How to calculate cumulative normal distribution

Question

I am looking for a function in Numpy or Scipy  or any rigorous Python library  that will give me the cumulative normal distribution function in Python

User · Answer

Taken from above    from scipy stats import norm  gt  gt  gt  norm cdf 1 96  0 9750021048517795  gt  gt  gt  norm cdf -1 96  0 024997895148220435   For a two-tailed test   Import numpy as np z   1 96 p value   2   norm cdf -np abs z   0 04999579029644087

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Adapted from here http   mail python org pipermail python-list 2000-June 039873 html  from math import   def erfcc x          Complementary error function         z   abs x      t   1     1    0 5 z      r   t   exp -z z-1 26551223 t  1 00002368 t   37409196          t   09678418 t  - 18628806 t   27886807          t  -1 13520398 t  1 48851587 t  - 82215223          t  17087277              if  x  gt   0            return r     else          return 2  - r  def ncdf x       return 1  - 0 5 erfcc x  2  0 5

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Starting Python 3 8  the standard library provides the NormalDist object as part of the statistics module   It can be used to get the cumulative distribution function  cdf - probability that a random sample X will be less than or equal to x  for a given mean  mu  and standard deviation  sigma    from statistics import NormalDist  NormalDist mu 0  sigma 1  cdf 1 96    0 9750021048517796   Which can be simplified for the standard normal distribution  mu   0 and sigma   1    NormalDist   cdf 1 96    0 9750021048517796  NormalDist   cdf -1 96    0 024997895148220428

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To build upon Unknown s example  the Python equivalent of the function normdist   implemented in a lot of libraries would be   def normcdf x  mu  sigma       t   x-mu      y   0 5 erfcc -t  sigma sqrt 2 0         if y gt 1 0          y   1 0      return y  def normpdf x  mu  sigma       u    x-mu  abs sigma      y    1  sqrt 2 pi  abs sigma    exp -u u 2      return y  def normdist x  mu  sigma  f       if f          y   normcdf x mu sigma      else          y   normpdf x mu sigma      return y

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Here s an example    gt  gt  gt  from scipy stats import norm  gt  gt  gt  norm cdf 1 96  0 9750021048517795  gt  gt  gt  norm cdf -1 96  0 024997895148220435   In other words  approximately 95  of the standard normal interval lies within two standard deviations  centered on a standard mean of zero   If you need the inverse CDF    gt  gt  gt  norm ppf norm cdf 1 96   array 1 9599999999999991

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It may be too late to answer the question but since Google still leads people here  I decide to write my solution here   That is  since Python 2 7  the math library has integrated the error function math erf x   The erf   function can be used to compute traditional statistical functions such as the cumulative standard normal distribution   from math import   def phi x         Cumulative distribution function for the standard normal distribution      return  1 0   erf x   sqrt 2 0      2 0   Ref   https   docs python org 2 library math html  https   docs python org 3 library math html  How are the Error Function and Standard Normal distribution function related

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Alex s answer shows you a solution for standard normal distribution  mean   0  standard deviation   1   If you have normal distribution with mean and std  which is sqr var   and you want to calculate   from scipy stats import norm    cdf x  lt  val  print norm cdf val  m  s     cdf x  gt  val  print 1 - norm cdf val  m  s     cdf v1  lt  x  lt  v2  print norm cdf v2  m  s  - norm cdf v1  m  s    Read more about cdf here and scipy implementation of normal distribution with many formulas here

User · Answer

Simple like this   import math def my cdf x       return 0 5  1 math erf x math sqrt 2      I found the formula in this page https   www danielsoper com statcalc formulas aspx id 55

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As Google gives this answer for the search netlogo pdf  here s the netlogo version of the above python code           Normal distribution cumulative density function     to-report normcdf  x mu sigma          let t x - mu         let y 0 5   erfcc   - t     sigma   sqrt 2 0           if   y   1 0     set y 1 0           report y     end         Normal distribution probability density function     to-report normpdf  x mu sigma          let u    x - mu    abs sigma         let y   1     sqrt  2   pi    abs sigma     exp   - u   u   2 0          report y     end         Complementary error function     to-report erfcc  x          let z abs x         let t 1 0    1 0   0 5   z          let r t    exp   - z   z -1 26551223   t    1 00002368   t    0 37409196               t    0 09678418   t    -0 18628806   t     27886807               t    -1 13520398  t    1 48851587  t    -0 82215223               t    17087277                   ifelse  x    0    report r    report 2 0 - r      end

[python] How to calculate cumulative normal distribution?

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