A normal continuous random variable.

Continuous random variables are defined from a standard form and may require some shape parameters to complete its specification. Any optional keyword parameters can be passed to the methods of the RV object as given below:

Parameters :

x : array-like


q : array-like

lower or upper tail probability

loc : array-like, optional

location parameter (default=0)

scale : array-like, optional

scale parameter (default=1)

size : int or tuple of ints, optional

shape of random variates (default computed from input arguments )

moments : str, optional

composed of letters [‘mvsk’] specifying which moments to compute where ‘m’ = mean, ‘v’ = variance, ‘s’ = (Fisher’s) skew and ‘k’ = (Fisher’s) kurtosis. (default=’mv’)

Alternatively, the object may be called (as a function) to fix the shape, :

location, and scale parameters returning a “frozen” continuous RV object: :

rv = norm(loc=0, scale=1) :

  • Frozen RV object with the same methods but holding the given shape, location, and scale fixed.


Normal distribution

The location (loc) keyword specifies the mean. The scale (scale) keyword specifies the standard deviation.

normal.pdf(x) = exp(-x**2/2)/sqrt(2*pi)


>>> import matplotlib.pyplot as plt
>>> numargs = norm.numargs
>>> [  ] = [0.9,] * numargs
>>> rv = norm()

Display frozen pdf

>>> x = np.linspace(0, np.minimum(rv.dist.b, 3))
>>> h = plt.plot(x, rv.pdf(x))

Check accuracy of cdf and ppf

>>> prb = norm.cdf(x, )
>>> h = plt.semilogy(np.abs(x - norm.ppf(prb, )) + 1e-20)

Random number generation

>>> R = norm.rvs(size=100)


rvs(loc=0, scale=1, size=1) Random variates.
pdf(x, loc=0, scale=1) Probability density function.
cdf(x, loc=0, scale=1) Cumulative density function.
sf(x, loc=0, scale=1) Survival function (1-cdf — sometimes more accurate).
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).
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.

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