scipy.stats.

probplot#

scipy.stats.probplot(x, sparams=(), dist='norm', fit=True, plot=None, rvalue=False)[source] #

Calculate quantiles for a probability plot, and optionally show the plot.

Generates a probability plot of sample data against the quantiles of a specified theoretical distribution (the normal distribution by default). probplot optionally calculates a best-fit line for the data and plots the results using Matplotlib or a given plot function.

Parameters:

xarray_like: Sample/response data from which probplot creates the plot.
sparamstuple, optional: Distribution-specific shape parameters (shape parameters plus location and scale).
diststr or stats.distributions instance, optional: Distribution or distribution function name. The default is ‘norm’ for a normal probability plot. Objects that look enough like a stats.distributions instance (i.e. they have a ppf method) are also accepted.
fitbool, optional: Fit a least-squares regression (best-fit) line to the sample data if True (default).
plotobject, optional: If given, plots the quantiles. If given and fit is True, also plots the least squares fit. plot is an object that has to have methods "plot" and "text". The matplotlib.pyplot module or a Matplotlib Axes object can be used, or a custom object with the same methods. Default is None, which means that no plot is created.
rvaluebool, optional: If plot is provided and fit is True, setting rvalue to True includes the coefficient of determination on the plot. Default is False.

Returns:

(osm, osr)tuple of ndarrays: Tuple of theoretical quantiles (osm, or order statistic medians) and ordered responses (osr). osr is simply sorted input x. For details on how osm is calculated see the Notes section.
(slope, intercept, r)tuple of floats, optional: Tuple containing the result of the least-squares fit, if that is performed by probplot. r is the square root of the coefficient of determination. If fit=False and plot=None, this tuple is not returned.

Notes

Even if plot is given, the figure is not shown or saved by probplot; plt.show() or plt.savefig('figname.png') should be used after calling probplot.

probplot generates a probability plot, which should not be confused with a Q-Q or a P-P plot. Statsmodels has more extensive functionality of this type, see statsmodels.api.ProbPlot.

The formula used for the theoretical quantiles (horizontal axis of the probability plot) is Filliben’s estimate:

quantiles = dist.ppf(val), for
 0.5**(1/n), for i = n
 val = (i - 0.3175) / (n + 0.365), for i = 2, ..., n-1
 1 - 0.5**(1/n), for i = 1

where i indicates the i-th ordered value and n is the total number of values.

Array API Standard Support

probplot has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	⛔
PyTorch	⛔	⛔
JAX	⛔	⛔
Dask	⛔	n/a

See Support for the array API standard for more information.

Examples

>>> importnumpyasnp
>>> fromscipyimport stats
>>> importmatplotlib.pyplotasplt
>>> nsample = 100
>>> rng = np.random.default_rng()

A t distribution with small degrees of freedom:

>>> ax1 = plt.subplot(221)
>>> x = stats.t.rvs(3, size=nsample, random_state=rng)
>>> res = stats.probplot(x, plot=plt)

A t distribution with larger degrees of freedom:

>>> ax2 = plt.subplot(222)
>>> x = stats.t.rvs(25, size=nsample, random_state=rng)
>>> res = stats.probplot(x, plot=plt)

A mixture of two normal distributions with broadcasting:

>>> ax3 = plt.subplot(223)
>>> x = stats.norm.rvs(loc=[0,5], scale=[1,1.5],
...  size=(nsample//2,2), random_state=rng).ravel()
>>> res = stats.probplot(x, plot=plt)

A standard normal distribution:

>>> ax4 = plt.subplot(224)
>>> x = stats.norm.rvs(loc=0, scale=1, size=nsample, random_state=rng)
>>> res = stats.probplot(x, plot=plt)

Produce a new figure with a loggamma distribution, using the dist and sparams keywords:

>>> fig = plt.figure()
>>> ax = fig.add_subplot(111)
>>> x = stats.loggamma.rvs(c=2.5, size=500, random_state=rng)
>>> res = stats.probplot(x, dist=stats.loggamma, sparams=(2.5,), plot=ax)
>>> ax.set_title("Probplot for loggamma dist with shape parameter 2.5")

Show the results with Matplotlib:

>>> plt.show()

../../_images/scipy-stats-probplot-1_00.png

../../_images/scipy-stats-probplot-1_01.png