from statsmodels.compat.python import lzip, string_types
import numpy as np
from scipy import stats
from statsmodels.regression.linear_model import OLS
from statsmodels.tools.tools import add_constant
from statsmodels.tools.decorators import cache_readonly
from statsmodels.distributions import ECDF
from . import utils
__all__ = ['qqplot', 'qqplot_2samples', 'qqline', 'ProbPlot']
[docs]class ProbPlot(object):
"""
Class for convenient construction of Q-Q, P-P, and probability plots.
Can take arguments specifying the parameters for dist or fit them
automatically. (See fit under kwargs.)
Parameters
----------
data : array-like
1d data array
dist : A scipy.stats or statsmodels distribution
Compare x against dist. The default is
scipy.stats.distributions.norm (a standard normal).
distargs : tuple
A tuple of arguments passed to dist to specify it fully
so dist.ppf may be called. distargs must not contain loc
or scale. These values must be passed using the loc or
scale inputs.
a : float
Offset for the plotting position of an expected order
statistic, for example. The plotting positions are given
by (i - a)/(nobs - 2*a + 1) for i in range(0,nobs+1)
loc : float
Location parameter for dist
scale : float
Scale parameter for dist
fit : boolean
If fit is false, loc, scale, and distargs are passed to the
distribution. If fit is True then the parameters for dist
are fit automatically using dist.fit. The quantiles are formed
from the standardized data, after subtracting the fitted loc
and dividing by the fitted scale.
See Also
--------
scipy.stats.probplot
Notes
-----
1) Depends on matplotlib.
2) If `fit` is True then the parameters are fit using the
distribution's `fit()` method.
3) The call signatures for the `qqplot`, `ppplot`, and `probplot`
methods are similar, so examples 1 through 4 apply to all
three methods.
4) The three plotting methods are summarized below:
ppplot : Probability-Probability plot
Compares the sample and theoretical probabilities (percentiles).
qqplot : Quantile-Quantile plot
Compares the sample and theoretical quantiles
probplot : Probability plot
Same as a Q-Q plot, however probabilities are shown in the scale of
the theoretical distribution (x-axis) and the y-axis contains
unscaled quantiles of the sample data.
Examples
--------
The first example shows a Q-Q plot for regression residuals
>>> # example 1
>>> import statsmodels.api as sm
>>> from matplotlib import pyplot as plt
>>> data = sm.datasets.longley.load(as_pandas=False)
>>> data.exog = sm.add_constant(data.exog)
>>> model = sm.OLS(data.endog, data.exog)
>>> mod_fit = model.fit()
>>> res = mod_fit.resid # residuals
>>> probplot = sm.ProbPlot(res)
>>> fig = probplot.qqplot()
>>> h = plt.title('Ex. 1 - qqplot - residuals of OLS fit')
>>> plt.show()
qqplot of the residuals against quantiles of t-distribution with 4
degrees of freedom:
>>> # example 2
>>> import scipy.stats as stats
>>> probplot = sm.ProbPlot(res, stats.t, distargs=(4,))
>>> fig = probplot.qqplot()
>>> h = plt.title('Ex. 2 - qqplot - residuals against quantiles of t-dist')
>>> plt.show()
qqplot against same as above, but with mean 3 and std 10:
>>> # example 3
>>> probplot = sm.ProbPlot(res, stats.t, distargs=(4,), loc=3, scale=10)
>>> fig = probplot.qqplot()
>>> h = plt.title('Ex. 3 - qqplot - resids vs quantiles of t-dist')
>>> plt.show()
Automatically determine parameters for t distribution including the
loc and scale:
>>> # example 4
>>> probplot = sm.ProbPlot(res, stats.t, fit=True)
>>> fig = probplot.qqplot(line='45')
>>> h = plt.title('Ex. 4 - qqplot - resids vs. quantiles of fitted t-dist')
>>> plt.show()
A second `ProbPlot` object can be used to compare two separate sample
sets by using the `other` kwarg in the `qqplot` and `ppplot` methods.
>>> # example 5
>>> import numpy as np
>>> x = np.random.normal(loc=8.25, scale=2.75, size=37)
>>> y = np.random.normal(loc=8.75, scale=3.25, size=37)
>>> pp_x = sm.ProbPlot(x, fit=True)
>>> pp_y = sm.ProbPlot(y, fit=True)
>>> fig = pp_x.qqplot(line='45', other=pp_y)
>>> h = plt.title('Ex. 5 - qqplot - compare two sample sets')
>>> plt.show()
In qqplot, sample size of `other` can be equal or larger than the first.
In case of larger, size of `other` samples will be reduced to match the
size of the first by interpolation
>>> # example 6
>>> x = np.random.normal(loc=8.25, scale=2.75, size=37)
>>> y = np.random.normal(loc=8.75, scale=3.25, size=57)
>>> pp_x = sm.ProbPlot(x, fit=True)
>>> pp_y = sm.ProbPlot(y, fit=True)
>>> fig = pp_x.qqplot(line='45', other=pp_y)
>>> title = 'Ex. 6 - qqplot - compare different sample sizes'
>>> h = plt.title(title)
>>> plt.show()
In ppplot, sample size of `other` and the first can be different. `other`
will be used to estimate an empirical cumulative distribution function
(ECDF). ECDF(x) will be plotted against p(x)=0.5/n, 1.5/n, ..., (n-0.5)/n
where x are sorted samples from the first.
>>> # example 7
>>> x = np.random.normal(loc=8.25, scale=2.75, size=37)
>>> y = np.random.normal(loc=8.75, scale=3.25, size=57)
>>> pp_x = sm.ProbPlot(x, fit=True)
>>> pp_y = sm.ProbPlot(y, fit=True)
>>> fig = pp_y.ppplot(line='45', other=pp_x)
>>> h = plt.title('Ex. 7A- ppplot - compare two sample sets, other=pp_x')
>>> fig = pp_x.ppplot(line='45', other=pp_y)
>>> h = plt.title('Ex. 7B- ppplot - compare two sample sets, other=pp_y')
>>> plt.show()
The following plot displays some options, follow the link to see the
code.
.. plot:: plots/graphics_gofplots_qqplot.py
"""
def __init__(self, data, dist=stats.norm, fit=False,
distargs=(), a=0, loc=0, scale=1):
self.data = data
self.a = a
self.nobs = data.shape[0]
self.distargs = distargs
self.fit = fit
if isinstance(dist, string_types):
dist = getattr(stats, dist)
self.fit_params = dist.fit(data)
if fit:
self.loc = self.fit_params[-2]
self.scale = self.fit_params[-1]
if len(self.fit_params) > 2:
self.dist = dist(*self.fit_params[:-2],
**dict(loc=0, scale=1))
else:
self.dist = dist(loc=0, scale=1)
elif distargs or loc != 0 or scale != 1:
try:
self.dist = dist(*distargs, **dict(loc=loc, scale=scale))
except Exception:
distargs = ', '.join([str(da) for da in distargs])
cmd = 'dist({distargs}, loc={loc}, scale={scale})'
cmd = cmd.format(distargs=distargs, loc=loc, scale=scale)
raise TypeError('Initializing the distribution failed. This '
'can occur if distargs contains loc or scale. '
'The distribution initialization command '
'is:\n{cmd}'.format(cmd=cmd))
self.loc = loc
self.scale = scale
else:
self.dist = dist
self.loc = loc
self.scale = scale
# propertes
self._cache = {}
[docs] @cache_readonly
def theoretical_percentiles(self):
"""Theoretical percentiles"""
return plotting_pos(self.nobs, self.a)
[docs] @cache_readonly
def theoretical_quantiles(self):
"""Theoretical quantiles"""
try:
return self.dist.ppf(self.theoretical_percentiles)
except TypeError:
msg = '%s requires more parameters to ' \
'compute ppf'.format(self.dist.name,)
raise TypeError(msg)
except:
msg = 'failed to compute the ppf of {0}'.format(self.dist.name,)
raise
[docs] @cache_readonly
def sorted_data(self):
"""sorted data"""
sorted_data = np.array(self.data, copy=True)
sorted_data.sort()
return sorted_data
[docs] @cache_readonly
def sample_quantiles(self):
"""sample quantiles"""
if self.fit and self.loc != 0 and self.scale != 1:
return (self.sorted_data-self.loc)/self.scale
else:
return self.sorted_data
[docs] @cache_readonly
def sample_percentiles(self):
"""Sample percentiles"""
quantiles = \
(self.sorted_data - self.fit_params[-2])/self.fit_params[-1]
return self.dist.cdf(quantiles)
[docs] def ppplot(self, xlabel=None, ylabel=None, line=None, other=None,
ax=None, **plotkwargs):
"""
P-P plot of the percentiles (probabilities) of x versus the
probabilities (percetiles) of a distribution.
Parameters
----------
xlabel : str or None, optional
User-provided lables for the x-axis. If None (default),
other values are used depending on the status of the kwarg `other`.
ylabel : str or None, optional
User-provided lables for the y-axis. If None (default),
other values are used depending on the status of the kwarg `other`.
line : str {'45', 's', 'r', q'} or None, optional
Options for the reference line to which the data is compared:
- '45': 45-degree line
- 's': standardized line, the expected order statistics are
scaled by the standard deviation of the given sample and have
the mean added to them
- 'r': A regression line is fit
- 'q': A line is fit through the quartiles.
- None: by default no reference line is added to the plot.
other : ProbPlot, array-like, or None, optional
If provided, ECDF(x) will be plotted against p(x) where x are
sorted samples from `self`. ECDF is an empirical cumulative
distribution function estimated from `other` and
p(x) = 0.5/n, 1.5/n, ..., (n-0.5)/n where n is the number of
samples in `self`. If an array-object is provided, it will be
turned into a `ProbPlot` instance default parameters. If not
provided (default), `self.dist(x)` is be plotted against p(x).
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure
being created.
**plotkwargs : additional matplotlib arguments to be passed to the
`plot` command.
Returns
-------
fig : Matplotlib figure instance
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
"""
if other is not None:
check_other = isinstance(other, ProbPlot)
if not check_other:
other = ProbPlot(other)
p_x = self.theoretical_percentiles
ecdf_x = ECDF(other.sample_quantiles)(self.sample_quantiles)
fig, ax = _do_plot(p_x, ecdf_x, self.dist, ax=ax, line=line,
**plotkwargs)
if xlabel is None:
xlabel = 'Probabilities of 2nd Sample'
if ylabel is None:
ylabel = 'Probabilities of 1st Sample'
else:
fig, ax = _do_plot(self.theoretical_percentiles,
self.sample_percentiles,
self.dist, ax=ax, line=line,
**plotkwargs)
if xlabel is None:
xlabel = "Theoretical Probabilities"
if ylabel is None:
ylabel = "Sample Probabilities"
ax.set_xlabel(xlabel)
ax.set_ylabel(ylabel)
ax.set_xlim([0.0, 1.0])
ax.set_ylim([0.0, 1.0])
return fig
[docs] def qqplot(self, xlabel=None, ylabel=None, line=None, other=None,
ax=None, **plotkwargs):
"""
Q-Q plot of the quantiles of x versus the quantiles/ppf of a
distribution or the quantiles of another `ProbPlot` instance.
Parameters
----------
xlabel, ylabel : str or None, optional
User-provided lables for the x-axis and y-axis. If None (default),
other values are used depending on the status of the kwarg `other`.
line : str {'45', 's', 'r', q'} or None, optional
Options for the reference line to which the data is compared:
- '45' - 45-degree line
- 's' - standardized line, the expected order statistics are scaled
by the standard deviation of the given sample and have the mean
added to them
- 'r' - A regression line is fit
- 'q' - A line is fit through the quartiles.
- None - by default no reference line is added to the plot.
other : `ProbPlot` instance, array-like, or None, optional
If provided, the sample quantiles of this `ProbPlot` instance are
plotted against the sample quantiles of the `other` `ProbPlot`
instance. Sample size of `other` must be equal or larger than
this `ProbPlot` instance. If the sample size is larger, sample
quantiles of `other` will be interpolated to match the sample size
of this `ProbPlot` instance. If an array-like object is provided,
it will be turned into a `ProbPlot` instance using default
parameters. If not provided (default), the theoretical quantiles
are used.
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure
being created.
**plotkwargs : additional matplotlib arguments to be passed to the
`plot` command.
Returns
-------
fig : Matplotlib figure instance
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
"""
if other is not None:
check_other = isinstance(other, ProbPlot)
if not check_other:
other = ProbPlot(other)
s_self = self.sample_quantiles
s_other = other.sample_quantiles
if len(s_self) > len(s_other):
raise ValueError("Sample size of `other` must be equal or " +
"larger than this `ProbPlot` instance")
elif len(s_self) < len(s_other):
# Use quantiles of the smaller set and interpolate quantiles of
# the larger data set
p = plotting_pos(self.nobs, self.a)
s_other = stats.mstats.mquantiles(s_other, p)
fig, ax = _do_plot(s_other, s_self, self.dist, ax=ax, line=line,
**plotkwargs)
if xlabel is None:
xlabel = 'Quantiles of 2nd Sample'
if ylabel is None:
ylabel = 'Quantiles of 1st Sample'
else:
fig, ax = _do_plot(self.theoretical_quantiles,
self.sample_quantiles,
self.dist, ax=ax, line=line,
**plotkwargs)
if xlabel is None:
xlabel = "Theoretical Quantiles"
if ylabel is None:
ylabel = "Sample Quantiles"
ax.set_xlabel(xlabel)
ax.set_ylabel(ylabel)
return fig
[docs] def probplot(self, xlabel=None, ylabel=None, line=None,
exceed=False, ax=None, **plotkwargs):
"""
Probability plot of the unscaled quantiles of x versus the
probabilities of a distibution (not to be confused with a P-P plot).
The x-axis is scaled linearly with the quantiles, but the probabilities
are used to label the axis.
Parameters
----------
xlabel, ylabel : str or None, optional
User-provided lables for the x-axis and y-axis. If None (default),
other values are used depending on the status of the kwarg `other`.
line : str {'45', 's', 'r', q'} or None, optional
Options for the reference line to which the data is compared:
- '45' - 45-degree line
- 's' - standardized line, the expected order statistics are scaled
by the standard deviation of the given sample and have the mean
added to them
- 'r' - A regression line is fit
- 'q' - A line is fit through the quartiles.
- None - by default no reference line is added to the plot.
exceed : boolean, optional
- If False (default) the raw sample quantiles are plotted against
the theoretical quantiles, show the probability that a sample
will not exceed a given value
- If True, the theoretical quantiles are flipped such that the
figure displays the probability that a sample will exceed a
given value.
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure
being created.
**plotkwargs : additional matplotlib arguments to be passed to the
`plot` command.
Returns
-------
fig : Matplotlib figure instance
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
"""
if exceed:
fig, ax = _do_plot(self.theoretical_quantiles[::-1],
self.sorted_data,
self.dist, ax=ax, line=line,
**plotkwargs)
if xlabel is None:
xlabel = 'Probability of Exceedance (%)'
else:
fig, ax = _do_plot(self.theoretical_quantiles,
self.sorted_data,
self.dist, ax=ax, line=line,
**plotkwargs)
if xlabel is None:
xlabel = 'Non-exceedance Probability (%)'
if ylabel is None:
ylabel = "Sample Quantiles"
ax.set_xlabel(xlabel)
ax.set_ylabel(ylabel)
_fmt_probplot_axis(ax, self.dist, self.nobs)
return fig
[docs]def qqplot(data, dist=stats.norm, distargs=(), a=0, loc=0, scale=1, fit=False,
line=None, ax=None, **plotkwargs):
"""
Q-Q plot of the quantiles of x versus the quantiles/ppf of a distribution.
Can take arguments specifying the parameters for dist or fit them
automatically. (See fit under Parameters.)
Parameters
----------
data : array-like
1d data array
dist : A scipy.stats or statsmodels distribution
Compare x against dist. The default
is scipy.stats.distributions.norm (a standard normal).
distargs : tuple
A tuple of arguments passed to dist to specify it fully
so dist.ppf may be called.
loc : float
Location parameter for dist
a : float
Offset for the plotting position of an expected order statistic, for
example. The plotting positions are given by (i - a)/(nobs - 2*a + 1)
for i in range(0,nobs+1)
scale : float
Scale parameter for dist
fit : boolean
If fit is false, loc, scale, and distargs are passed to the
distribution. If fit is True then the parameters for dist
are fit automatically using dist.fit. The quantiles are formed
from the standardized data, after subtracting the fitted loc
and dividing by the fitted scale.
line : str {'45', 's', 'r', q'} or None
Options for the reference line to which the data is compared:
- '45' - 45-degree line
- 's' - standardized line, the expected order statistics are scaled
by the standard deviation of the given sample and have the mean
added to them
- 'r' - A regression line is fit
- 'q' - A line is fit through the quartiles.
- None - by default no reference line is added to the plot.
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure being
created.
**plotkwargs : additional matplotlib arguments to be passed to the
`plot` command.
Returns
-------
fig : Matplotlib figure instance
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
scipy.stats.probplot
Examples
--------
>>> import statsmodels.api as sm
>>> from matplotlib import pyplot as plt
>>> data = sm.datasets.longley.load(as_pandas=False)
>>> data.exog = sm.add_constant(data.exog)
>>> mod_fit = sm.OLS(data.endog, data.exog).fit()
>>> res = mod_fit.resid # residuals
>>> fig = sm.qqplot(res)
>>> plt.show()
qqplot of the residuals against quantiles of t-distribution with 4 degrees
of freedom:
>>> import scipy.stats as stats
>>> fig = sm.qqplot(res, stats.t, distargs=(4,))
>>> plt.show()
qqplot against same as above, but with mean 3 and std 10:
>>> fig = sm.qqplot(res, stats.t, distargs=(4,), loc=3, scale=10)
>>> plt.show()
Automatically determine parameters for t distribution including the
loc and scale:
>>> fig = sm.qqplot(res, stats.t, fit=True, line='45')
>>> plt.show()
The following plot displays some options, follow the link to see the code.
.. plot:: plots/graphics_gofplots_qqplot.py
Notes
-----
Depends on matplotlib. If `fit` is True then the parameters are fit using
the distribution's fit() method.
"""
probplot = ProbPlot(data, dist=dist, distargs=distargs,
fit=fit, a=a, loc=loc, scale=scale)
fig = probplot.qqplot(ax=ax, line=line, **plotkwargs)
return fig
[docs]def qqplot_2samples(data1, data2, xlabel=None, ylabel=None, line=None,
ax=None):
"""
Q-Q Plot of two samples' quantiles.
Can take either two `ProbPlot` instances or two array-like objects. In the
case of the latter, both inputs will be converted to `ProbPlot` instances
using only the default values - so use `ProbPlot` instances if
finer-grained control of the quantile computations is required.
Parameters
----------
data1, data2 : array-like (1d) or `ProbPlot` instances
xlabel, ylabel : str or None
User-provided labels for the x-axis and y-axis. If None (default),
other values are used.
line : str {'45', 's', 'r', q'} or None
Options for the reference line to which the data is compared:
- '45' - 45-degree line
- 's' - standardized line, the expected order statistics are scaled
by the standard deviation of the given sample and have the mean
added to them
- 'r' - A regression line is fit
- 'q' - A line is fit through the quartiles.
- None - by default no reference line is added to the plot.
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure being
created.
Returns
-------
fig : Matplotlib figure instance
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
scipy.stats.probplot
Examples
--------
>>> import statsmodels.api as sm
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from statsmodels.graphics.gofplots import qqplot_2samples
>>> x = np.random.normal(loc=8.5, scale=2.5, size=37)
>>> y = np.random.normal(loc=8.0, scale=3.0, size=37)
>>> pp_x = sm.ProbPlot(x)
>>> pp_y = sm.ProbPlot(y)
>>> qqplot_2samples(pp_x, pp_y)
>>> plt.show()
.. plot:: plots/graphics_gofplots_qqplot_2samples.py
>>> fig = qqplot_2samples(pp_x, pp_y, xlabel=None, ylabel=None, \
... line=None, ax=None)
Notes
-----
1) Depends on matplotlib.
2) If `data1` and `data2` are not `ProbPlot` instances, instances will be
created using the default parameters. Therefore, it is recommended to use
`ProbPlot` instance if fine-grained control is needed in the computation
of the quantiles.
"""
if not isinstance(data1, ProbPlot):
data1 = ProbPlot(data1)
if not isinstance(data2, ProbPlot):
data2 = ProbPlot(data2)
fig = data1.qqplot(xlabel=xlabel, ylabel=ylabel,
line=line, other=data2, ax=ax)
return fig
[docs]def qqline(ax, line, x=None, y=None, dist=None, fmt='r-'):
"""
Plot a reference line for a qqplot.
Parameters
----------
ax : matplotlib axes instance
The axes on which to plot the line
line : str {'45','r','s','q'}
Options for the reference line to which the data is compared.:
- '45' - 45-degree line
- 's' - standardized line, the expected order statistics are scaled by
the standard deviation of the given sample and have the mean
added to them
- 'r' - A regression line is fit
- 'q' - A line is fit through the quartiles.
- None - By default no reference line is added to the plot.
x : array
X data for plot. Not needed if line is '45'.
y : array
Y data for plot. Not needed if line is '45'.
dist : scipy.stats.distribution
A scipy.stats distribution, needed if line is 'q'.
Notes
-----
There is no return value. The line is plotted on the given `ax`.
Examples
--------
Import the food expenditure dataset. Plot annual food expendeture on x-axis
and household income on y-axis. Use qqline to add regression line into the
plot.
>>> import statsmodels.api as sm
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from statsmodels.graphics.gofplots import qqline
>>> foodexp = sm.datasets.engel.load(as_pandas=False)
>>> x = foodexp.exog
>>> y = foodexp.endog
>>> ax = plt.subplot(111)
>>> plt.scatter(x, y)
>>> ax.set_xlabel(foodexp.exog_name[0])
>>> ax.set_ylabel(foodexp.endog_name)
>>> qqline(ax, 'r', x, y)
>>> plt.show()
.. plot:: plots/graphics_gofplots_qqplot_qqline.py
"""
if line == '45':
end_pts = lzip(ax.get_xlim(), ax.get_ylim())
end_pts[0] = min(end_pts[0])
end_pts[1] = max(end_pts[1])
ax.plot(end_pts, end_pts, fmt)
ax.set_xlim(end_pts)
ax.set_ylim(end_pts)
return # does this have any side effects?
if x is None and y is None:
raise ValueError("If line is not 45, x and y cannot be None.")
elif line == 'r':
# could use ax.lines[0].get_xdata(), get_ydata(),
# but don't know axes are 'clean'
y = OLS(y, add_constant(x)).fit().fittedvalues
ax.plot(x,y,fmt)
elif line == 's':
m,b = y.std(), y.mean()
ref_line = x*m + b
ax.plot(x, ref_line, fmt)
elif line == 'q':
_check_for_ppf(dist)
q25 = stats.scoreatpercentile(y, 25)
q75 = stats.scoreatpercentile(y, 75)
theoretical_quartiles = dist.ppf([0.25, 0.75])
m = (q75 - q25) / np.diff(theoretical_quartiles)
b = q25 - m*theoretical_quartiles[0]
ax.plot(x, m*x + b, fmt)
# about 10x faster than plotting_position in sandbox and mstats
def plotting_pos(nobs, a):
"""
Generates sequence of plotting positions
Parameters
----------
nobs : int
Number of probability points to plot
a : float
Offset for the plotting position of an expected order statistic, for
example.
Returns
-------
plotting_positions : array
The plotting positions
Notes
-----
The plotting positions are given by (i - a)/(nobs - 2*a + 1) for i in
range(0,nobs+1)
See Also
--------
scipy.stats.mstats.plotting_positions
"""
return (np.arange(1., nobs + 1) - a)/(nobs - 2 * a + 1)
def _fmt_probplot_axis(ax, dist, nobs):
"""
Formats a theoretical quantile axis to display the corresponding
probabilities on the quantiles' scale.
Parameteters
------------
ax : Matplotlib AxesSubplot instance, optional
The axis to be formatted
nobs : scalar
Numbero of observations in the sample
dist : scipy.stats.distribution
A scipy.stats distribution sufficiently specified to impletment its
ppf() method.
Returns
-------
There is no return value. This operates on `ax` in place
"""
_check_for_ppf(dist)
if nobs < 50:
axis_probs = np.array([1, 2, 5, 10, 20, 30, 40, 50, 60,
70, 80, 90, 95, 98, 99, ]) / 100.0
elif nobs < 500:
axis_probs = np.array([0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 30, 40, 50, 60,
70, 80, 90, 95, 98, 99, 99.5, 99.8,
99.9]) / 100.0
else:
axis_probs = np.array([0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10,
20, 30, 40, 50, 60, 70, 80, 90, 95, 98, 99,
99.5, 99.8, 99.9, 99.95, 99.98, 99.99]) / 100.0
axis_qntls = dist.ppf(axis_probs)
ax.set_xticks(axis_qntls)
ax.set_xticklabels(axis_probs*100, rotation=45,
rotation_mode='anchor',
horizontalalignment='right',
verticalalignment='center')
ax.set_xlim([axis_qntls.min(), axis_qntls.max()])
def _do_plot(x, y, dist=None, line=False, ax=None, fmt='bo', **kwargs):
"""
Boiler plate plotting function for the `ppplot`, `qqplot`, and
`probplot` methods of the `ProbPlot` class
Parameteters
------------
x, y : array-like
Data to be plotted
dist : scipy.stats.distribution
A scipy.stats distribution, needed if `line` is 'q'.
line : str {'45', 's', 'r', q'} or None
Options for the reference line to which the data is compared.
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure being
created.
fmt : str, optional
matplotlib-compatible formatting string for the data markers
kwargs : keywords
These are passed to matplotlib.plot
Returns
-------
fig : Matplotlib Figure instance
ax : Matplotlib AxesSubplot instance (see Parameters)
"""
fig, ax = utils.create_mpl_ax(ax)
ax.set_xmargin(0.02)
ax.plot(x, y, fmt, **kwargs)
if line:
if line not in ['r','q','45','s']:
msg = "%s option for line not understood" % line
raise ValueError(msg)
qqline(ax, line, x=x, y=y, dist=dist)
return fig, ax
def _check_for_ppf(dist):
if not hasattr(dist, 'ppf'):
raise ValueError("distribution must have a ppf method")
