A normal continuous random variable.
The location (loc) keyword specifies the mean.
The scale (scale) keyword specifies the standard deviation.
As an instance of the `rv_continuous` class, `norm` object inherits from it
a collection of generic methods (see below for the full list),
and completes them with details specific for this particular distribution.
Methods
-------
rvs(loc=0, scale=1, size=1, random_state=None)
Random variates.
pdf(x, loc=0, scale=1)
Probability density function.
logpdf(x, loc=0, scale=1)
Log of the probability density function.
cdf(x, loc=0, scale=1)
Cumulative distribution function.
logcdf(x, loc=0, scale=1)
Log of the cumulative distribution function.
sf(x, loc=0, scale=1)
Survival function (also defined as ``1 - cdf``, but `sf` is sometimes more accurate).
logsf(x, loc=0, scale=1)
Log of the survival function.
ppf(q, loc=0, scale=1)
Percent point function (inverse of ``cdf`` --- percentiles).
isf(q, loc=0, scale=1)
Inverse survival function (inverse of ``sf``).
moment(n, loc=0, scale=1)
Non-central moment of order n
stats(loc=0, scale=1, moments='mv')
Mean('m'), variance('v'), skew('s'), and/or kurtosis('k').
entropy(loc=0, scale=1)
(Differential) entropy of the RV.
fit(data, loc=0, scale=1)
Parameter estimates for generic data.
expect(func, args=(), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)
Expected value of a function (of one argument) with respect to the distribution.
median(loc=0, scale=1)
Median of the distribution.
mean(loc=0, scale=1)
Mean of the distribution.
var(loc=0, scale=1)
Variance of the distribution.
std(loc=0, scale=1)
Standard deviation of the distribution.
interval(alpha, loc=0, scale=1)
Endpoints of the range that contains alpha percent of the distribution
Notes
-----
The probability density function for `norm` is:
.. math::
f(x) = \frac{\exp(-x^2/2)}{\sqrt{2\pi}}
The survival function, ``norm.sf``, is also referred to as the
Q-function in some contexts (see, e.g.,
`Wikipedia's <https://en.wikipedia.org/wiki/Q-function>`_ definition).
The probability density above is defined in the "standardized" form. To shift
and/or scale the distribution use the ``loc`` and ``scale`` parameters.
Specifically, ``norm.pdf(x, loc, scale)`` is identically
equivalent to ``norm.pdf(y) / scale`` with
``y = (x - loc) / scale``.
Examples
--------
>>> from scipy.stats import norm
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)
Calculate a few first moments:
>>> mean, var, skew, kurt = norm.stats(moments='mvsk')
Display the probability density function (``pdf``):
>>> x = np.linspace(norm.ppf(0.01),
... norm.ppf(0.99), 100)
>>> ax.plot(x, norm.pdf(x),
... 'r-', lw=5, alpha=0.6, label='norm pdf')
Alternatively, the distribution object can be called (as a function)
to fix the shape, location and scale parameters. This returns a "frozen"
RV object holding the given parameters fixed.
Freeze the distribution and display the frozen ``pdf``:
>>> rv = norm()
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
Check accuracy of ``cdf`` and ``ppf``:
>>> vals = norm.ppf([0.001, 0.5, 0.999])
>>> np.allclose([0.001, 0.5, 0.999], norm.cdf(vals))
True
Generate random numbers:
>>> r = norm.rvs(size=1000)
And compare the histogram:
>>> ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()