Paramnormal Activity

paramnormal.activity.random(distro, **params)[source]

Generate random data from a probability distribution.

Parameters:

distro : str or paramnormal class

The distribution from which the random data will be generated.

params : keyword arguments of floats

The parameters required to define the distribution. See each distribution’s docstring for more info.

shape : int or tuple of ints, optional

The shape of the array into which the generated data will be placed. If None, a scalar will be retured.
Returns:

random : numpy.array or scalar

The random array (or scalar) generated.

Examples

>>> import numpy
>>> import paramnormal
>>> numpy.random.seed(0)
>>> # define dist with a string
>>> paramnormal.activity.random('normal', mu=5, sigma=1.75, shape=1)
array([ 8.08709161])
>>> # or you can specify the actual class
>>> paramnormal.activity.random(paramnormal.normal, mu=5, sigma=1.75, shape=None)
5.700275114642641
>>> # greek letters still work
>>> paramnormal.activity.random('beta', α=2.5, β=1.2, shape=(3,3))
array([[ 0.43771761,  0.84131634,  0.4390664 ],
       [ 0.7037142 ,  0.88282672,  0.09080825],
       [ 0.98747135,  0.63227551,  0.98108498]])
paramnormal.activity.fit(distro, data, as_params=True, **guesses)[source]

Estimate the distribution parameters of sample data.

Parameters:

distro : str or paramnormal class

The distribution from which the random data will be generated.

data : array-like

The data from which the distribution will be fit.

guesses : named arguments of floats

Inital guess values for certain parameters of the distribution. See the class docstring for more information on the parameters.
Returns:

params : namedtuple

A namedtuple containing all of the paramaters of the distribution.

Examples

>>> import numpy
>>> import paramnormal
>>> numpy.random.seed(0)
>>> x = numpy.random.normal(loc=5.75, scale=2.25, size=37)
>>> paramnormal.activity.fit('normal', x)
params(mu=6.4790576880446782, sigma=2.4437818960405617)

>>> paramnormal.activity.fit('normal', x, sigma=2)
params(mu=6.4790576880446782, sigma=2)
paramnormal.activity.plot(distro, which='PDF', data=None, fit_dist=True, ax=None, pad=0.05, xscale='linear', line_opts=None, **guesses)[source]

Plot the PDF of a dataset and other representations of the distribution (histogram, kernel density estimate, and rug plot).

Parameters:

distro : str or distribution

The (name of) the distribution to be plotted.

data : array-like, optional

An array-like object that can be passed to distplot() and fit().

fit_dist : bool, optional

Toggles fitting distro to data. If False, distro must be a fully specified distribution so that the PDF can be plotted.

ax : matplotlib.Axes, optional

Axes on which the everything gets drawn. If not provided, a new one is created.

pad : float, optional

The fraction of beyond min and max values of data where the PDF will be drawn.

xscale : str, optional

Specfifies a ‘log’ or ‘linear’ scale on the plot.

line_opts : dict, optional

Plotting options passed to plot() when drawing the PDF.

distplot : bool, Optional

Toggles the use of distplot(). The default is False.

distplot_opts : dict, optional

Dictionary of parameters to be passed to distplot().

guesses : keyword arguments, optional

Additional parameters for specifying the distribution.
Returns:

ax : matplotlib.Axes

See also

seaborn.distplot

Examples

Plot a simple PDF of a fully-specified normal distribution.

>>> import numpy
>>> import seaborn
>>> import paramnormal
>>> clean_bkgd = {'axes.facecolor': 'none', 'figure.facecolor': 'none'}
>>> seaborn.set(style='ticks', rc=clean_bkgd)
>>> norm_dist = paramnormal.normal(μ=5.4, σ=2.5)
>>> ax = paramnormal.activity.plot(norm_dist)
../_images/activity-1.png

Pass a data sample to fit the distribution on-the-fly.

>>> paramnormal.utils.seed(0)
>>> data = paramnormal.activity.random('normal', μ=5.4, σ=2.5, shape=(37))
>>> ax = paramnormal.activity.plot('normal', data=data)
../_images/activity-2.png

Use seaborn to show other representations of the distribution of real data:

>>> ax = paramnormal.activity.plot('normal', data=data, distplot=True)
>>> ax.legend(loc='upper left')

Use line_opts and distplot_opts to customize more complex plots.

>>> paramnormal.utils.seed(0)
>>> data = paramnormal.activity.random('lognormal', μ=0.75, σ=1.2, shape=125)
>>> logdata = numpy.log10(data)
>>> line_opts = dict(color='firebrick', lw=3.5, label='Fit PDF')
>>> distplot_opts = dict(rug=True, kde=False, norm_hist=True)
>>> ax = paramnormal.activity.plot('lognormal', data=data, distplot=True,
...                                xscale='log', pad=0.01,
...                                line_opts=line_opts,
...                                distplot_opts=distplot_opts)

Notice that the bins in log-space don’t work so well. We can compute them outselves.

>>> paramnormal.utils.seed(0)
>>> data = paramnormal.activity.random('lognormal', μ=0.75, σ=1.2, shape=125)
>>> logdata = numpy.log10(data)
>>> bins = numpy.logspace(logdata.min(), logdata.max(), num=30)
>>> distplot_opts = dict(rug=True, kde=False, norm_hist=True, bins=bins)
>>> ax = paramnormal.activity.plot('lognormal', data=data, distplot=True,
...                                xscale='log', pad=0.01,
...                                line_opts=line_opts,
...                                distplot_opts=distplot_opts)