/*****************************************************************************
*                                                                            *
*   PDFNORM.SPL Copyright (C) 2000-2016 DSP Development Corporation          *
*                               All Rights Reserved                          *
*                                                                            *
*   Author:      Randy Race                                                  *
*                                                                            *
*   Synopsis:    Probabilty density function of a normal distribution        *
*                                                                            *
*   Revisions:    7 Apr 2000  RRR  Creation                                  *
*                29 Mar 2013  RRR  standard deviation normalization          *
*                 7 Nov 2016  RRR  array input support                       *
*                                                                            *
*****************************************************************************/

#if @HELP_PDFNORM

    PDFNORM

    Purpose: Returns the probability density function of a normal distribution

    Syntax:  PDFNORM(z, mean, std)

                 z - real or series, the z value

              mean - an optional real, the mean of the distribution,
                     defaults to 0.0

               std - an optional real, the standard deviation of the
                     distribution where std > 0. Defaults to 1.0

    Returns: A real or series, the value of the normal distribution for
             the input value(s).

    Example:
             pdfnorm(0)

             returns 1, the value of a normal distribution with a mean of
             0.0 and a standard deviation of 1.0 at z = 0.0.

    Example:
             pdfnorm(-8..0.01..8)

             displays the normal distribution with a mean of 0.0 and
             a standard deviation of 1.0 over the range -8 to 8.

    Example:
             pdfnorm(-8..0.01..8, 0, 2.0)

             Same as above except the standard deviation of the distribution
             is set to 2.0.

    Example:
             W1: hist(gnorm(10000, 1, 10, 3), 200)
             W2: pdfnorm(xvals(W1), 10, 3);overp(rescale(W1, min, max), lred)

             Compares the calculated normal distribution of random values
             with mean 10 and standard deviation 3 in W1 with the analytic
             distribution in W2;

    Remarks:
             STD is set to NaN if STD <= 0.0.

             See PROBN to calculate the normal cumulative distribution
             function.

    See Also:
             Gnorm
             Grand
             Invprobn
             Probn
             Rand
             Randn
#endif



/* area under gaussian from -infinity to z */
pdfnorm(z, mean, std)
{
        local x;

        if (argc < 3)
        {
                if (argc < 2)
                {
                        if (argc < 1) error("pdfnorm - input value required");
                        
                        mean = 0;
                }
                
                std = 1;
        }

        /* check out of range */        
        std[find(std <= 0)] = nan;

        /* normalize */
        x = (z - mean) / std;

        return(exp(-0.5 * x*x) / (sqrt(2*pi) * std));
}