original_docstring: Inverse Cumulative Distribution Function for Normal Distribution.
  
      The cumulative distribution function (CDF) of the random variable X
      has the following definition: 
      .. math:: 
                      \\mathbb{F}_X(t) = \\mathbb{P}(X \\le t)
      The notation \\mathbb{F}_X(t) means that \\mathbb{F} is the cdf for 
      the random variable \\mathbb{X} but it is a function of t. It can be 
      defined for any kind of random variable (discrete, continuous, and 
      mixed).
  
      Parameters
      ----------
      p : Array-like
          Sample vector of real numbers
  
      Note
      ----
      The original function was obtained from the google courtesy of
      Dr. John Cook and his group of consultants. The following code 
      first appeared as A literate program to compute the inverse of 
      the normal CDF. See that page for a detailed explanation of the 
      algorithm. Ultimately had to swap it out because it could only
      handle positive values.
      Source: Author  : John D. Cook
               Date   : December 1, 2019
              Title   : Inverse Normal CDF
            Website   : https://www.johndcook.com/blog/python_phi_inverse/
      
      The second algorithm was obtained from stackoverflow
      https://stackoverflow.com/questions/809362/how-to-calculate-cumulative-normal-distribution
      
docstring: Inverse Cumulative Distribution Function for Normal Distribution.
  
  Parameters
  
  p : Array-like
  Sample vector of real numbers
  
  Note
  
  The original function was obtained from the google courtesy of
  Dr. John Cook and his group of consultants. The following code
  first appeared as A literate program to compute the inverse of
  the normal CDF. See that page for a detailed explanation of the
  algorithm. Ultimately had to swap it out because it could only
  handle positive values.
  Source: Author  : John D.
  
  
docstring_tokens: Inverse Cumulative Distribution Function for Normal Distribution . Parameters p : Array - like Sample vector of real numbers Note The original function was obtained from the google courtesy of Dr . John Cook and his group of consultants . The following code first appeared as A literate program to compute the inverse of the normal CDF . See that page for a detailed explanation of the algorithm . Ultimately had to swap it out because it could only handle positive values . Source : Author : John D .
code: def quantile(p):
      """Inverse Cumulative Distribution Function for Normal Distribution.
  
      The cumulative distribution function (CDF) of the random variable X
      has the following definition: 
      .. math:: 
                      \\mathbb{F}_X(t) = \\mathbb{P}(X \\le t)
      The notation \\mathbb{F}_X(t) means that \\mathbb{F} is the cdf for 
      the random variable \\mathbb{X} but it is a function of t. It can be 
      defined for any kind of random variable (discrete, continuous, and 
      mixed).
  
      Parameters
      ----------
      p : Array-like
          Sample vector of real numbers
  
      Note
      ----
      The original function was obtained from the google courtesy of
      Dr. John Cook and his group of consultants. The following code 
      first appeared as A literate program to compute the inverse of 
      the normal CDF. See that page for a detailed explanation of the 
      algorithm. Ultimately had to swap it out because it could only
      handle positive values.
      Source: Author  : John D. Cook
               Date   : December 1, 2019
              Title   : Inverse Normal CDF
            Website   : https://www.johndcook.com/blog/python_phi_inverse/
      
      The second algorithm was obtained from stackoverflow
      https://stackoverflow.com/questions/809362/how-to-calculate-cumulative-normal-distribution
      """  
      #'Cumulative distribution function for the standard normal distribution'
      #i_cdf = normal_CDF_inverse(p)    
      return (1.0 + erf(p / np.sqrt(2.0))) / 2.0    
      #i_cdf = normal_CDF_inverse(p)    
code_tokens: def quantile ( p ) : return ( 1.0 + erf ( p / np . sqrt ( 2.0 ) ) ) / 2.0
short_docstring: Inverse Cumulative Distribution Function for Normal Distribution.
short_docstring_tokens: Inverse Cumulative Distribution Function for Normal Distribution .
comment: """Inverse Cumulative Distribution Function for Normal Distribution.
  
      The cumulative distribution function (CDF) of the random variable X
      has the following definition: 
      .. math:: 
                      \\mathbb{F}_X(t) = \\mathbb{P}(X \\le t)
      The notation \\mathbb{F}_X(t) means that \\mathbb{F} is the cdf for 
      the random variable \\mathbb{X} but it is a function of t. It can be 
      defined for any kind of random variable (discrete, continuous, and 
      mixed).
  
      Parameters
      ----------
      p : Array-like
          Sample vector of real numbers
  
      Note
      ----
      The original function was obtained from the google courtesy of
      Dr. John Cook and his group of consultants. The following code 
      first appeared as A literate program to compute the inverse of 
      the normal CDF. See that page for a detailed explanation of the 
      algorithm. Ultimately had to swap it out because it could only
      handle positive values.
      Source: Author  : John D. Cook
               Date   : December 1, 2019
              Title   : Inverse Normal CDF
            Website   : https://www.johndcook.com/blog/python_phi_inverse/
      
      The second algorithm was obtained from stackoverflow
      https://stackoverflow.com/questions/809362/how-to-calculate-cumulative-normal-distribution
      """$SEP$#'Cumulative distribution function for the standard normal distribution'$SEP$#i_cdf = normal_CDF_inverse(p)    $SEP$#i_cdf = normal_CDF_inverse(p)    