pystats_norm.qnorm
==================

.. py:module:: pystats_norm.qnorm


Functions
---------

.. autoapisummary::

   pystats_norm.qnorm.qnorm


Module Contents
---------------

.. py:function:: qnorm(p, mean=0, sd=1, lower_tail=True)

   Quantile (Inverse Cumulative Distribution Function) of the normal distribution.

   :param p: The probability for which to find the quantile. Must be between 0 and 1 (exclusive).
   :type p: np.float64
   :param mean: The mean (average) of the normal distribution. Default is 0.
   :type mean: np.float64, optional
   :param sd: The standard deviation of the normal distribution. Default is 1.
   :type sd: np.float64, optional
   :param lower_tail: If True, return the probability to the left of p in the normal distribution.
                      If False, return the probability to the right of p in the normal distribution.
                      Default is True.
   :type lower_tail: bool, optional

   :returns: * *np.float64* -- Returns the value of the inverse cumulative density function (cdf) of the normal distribution
               given a certain random variable p, a population mean μ, and the population standard deviation σ.
             * *Formula*
             * *-------*
             * *If lower_tail=True* -- Q(p; μ, σ) = μ + σ * sqrt(2) * erfinv(2p - 1)
             * *If lower_tail=False* -- Q(p; μ, σ) = μ - σ * sqrt(2) * erfinv(2p - 1)
             * *The quantile represents the value below which a given proportion of the distribution*
             * falls. It is characterized by the mean (`μ`) and standard deviation (`σ`), determining
             * *the center and spread of the distribution.*

   .. rubric:: Example

   >>> qnorm(0.8413447460685429, mean=0, sd=1, lower_tail=True)
   1.0