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<article id="content">
<header>
<h1 class="title"><code>distributions</code> module</h1>
</header>
<section id="section-intro">
<details class="source">
<summary>Source code</summary>
<pre><code class="python">import numpy as np
import scipy.stats as st


# Bulge distributions
class radialPlummer(st.rv_continuous):
    def _pdf(self, x):#(3M/4πa3)(1+(r/a)2)−5/2
        return 3/(4*np.pi**3) * (1 + x**2)**(-5/2) * 4*np.pi*x**2
PLUMMER = radialPlummer(a=0, b=5, name=&#39;rPlummer&#39;)

# [TODO: Check Hernquist. Not currently in use]
class radialHernquist(st.rv_continuous):
    def _pdf(self, x):
        return 1/(2*np.pi) * 1/(x**4) * 4*np.pi*x**2
HERNQUIST = radialHernquist(a=0, b=5, name=&#39;rHernquist&#39;)


# Disk distributions
class radialUniform(st.rv_continuous):
    def _pdf(self, x):
        return 2*x if x&lt;1 else 0
UNIFORM = radialUniform(a=0, b=10, name=&#39;rUniform&#39;)

class radialExp(st.rv_continuous):
    def _pdf(self, x):
        return x*np.exp(-x)
EXP = radialExp(a=0, b=10, name=&#39;rExp&#39;)


# Halo distributions
class radialNFW(st.rv_continuous):
    def _pdf(self, x):
        y = 1 / (x * (1 + x)**2) * x**2
        # Normalize pdf in (0, 5) range
        y /= (-5/6 + np.log(6))
NFW = radialNFW(a=0, b=5, name=&#39;rNFW&#39;)</code></pre>
</details>
</section>
<section>
</section>
<section>
</section>
<section>
</section>
<section>
<h2 class="section-title" id="header-classes">Classes</h2>
<dl>
<dt id="distributions.radialExp"><code class="flex name class">
<span>class <span class="ident">radialExp</span></span>
<span>(</span><span><small>ancestors:</small> scipy.stats._distn_infrastructure.rv_continuous, scipy.stats._distn_infrastructure.rv_generic)</span>
</code></dt>
<dd>
<section class="desc"><p>A generic continuous random variable class meant for subclassing.</p>
<p><code>rv_continuous</code> is a base class to construct specific distribution classes
and instances for continuous random variables. It cannot be used
directly as a distribution.</p>
<h2 id="parameters">Parameters</h2>
<dl>
<dt><strong><code>momtype</code></strong> :&ensp;<code>int</code>, optional</dt>
<dd>The type of generic moment calculation to use: 0 for pdf, 1 (default)
for ppf.</dd>
<dt><strong><code>a</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>Lower bound of the support of the distribution, default is minus
infinity.</dd>
<dt><strong><code>b</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>Upper bound of the support of the distribution, default is plus
infinity.</dd>
<dt><strong><code>xtol</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>The tolerance for fixed point calculation for generic ppf.</dd>
<dt><strong><code>badvalue</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>The value in a result arrays that indicates a value that for which
some argument restriction is violated, default is np.nan.</dd>
<dt><strong><code>name</code></strong> :&ensp;<code>str</code>, optional</dt>
<dd>The name of the instance. This string is used to construct the default
example for distributions.</dd>
<dt><strong><code>longname</code></strong> :&ensp;<code>str</code>, optional</dt>
<dd>This string is used as part of the first line of the docstring returned
when a subclass has no docstring of its own. Note: <code>longname</code> exists
for backwards compatibility, do not use for new subclasses.</dd>
<dt><strong><code>shapes</code></strong> :&ensp;<code>str</code>, optional</dt>
<dd>The shape of the distribution. For example <code>"m, n"</code> for a
distribution that takes two integers as the two shape arguments for all
its methods. If not provided, shape parameters will be inferred from
the signature of the private methods, <code>_pdf</code> and <code>_cdf</code> of the
instance.</dd>
<dt><strong><code>extradoc</code></strong> :&ensp; <code>str</code>, optional, <code>deprecated</code></dt>
<dd>This string is used as the last part of the docstring returned when a
subclass has no docstring of its own. Note: <code>extradoc</code> exists for
backwards compatibility, do not use for new subclasses.</dd>
<dt><strong><code>seed</code></strong> :&ensp;<code>None</code> or <code>int</code> or <code>numpy.random.RandomState</code> <code>instance</code>, optional</dt>
<dd>This parameter defines the RandomState object to use for drawing
random variates.
If None (or np.random), the global np.random state is used.
If integer, it is used to seed the local RandomState instance.
Default is None.</dd>
</dl>
<h2 id="methods">Methods</h2>
<p>rvs
pdf
logpdf
cdf
logcdf
sf
logsf
ppf
isf
moment
stats
entropy
expect
median
mean
std
var
interval
<strong>call</strong>
fit
fit_loc_scale
nnlf</p>
<h2 id="notes">Notes</h2>
<p>Public methods of an instance of a distribution class (e.g., <code>pdf</code>,
<code>cdf</code>) check their arguments and pass valid arguments to private,
computational methods (<code>_pdf</code>, <code>_cdf</code>). For <code>pdf(x)</code>, <code>x</code> is valid
if it is within the support of a distribution, <code>self.a &lt;= x &lt;= self.b</code>.
Whether a shape parameter is valid is decided by an <code>_argcheck</code> method
(which defaults to checking that its arguments are strictly positive.)</p>
<p><strong>Subclassing</strong></p>
<p>New random variables can be defined by subclassing the <code>rv_continuous</code> class
and re-defining at least the <code>_pdf</code> or the <code>_cdf</code> method (normalized
to location 0 and scale 1).</p>
<p>If positive argument checking is not correct for your RV
then you will also need to re-define the <code>_argcheck</code> method.</p>
<p>Correct, but potentially slow defaults exist for the remaining
methods but for speed and/or accuracy you can over-ride::</p>
<p>_logpdf, _cdf, _logcdf, _ppf, _rvs, _isf, _sf, _logsf</p>
<p>Rarely would you override <code>_isf</code>, <code>_sf</code> or <code>_logsf</code>, but you could.</p>
<p><strong>Methods that can be overwritten by subclasses</strong>
::</p>
<p>_rvs
_pdf
_cdf
_sf
_ppf
_isf
_stats
_munp
_entropy
_argcheck</p>
<p>There are additional (internal and private) generic methods that can
be useful for cross-checking and for debugging, but might work in all
cases when directly called.</p>
<p>A note on <code>shapes</code>: subclasses need not specify them explicitly. In this
case, <code>shapes</code> will be automatically deduced from the signatures of the
overridden methods (<code>pdf</code>, <code>cdf</code> etc).
If, for some reason, you prefer to avoid relying on introspection, you can
specify <code>shapes</code> explicitly as an argument to the instance constructor.</p>
<p><strong>Frozen Distributions</strong></p>
<p>Normally, you must provide shape parameters (and, optionally, location and
scale parameters to each call of a method of a distribution.</p>
<p>Alternatively, the object may be called (as a function) to fix the shape,
location, and scale parameters returning a "frozen" continuous RV object:</p>
<p>rv = generic(<shape(s)>, loc=0, scale=1)
frozen RV object with the same methods but holding the given shape,
location, and scale fixed</p>
<p><strong>Statistics</strong></p>
<p>Statistics are computed using numerical integration by default.
For speed you can redefine this using <code>_stats</code>:</p>
<ul>
<li>take shape parameters and return mu, mu2, g1, g2</li>
<li>If you can't compute one of these, return it as None</li>
<li>Can also be defined with a keyword argument <code>moments</code>, which is a
string composed of "m", "v", "s", and/or "k".
Only the components appearing in string should be computed and
returned in the order "m", "v", "s", or "k"
with missing values
returned as None.</li>
</ul>
<p>Alternatively, you can override <code>_munp</code>, which takes <code>n</code> and shape
parameters and returns the n-th non-central moment of the distribution.</p>
<h2 id="examples">Examples</h2>
<p>To create a new Gaussian distribution, we would do the following:</p>
<pre><code>&gt;&gt;&gt; from scipy.stats import rv_continuous
&gt;&gt;&gt; class gaussian_gen(rv_continuous):
...     "Gaussian distribution"
...     def _pdf(self, x):
...         return np.exp(-x**2 / 2.) / np.sqrt(2.0 * np.pi)
&gt;&gt;&gt; gaussian = gaussian_gen(name='gaussian')
</code></pre>
<p><code>scipy.stats</code> distributions are <em>instances</em>, so here we subclass
<code>rv_continuous</code> and create an instance. With this, we now have
a fully functional distribution with all relevant methods automagically
generated by the framework.</p>
<p>Note that above we defined a standard normal distribution, with zero mean
and unit variance. Shifting and scaling of the distribution can be done
by using <code>loc</code> and <code>scale</code> parameters: <code>gaussian.pdf(x, loc, scale)</code>
essentially computes <code>y = (x - loc) / scale</code> and
<code>gaussian._pdf(y) / scale</code>.</p></section>
<details class="source">
<summary>Source code</summary>
<pre><code class="python">class radialExp(st.rv_continuous):
    def _pdf(self, x):
        return x*np.exp(-x)</code></pre>
</details>
</dd>
<dt id="distributions.radialHernquist"><code class="flex name class">
<span>class <span class="ident">radialHernquist</span></span>
<span>(</span><span><small>ancestors:</small> scipy.stats._distn_infrastructure.rv_continuous, scipy.stats._distn_infrastructure.rv_generic)</span>
</code></dt>
<dd>
<section class="desc"><p>A generic continuous random variable class meant for subclassing.</p>
<p><code>rv_continuous</code> is a base class to construct specific distribution classes
and instances for continuous random variables. It cannot be used
directly as a distribution.</p>
<h2 id="parameters">Parameters</h2>
<dl>
<dt><strong><code>momtype</code></strong> :&ensp;<code>int</code>, optional</dt>
<dd>The type of generic moment calculation to use: 0 for pdf, 1 (default)
for ppf.</dd>
<dt><strong><code>a</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>Lower bound of the support of the distribution, default is minus
infinity.</dd>
<dt><strong><code>b</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>Upper bound of the support of the distribution, default is plus
infinity.</dd>
<dt><strong><code>xtol</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>The tolerance for fixed point calculation for generic ppf.</dd>
<dt><strong><code>badvalue</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>The value in a result arrays that indicates a value that for which
some argument restriction is violated, default is np.nan.</dd>
<dt><strong><code>name</code></strong> :&ensp;<code>str</code>, optional</dt>
<dd>The name of the instance. This string is used to construct the default
example for distributions.</dd>
<dt><strong><code>longname</code></strong> :&ensp;<code>str</code>, optional</dt>
<dd>This string is used as part of the first line of the docstring returned
when a subclass has no docstring of its own. Note: <code>longname</code> exists
for backwards compatibility, do not use for new subclasses.</dd>
<dt><strong><code>shapes</code></strong> :&ensp;<code>str</code>, optional</dt>
<dd>The shape of the distribution. For example <code>"m, n"</code> for a
distribution that takes two integers as the two shape arguments for all
its methods. If not provided, shape parameters will be inferred from
the signature of the private methods, <code>_pdf</code> and <code>_cdf</code> of the
instance.</dd>
<dt><strong><code>extradoc</code></strong> :&ensp; <code>str</code>, optional, <code>deprecated</code></dt>
<dd>This string is used as the last part of the docstring returned when a
subclass has no docstring of its own. Note: <code>extradoc</code> exists for
backwards compatibility, do not use for new subclasses.</dd>
<dt><strong><code>seed</code></strong> :&ensp;<code>None</code> or <code>int</code> or <code>numpy.random.RandomState</code> <code>instance</code>, optional</dt>
<dd>This parameter defines the RandomState object to use for drawing
random variates.
If None (or np.random), the global np.random state is used.
If integer, it is used to seed the local RandomState instance.
Default is None.</dd>
</dl>
<h2 id="methods">Methods</h2>
<p>rvs
pdf
logpdf
cdf
logcdf
sf
logsf
ppf
isf
moment
stats
entropy
expect
median
mean
std
var
interval
<strong>call</strong>
fit
fit_loc_scale
nnlf</p>
<h2 id="notes">Notes</h2>
<p>Public methods of an instance of a distribution class (e.g., <code>pdf</code>,
<code>cdf</code>) check their arguments and pass valid arguments to private,
computational methods (<code>_pdf</code>, <code>_cdf</code>). For <code>pdf(x)</code>, <code>x</code> is valid
if it is within the support of a distribution, <code>self.a &lt;= x &lt;= self.b</code>.
Whether a shape parameter is valid is decided by an <code>_argcheck</code> method
(which defaults to checking that its arguments are strictly positive.)</p>
<p><strong>Subclassing</strong></p>
<p>New random variables can be defined by subclassing the <code>rv_continuous</code> class
and re-defining at least the <code>_pdf</code> or the <code>_cdf</code> method (normalized
to location 0 and scale 1).</p>
<p>If positive argument checking is not correct for your RV
then you will also need to re-define the <code>_argcheck</code> method.</p>
<p>Correct, but potentially slow defaults exist for the remaining
methods but for speed and/or accuracy you can over-ride::</p>
<p>_logpdf, _cdf, _logcdf, _ppf, _rvs, _isf, _sf, _logsf</p>
<p>Rarely would you override <code>_isf</code>, <code>_sf</code> or <code>_logsf</code>, but you could.</p>
<p><strong>Methods that can be overwritten by subclasses</strong>
::</p>
<p>_rvs
_pdf
_cdf
_sf
_ppf
_isf
_stats
_munp
_entropy
_argcheck</p>
<p>There are additional (internal and private) generic methods that can
be useful for cross-checking and for debugging, but might work in all
cases when directly called.</p>
<p>A note on <code>shapes</code>: subclasses need not specify them explicitly. In this
case, <code>shapes</code> will be automatically deduced from the signatures of the
overridden methods (<code>pdf</code>, <code>cdf</code> etc).
If, for some reason, you prefer to avoid relying on introspection, you can
specify <code>shapes</code> explicitly as an argument to the instance constructor.</p>
<p><strong>Frozen Distributions</strong></p>
<p>Normally, you must provide shape parameters (and, optionally, location and
scale parameters to each call of a method of a distribution.</p>
<p>Alternatively, the object may be called (as a function) to fix the shape,
location, and scale parameters returning a "frozen" continuous RV object:</p>
<p>rv = generic(<shape(s)>, loc=0, scale=1)
frozen RV object with the same methods but holding the given shape,
location, and scale fixed</p>
<p><strong>Statistics</strong></p>
<p>Statistics are computed using numerical integration by default.
For speed you can redefine this using <code>_stats</code>:</p>
<ul>
<li>take shape parameters and return mu, mu2, g1, g2</li>
<li>If you can't compute one of these, return it as None</li>
<li>Can also be defined with a keyword argument <code>moments</code>, which is a
string composed of "m", "v", "s", and/or "k".
Only the components appearing in string should be computed and
returned in the order "m", "v", "s", or "k"
with missing values
returned as None.</li>
</ul>
<p>Alternatively, you can override <code>_munp</code>, which takes <code>n</code> and shape
parameters and returns the n-th non-central moment of the distribution.</p>
<h2 id="examples">Examples</h2>
<p>To create a new Gaussian distribution, we would do the following:</p>
<pre><code>&gt;&gt;&gt; from scipy.stats import rv_continuous
&gt;&gt;&gt; class gaussian_gen(rv_continuous):
...     "Gaussian distribution"
...     def _pdf(self, x):
...         return np.exp(-x**2 / 2.) / np.sqrt(2.0 * np.pi)
&gt;&gt;&gt; gaussian = gaussian_gen(name='gaussian')
</code></pre>
<p><code>scipy.stats</code> distributions are <em>instances</em>, so here we subclass
<code>rv_continuous</code> and create an instance. With this, we now have
a fully functional distribution with all relevant methods automagically
generated by the framework.</p>
<p>Note that above we defined a standard normal distribution, with zero mean
and unit variance. Shifting and scaling of the distribution can be done
by using <code>loc</code> and <code>scale</code> parameters: <code>gaussian.pdf(x, loc, scale)</code>
essentially computes <code>y = (x - loc) / scale</code> and
<code>gaussian._pdf(y) / scale</code>.</p></section>
<details class="source">
<summary>Source code</summary>
<pre><code class="python">class radialHernquist(st.rv_continuous):
    def _pdf(self, x):
        return 1/(2*np.pi) * 1/(x**4) * 4*np.pi*x**2</code></pre>
</details>
</dd>
<dt id="distributions.radialNFW"><code class="flex name class">
<span>class <span class="ident">radialNFW</span></span>
<span>(</span><span><small>ancestors:</small> scipy.stats._distn_infrastructure.rv_continuous, scipy.stats._distn_infrastructure.rv_generic)</span>
</code></dt>
<dd>
<section class="desc"><p>A generic continuous random variable class meant for subclassing.</p>
<p><code>rv_continuous</code> is a base class to construct specific distribution classes
and instances for continuous random variables. It cannot be used
directly as a distribution.</p>
<h2 id="parameters">Parameters</h2>
<dl>
<dt><strong><code>momtype</code></strong> :&ensp;<code>int</code>, optional</dt>
<dd>The type of generic moment calculation to use: 0 for pdf, 1 (default)
for ppf.</dd>
<dt><strong><code>a</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>Lower bound of the support of the distribution, default is minus
infinity.</dd>
<dt><strong><code>b</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>Upper bound of the support of the distribution, default is plus
infinity.</dd>
<dt><strong><code>xtol</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>The tolerance for fixed point calculation for generic ppf.</dd>
<dt><strong><code>badvalue</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>The value in a result arrays that indicates a value that for which
some argument restriction is violated, default is np.nan.</dd>
<dt><strong><code>name</code></strong> :&ensp;<code>str</code>, optional</dt>
<dd>The name of the instance. This string is used to construct the default
example for distributions.</dd>
<dt><strong><code>longname</code></strong> :&ensp;<code>str</code>, optional</dt>
<dd>This string is used as part of the first line of the docstring returned
when a subclass has no docstring of its own. Note: <code>longname</code> exists
for backwards compatibility, do not use for new subclasses.</dd>
<dt><strong><code>shapes</code></strong> :&ensp;<code>str</code>, optional</dt>
<dd>The shape of the distribution. For example <code>"m, n"</code> for a
distribution that takes two integers as the two shape arguments for all
its methods. If not provided, shape parameters will be inferred from
the signature of the private methods, <code>_pdf</code> and <code>_cdf</code> of the
instance.</dd>
<dt><strong><code>extradoc</code></strong> :&ensp; <code>str</code>, optional, <code>deprecated</code></dt>
<dd>This string is used as the last part of the docstring returned when a
subclass has no docstring of its own. Note: <code>extradoc</code> exists for
backwards compatibility, do not use for new subclasses.</dd>
<dt><strong><code>seed</code></strong> :&ensp;<code>None</code> or <code>int</code> or <code>numpy.random.RandomState</code> <code>instance</code>, optional</dt>
<dd>This parameter defines the RandomState object to use for drawing
random variates.
If None (or np.random), the global np.random state is used.
If integer, it is used to seed the local RandomState instance.
Default is None.</dd>
</dl>
<h2 id="methods">Methods</h2>
<p>rvs
pdf
logpdf
cdf
logcdf
sf
logsf
ppf
isf
moment
stats
entropy
expect
median
mean
std
var
interval
<strong>call</strong>
fit
fit_loc_scale
nnlf</p>
<h2 id="notes">Notes</h2>
<p>Public methods of an instance of a distribution class (e.g., <code>pdf</code>,
<code>cdf</code>) check their arguments and pass valid arguments to private,
computational methods (<code>_pdf</code>, <code>_cdf</code>). For <code>pdf(x)</code>, <code>x</code> is valid
if it is within the support of a distribution, <code>self.a &lt;= x &lt;= self.b</code>.
Whether a shape parameter is valid is decided by an <code>_argcheck</code> method
(which defaults to checking that its arguments are strictly positive.)</p>
<p><strong>Subclassing</strong></p>
<p>New random variables can be defined by subclassing the <code>rv_continuous</code> class
and re-defining at least the <code>_pdf</code> or the <code>_cdf</code> method (normalized
to location 0 and scale 1).</p>
<p>If positive argument checking is not correct for your RV
then you will also need to re-define the <code>_argcheck</code> method.</p>
<p>Correct, but potentially slow defaults exist for the remaining
methods but for speed and/or accuracy you can over-ride::</p>
<p>_logpdf, _cdf, _logcdf, _ppf, _rvs, _isf, _sf, _logsf</p>
<p>Rarely would you override <code>_isf</code>, <code>_sf</code> or <code>_logsf</code>, but you could.</p>
<p><strong>Methods that can be overwritten by subclasses</strong>
::</p>
<p>_rvs
_pdf
_cdf
_sf
_ppf
_isf
_stats
_munp
_entropy
_argcheck</p>
<p>There are additional (internal and private) generic methods that can
be useful for cross-checking and for debugging, but might work in all
cases when directly called.</p>
<p>A note on <code>shapes</code>: subclasses need not specify them explicitly. In this
case, <code>shapes</code> will be automatically deduced from the signatures of the
overridden methods (<code>pdf</code>, <code>cdf</code> etc).
If, for some reason, you prefer to avoid relying on introspection, you can
specify <code>shapes</code> explicitly as an argument to the instance constructor.</p>
<p><strong>Frozen Distributions</strong></p>
<p>Normally, you must provide shape parameters (and, optionally, location and
scale parameters to each call of a method of a distribution.</p>
<p>Alternatively, the object may be called (as a function) to fix the shape,
location, and scale parameters returning a "frozen" continuous RV object:</p>
<p>rv = generic(<shape(s)>, loc=0, scale=1)
frozen RV object with the same methods but holding the given shape,
location, and scale fixed</p>
<p><strong>Statistics</strong></p>
<p>Statistics are computed using numerical integration by default.
For speed you can redefine this using <code>_stats</code>:</p>
<ul>
<li>take shape parameters and return mu, mu2, g1, g2</li>
<li>If you can't compute one of these, return it as None</li>
<li>Can also be defined with a keyword argument <code>moments</code>, which is a
string composed of "m", "v", "s", and/or "k".
Only the components appearing in string should be computed and
returned in the order "m", "v", "s", or "k"
with missing values
returned as None.</li>
</ul>
<p>Alternatively, you can override <code>_munp</code>, which takes <code>n</code> and shape
parameters and returns the n-th non-central moment of the distribution.</p>
<h2 id="examples">Examples</h2>
<p>To create a new Gaussian distribution, we would do the following:</p>
<pre><code>&gt;&gt;&gt; from scipy.stats import rv_continuous
&gt;&gt;&gt; class gaussian_gen(rv_continuous):
...     "Gaussian distribution"
...     def _pdf(self, x):
...         return np.exp(-x**2 / 2.) / np.sqrt(2.0 * np.pi)
&gt;&gt;&gt; gaussian = gaussian_gen(name='gaussian')
</code></pre>
<p><code>scipy.stats</code> distributions are <em>instances</em>, so here we subclass
<code>rv_continuous</code> and create an instance. With this, we now have
a fully functional distribution with all relevant methods automagically
generated by the framework.</p>
<p>Note that above we defined a standard normal distribution, with zero mean
and unit variance. Shifting and scaling of the distribution can be done
by using <code>loc</code> and <code>scale</code> parameters: <code>gaussian.pdf(x, loc, scale)</code>
essentially computes <code>y = (x - loc) / scale</code> and
<code>gaussian._pdf(y) / scale</code>.</p></section>
<details class="source">
<summary>Source code</summary>
<pre><code class="python">class radialNFW(st.rv_continuous):
    def _pdf(self, x):
        y = 1 / (x * (1 + x)**2) * x**2
        # Normalize pdf in (0, 5) range
        y /= (-5/6 + np.log(6))</code></pre>
</details>
</dd>
<dt id="distributions.radialPlummer"><code class="flex name class">
<span>class <span class="ident">radialPlummer</span></span>
<span>(</span><span><small>ancestors:</small> scipy.stats._distn_infrastructure.rv_continuous, scipy.stats._distn_infrastructure.rv_generic)</span>
</code></dt>
<dd>
<section class="desc"><p>A generic continuous random variable class meant for subclassing.</p>
<p><code>rv_continuous</code> is a base class to construct specific distribution classes
and instances for continuous random variables. It cannot be used
directly as a distribution.</p>
<h2 id="parameters">Parameters</h2>
<dl>
<dt><strong><code>momtype</code></strong> :&ensp;<code>int</code>, optional</dt>
<dd>The type of generic moment calculation to use: 0 for pdf, 1 (default)
for ppf.</dd>
<dt><strong><code>a</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>Lower bound of the support of the distribution, default is minus
infinity.</dd>
<dt><strong><code>b</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>Upper bound of the support of the distribution, default is plus
infinity.</dd>
<dt><strong><code>xtol</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>The tolerance for fixed point calculation for generic ppf.</dd>
<dt><strong><code>badvalue</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>The value in a result arrays that indicates a value that for which
some argument restriction is violated, default is np.nan.</dd>
<dt><strong><code>name</code></strong> :&ensp;<code>str</code>, optional</dt>
<dd>The name of the instance. This string is used to construct the default
example for distributions.</dd>
<dt><strong><code>longname</code></strong> :&ensp;<code>str</code>, optional</dt>
<dd>This string is used as part of the first line of the docstring returned
when a subclass has no docstring of its own. Note: <code>longname</code> exists
for backwards compatibility, do not use for new subclasses.</dd>
<dt><strong><code>shapes</code></strong> :&ensp;<code>str</code>, optional</dt>
<dd>The shape of the distribution. For example <code>"m, n"</code> for a
distribution that takes two integers as the two shape arguments for all
its methods. If not provided, shape parameters will be inferred from
the signature of the private methods, <code>_pdf</code> and <code>_cdf</code> of the
instance.</dd>
<dt><strong><code>extradoc</code></strong> :&ensp; <code>str</code>, optional, <code>deprecated</code></dt>
<dd>This string is used as the last part of the docstring returned when a
subclass has no docstring of its own. Note: <code>extradoc</code> exists for
backwards compatibility, do not use for new subclasses.</dd>
<dt><strong><code>seed</code></strong> :&ensp;<code>None</code> or <code>int</code> or <code>numpy.random.RandomState</code> <code>instance</code>, optional</dt>
<dd>This parameter defines the RandomState object to use for drawing
random variates.
If None (or np.random), the global np.random state is used.
If integer, it is used to seed the local RandomState instance.
Default is None.</dd>
</dl>
<h2 id="methods">Methods</h2>
<p>rvs
pdf
logpdf
cdf
logcdf
sf
logsf
ppf
isf
moment
stats
entropy
expect
median
mean
std
var
interval
<strong>call</strong>
fit
fit_loc_scale
nnlf</p>
<h2 id="notes">Notes</h2>
<p>Public methods of an instance of a distribution class (e.g., <code>pdf</code>,
<code>cdf</code>) check their arguments and pass valid arguments to private,
computational methods (<code>_pdf</code>, <code>_cdf</code>). For <code>pdf(x)</code>, <code>x</code> is valid
if it is within the support of a distribution, <code>self.a &lt;= x &lt;= self.b</code>.
Whether a shape parameter is valid is decided by an <code>_argcheck</code> method
(which defaults to checking that its arguments are strictly positive.)</p>
<p><strong>Subclassing</strong></p>
<p>New random variables can be defined by subclassing the <code>rv_continuous</code> class
and re-defining at least the <code>_pdf</code> or the <code>_cdf</code> method (normalized
to location 0 and scale 1).</p>
<p>If positive argument checking is not correct for your RV
then you will also need to re-define the <code>_argcheck</code> method.</p>
<p>Correct, but potentially slow defaults exist for the remaining
methods but for speed and/or accuracy you can over-ride::</p>
<p>_logpdf, _cdf, _logcdf, _ppf, _rvs, _isf, _sf, _logsf</p>
<p>Rarely would you override <code>_isf</code>, <code>_sf</code> or <code>_logsf</code>, but you could.</p>
<p><strong>Methods that can be overwritten by subclasses</strong>
::</p>
<p>_rvs
_pdf
_cdf
_sf
_ppf
_isf
_stats
_munp
_entropy
_argcheck</p>
<p>There are additional (internal and private) generic methods that can
be useful for cross-checking and for debugging, but might work in all
cases when directly called.</p>
<p>A note on <code>shapes</code>: subclasses need not specify them explicitly. In this
case, <code>shapes</code> will be automatically deduced from the signatures of the
overridden methods (<code>pdf</code>, <code>cdf</code> etc).
If, for some reason, you prefer to avoid relying on introspection, you can
specify <code>shapes</code> explicitly as an argument to the instance constructor.</p>
<p><strong>Frozen Distributions</strong></p>
<p>Normally, you must provide shape parameters (and, optionally, location and
scale parameters to each call of a method of a distribution.</p>
<p>Alternatively, the object may be called (as a function) to fix the shape,
location, and scale parameters returning a "frozen" continuous RV object:</p>
<p>rv = generic(<shape(s)>, loc=0, scale=1)
frozen RV object with the same methods but holding the given shape,
location, and scale fixed</p>
<p><strong>Statistics</strong></p>
<p>Statistics are computed using numerical integration by default.
For speed you can redefine this using <code>_stats</code>:</p>
<ul>
<li>take shape parameters and return mu, mu2, g1, g2</li>
<li>If you can't compute one of these, return it as None</li>
<li>Can also be defined with a keyword argument <code>moments</code>, which is a
string composed of "m", "v", "s", and/or "k".
Only the components appearing in string should be computed and
returned in the order "m", "v", "s", or "k"
with missing values
returned as None.</li>
</ul>
<p>Alternatively, you can override <code>_munp</code>, which takes <code>n</code> and shape
parameters and returns the n-th non-central moment of the distribution.</p>
<h2 id="examples">Examples</h2>
<p>To create a new Gaussian distribution, we would do the following:</p>
<pre><code>&gt;&gt;&gt; from scipy.stats import rv_continuous
&gt;&gt;&gt; class gaussian_gen(rv_continuous):
...     "Gaussian distribution"
...     def _pdf(self, x):
...         return np.exp(-x**2 / 2.) / np.sqrt(2.0 * np.pi)
&gt;&gt;&gt; gaussian = gaussian_gen(name='gaussian')
</code></pre>
<p><code>scipy.stats</code> distributions are <em>instances</em>, so here we subclass
<code>rv_continuous</code> and create an instance. With this, we now have
a fully functional distribution with all relevant methods automagically
generated by the framework.</p>
<p>Note that above we defined a standard normal distribution, with zero mean
and unit variance. Shifting and scaling of the distribution can be done
by using <code>loc</code> and <code>scale</code> parameters: <code>gaussian.pdf(x, loc, scale)</code>
essentially computes <code>y = (x - loc) / scale</code> and
<code>gaussian._pdf(y) / scale</code>.</p></section>
<details class="source">
<summary>Source code</summary>
<pre><code class="python">class radialPlummer(st.rv_continuous):
    def _pdf(self, x):#(3M/4πa3)(1+(r/a)2)−5/2
        return 3/(4*np.pi**3) * (1 + x**2)**(-5/2) * 4*np.pi*x**2</code></pre>
</details>
</dd>
<dt id="distributions.radialUniform"><code class="flex name class">
<span>class <span class="ident">radialUniform</span></span>
<span>(</span><span><small>ancestors:</small> scipy.stats._distn_infrastructure.rv_continuous, scipy.stats._distn_infrastructure.rv_generic)</span>
</code></dt>
<dd>
<section class="desc"><p>A generic continuous random variable class meant for subclassing.</p>
<p><code>rv_continuous</code> is a base class to construct specific distribution classes
and instances for continuous random variables. It cannot be used
directly as a distribution.</p>
<h2 id="parameters">Parameters</h2>
<dl>
<dt><strong><code>momtype</code></strong> :&ensp;<code>int</code>, optional</dt>
<dd>The type of generic moment calculation to use: 0 for pdf, 1 (default)
for ppf.</dd>
<dt><strong><code>a</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>Lower bound of the support of the distribution, default is minus
infinity.</dd>
<dt><strong><code>b</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>Upper bound of the support of the distribution, default is plus
infinity.</dd>
<dt><strong><code>xtol</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>The tolerance for fixed point calculation for generic ppf.</dd>
<dt><strong><code>badvalue</code></strong> :&ensp;<code>float</code>, optional</dt>
<dd>The value in a result arrays that indicates a value that for which
some argument restriction is violated, default is np.nan.</dd>
<dt><strong><code>name</code></strong> :&ensp;<code>str</code>, optional</dt>
<dd>The name of the instance. This string is used to construct the default
example for distributions.</dd>
<dt><strong><code>longname</code></strong> :&ensp;<code>str</code>, optional</dt>
<dd>This string is used as part of the first line of the docstring returned
when a subclass has no docstring of its own. Note: <code>longname</code> exists
for backwards compatibility, do not use for new subclasses.</dd>
<dt><strong><code>shapes</code></strong> :&ensp;<code>str</code>, optional</dt>
<dd>The shape of the distribution. For example <code>"m, n"</code> for a
distribution that takes two integers as the two shape arguments for all
its methods. If not provided, shape parameters will be inferred from
the signature of the private methods, <code>_pdf</code> and <code>_cdf</code> of the
instance.</dd>
<dt><strong><code>extradoc</code></strong> :&ensp; <code>str</code>, optional, <code>deprecated</code></dt>
<dd>This string is used as the last part of the docstring returned when a
subclass has no docstring of its own. Note: <code>extradoc</code> exists for
backwards compatibility, do not use for new subclasses.</dd>
<dt><strong><code>seed</code></strong> :&ensp;<code>None</code> or <code>int</code> or <code>numpy.random.RandomState</code> <code>instance</code>, optional</dt>
<dd>This parameter defines the RandomState object to use for drawing
random variates.
If None (or np.random), the global np.random state is used.
If integer, it is used to seed the local RandomState instance.
Default is None.</dd>
</dl>
<h2 id="methods">Methods</h2>
<p>rvs
pdf
logpdf
cdf
logcdf
sf
logsf
ppf
isf
moment
stats
entropy
expect
median
mean
std
var
interval
<strong>call</strong>
fit
fit_loc_scale
nnlf</p>
<h2 id="notes">Notes</h2>
<p>Public methods of an instance of a distribution class (e.g., <code>pdf</code>,
<code>cdf</code>) check their arguments and pass valid arguments to private,
computational methods (<code>_pdf</code>, <code>_cdf</code>). For <code>pdf(x)</code>, <code>x</code> is valid
if it is within the support of a distribution, <code>self.a &lt;= x &lt;= self.b</code>.
Whether a shape parameter is valid is decided by an <code>_argcheck</code> method
(which defaults to checking that its arguments are strictly positive.)</p>
<p><strong>Subclassing</strong></p>
<p>New random variables can be defined by subclassing the <code>rv_continuous</code> class
and re-defining at least the <code>_pdf</code> or the <code>_cdf</code> method (normalized
to location 0 and scale 1).</p>
<p>If positive argument checking is not correct for your RV
then you will also need to re-define the <code>_argcheck</code> method.</p>
<p>Correct, but potentially slow defaults exist for the remaining
methods but for speed and/or accuracy you can over-ride::</p>
<p>_logpdf, _cdf, _logcdf, _ppf, _rvs, _isf, _sf, _logsf</p>
<p>Rarely would you override <code>_isf</code>, <code>_sf</code> or <code>_logsf</code>, but you could.</p>
<p><strong>Methods that can be overwritten by subclasses</strong>
::</p>
<p>_rvs
_pdf
_cdf
_sf
_ppf
_isf
_stats
_munp
_entropy
_argcheck</p>
<p>There are additional (internal and private) generic methods that can
be useful for cross-checking and for debugging, but might work in all
cases when directly called.</p>
<p>A note on <code>shapes</code>: subclasses need not specify them explicitly. In this
case, <code>shapes</code> will be automatically deduced from the signatures of the
overridden methods (<code>pdf</code>, <code>cdf</code> etc).
If, for some reason, you prefer to avoid relying on introspection, you can
specify <code>shapes</code> explicitly as an argument to the instance constructor.</p>
<p><strong>Frozen Distributions</strong></p>
<p>Normally, you must provide shape parameters (and, optionally, location and
scale parameters to each call of a method of a distribution.</p>
<p>Alternatively, the object may be called (as a function) to fix the shape,
location, and scale parameters returning a "frozen" continuous RV object:</p>
<p>rv = generic(<shape(s)>, loc=0, scale=1)
frozen RV object with the same methods but holding the given shape,
location, and scale fixed</p>
<p><strong>Statistics</strong></p>
<p>Statistics are computed using numerical integration by default.
For speed you can redefine this using <code>_stats</code>:</p>
<ul>
<li>take shape parameters and return mu, mu2, g1, g2</li>
<li>If you can't compute one of these, return it as None</li>
<li>Can also be defined with a keyword argument <code>moments</code>, which is a
string composed of "m", "v", "s", and/or "k".
Only the components appearing in string should be computed and
returned in the order "m", "v", "s", or "k"
with missing values
returned as None.</li>
</ul>
<p>Alternatively, you can override <code>_munp</code>, which takes <code>n</code> and shape
parameters and returns the n-th non-central moment of the distribution.</p>
<h2 id="examples">Examples</h2>
<p>To create a new Gaussian distribution, we would do the following:</p>
<pre><code>&gt;&gt;&gt; from scipy.stats import rv_continuous
&gt;&gt;&gt; class gaussian_gen(rv_continuous):
...     "Gaussian distribution"
...     def _pdf(self, x):
...         return np.exp(-x**2 / 2.) / np.sqrt(2.0 * np.pi)
&gt;&gt;&gt; gaussian = gaussian_gen(name='gaussian')
</code></pre>
<p><code>scipy.stats</code> distributions are <em>instances</em>, so here we subclass
<code>rv_continuous</code> and create an instance. With this, we now have
a fully functional distribution with all relevant methods automagically
generated by the framework.</p>
<p>Note that above we defined a standard normal distribution, with zero mean
and unit variance. Shifting and scaling of the distribution can be done
by using <code>loc</code> and <code>scale</code> parameters: <code>gaussian.pdf(x, loc, scale)</code>
essentially computes <code>y = (x - loc) / scale</code> and
<code>gaussian._pdf(y) / scale</code>.</p></section>
<details class="source">
<summary>Source code</summary>
<pre><code class="python">class radialUniform(st.rv_continuous):
    def _pdf(self, x):
        return 2*x if x&lt;1 else 0</code></pre>
</details>
</dd>
</dl>
</section>
</article>
<nav id="sidebar">
<h1>Index</h1>
<div class="toc">
<ul></ul>
</div>
<ul id="index">
<li><h3><a href="#header-classes">Classes</a></h3>
<ul>
<li>
<h4><code><a title="distributions.radialExp" href="#distributions.radialExp">radialExp</a></code></h4>
</li>
<li>
<h4><code><a title="distributions.radialHernquist" href="#distributions.radialHernquist">radialHernquist</a></code></h4>
</li>
<li>
<h4><code><a title="distributions.radialNFW" href="#distributions.radialNFW">radialNFW</a></code></h4>
</li>
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<h4><code><a title="distributions.radialPlummer" href="#distributions.radialPlummer">radialPlummer</a></code></h4>
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<h4><code><a title="distributions.radialUniform" href="#distributions.radialUniform">radialUniform</a></code></h4>
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