page_title: Rectified Gaussian distribution
section_title: Density function
hierarchical_section_title: Rectified Gaussian distribution / Density function
caption_attribution_description: English: rectified gaussian
context_page_description: In probability theory, the rectified Gaussian distribution is a modification of the Gaussian distribution when its negative elements are reset to 0. It is essentially a mixture of a discrete distribution and a continuous distribution as a result of censoring.
context_section_description: The probability density function of a rectified Gaussian distribution, for which random variables X having this distribution, derived from the normal distribution  are displayed as  ,   is given by
  Here,  is the cumulative distribution function (cdf) of the standard normal distribution:
   is the Dirac delta function
  and,  is the unit step function:
caption: A comparison of Gaussian distribution, rectified Gaussian distribution, and truncated Gaussian distribution.
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