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Rectified Gaussian distribution : ウィキペディア英語版
Rectified Gaussian distribution

In probability theory, the rectified Gaussian distribution is a modification of the Gaussian distribution when its negative elements are reset to 0 (analogous to an electronic rectifier). It is essentially a mixture of a discrete distribution (constant 0) and a continuous distribution (a truncated Gaussian distribution with interval (0,\infty)).
== Density function ==
The probability density function of a rectified Gaussian distribution, for which random variables ''X'' having this distribution are displayed as X \sim \mathcal^)\delta(x)+ \frac}\textrm(x).

Here, \Phi(x) is the cumulative distribution function (cdf) of the standard normal distribution:
:
\Phi(x) = \frac^x e^ \, dt
\quad x\in\mathbb,

\delta(x) is the Dirac delta function
: \delta(x) = \begin +\infty, & x = 0 \\ 0, & x \ne 0 \end
and, \textrm(x) is the unit step function:
:\textrm(x)=\begin 0, & x \leq 0, \\ 1, & x > 0. \end

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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