator of $f(x)$ [*]
$F(x)$ distribution function of $X$  
$F(x,y)$ joint distribution function of $X$ and $Y$  
$F_{X}(x), F_{Y}(y)$ marginal distribution functions of $X$ and $Y$  
$F_{X_{1}}(x_{1}), \ldots, f_{X_{p}}(x_{p})$ marginal distribution functions of $X_{1},\ldots, X_{p}$  
$\varphi(x)$ density of the standard normal distribution  
$\Phi(x)$ standard normal distribution function  
$\varphi_X(t)$ characteristic function of $X$  
$m_k$ $k$-th moment of $X$  
$\kappa_j$ cumulants or semi-invariants of $X$