Help on module particula.util.distribution_discretization in particula.util:
NAME
particula.util.distribution_discretization - discretization of the distribution of the particles
FUNCTIONS
discretize(interval=None, disttype='lognormal', gsigma=array(1.25), mode=<Quantity(1e-07, 'meter')>, nparticles=array(100000.), **kwargs)
discretize the distribution of the particles
Args:
interval (float) the size interval of the distribution
distype (str) the type of distribution, "lognormal" for now
gsigma (float) geometric standard deviation of distribution
mode (float) pdf scale (corresponds to mode in lognormal)
DATA
lognorm = <scipy.stats._continuous_distns.lognorm_gen object>
A lognormal continuous random variable.
As an instance of the `rv_continuous` class, `lognorm` object inherits from it
a collection of generic methods (see below for the full list),
and completes them with details specific for this particular distribution.
Methods
-------
rvs(s, loc=0, scale=1, size=1, random_state=None)
Random variates.
pdf(x, s, loc=0, scale=1)
Probability density function.
logpdf(x, s, loc=0, scale=1)
Log of the probability density function.
cdf(x, s, loc=0, scale=1)
Cumulative distribution function.
logcdf(x, s, loc=0, scale=1)
Log of the cumulative distribution function.
sf(x, s, loc=0, scale=1)
Survival function (also defined as ``1 - cdf``, but `sf` is sometimes more accurate).
logsf(x, s, loc=0, scale=1)
Log of the survival function.
ppf(q, s, loc=0, scale=1)
Percent point function (inverse of ``cdf`` --- percentiles).
isf(q, s, loc=0, scale=1)
Inverse survival function (inverse of ``sf``).
moment(order, s, loc=0, scale=1)
Non-central moment of the specified order.
stats(s, loc=0, scale=1, moments='mv')
Mean('m'), variance('v'), skew('s'), and/or kurtosis('k').
entropy(s, loc=0, scale=1)
(Differential) entropy of the RV.
fit(data)
Parameter estimates for generic data.
See `scipy.stats.rv_continuous.fit <https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.fit.html#scipy.stats.rv_continuous.fit>`__ for detailed documentation of the
keyword arguments.
expect(func, args=(s,), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)
Expected value of a function (of one argument) with respect to the distribution.
median(s, loc=0, scale=1)
Median of the distribution.
mean(s, loc=0, scale=1)
Mean of the distribution.
var(s, loc=0, scale=1)
Variance of the distribution.
std(s, loc=0, scale=1)
Standard deviation of the distribution.
interval(confidence, s, loc=0, scale=1)
Confidence interval with equal areas around the median.
Notes
-----
The probability density function for `lognorm` is:
.. math::
f(x, s) = \frac{1}{s x \sqrt{2\pi}}
\exp\left(-\frac{\log^2(x)}{2s^2}\right)
for :math:`x > 0`, :math:`s > 0`.
`lognorm` takes ``s`` as a shape parameter for :math:`s`.
The probability density above is defined in the "standardized" form. To shift
and/or scale the distribution use the ``loc`` and ``scale`` parameters.
Specifically, ``lognorm.pdf(x, s, loc, scale)`` is identically
equivalent to ``lognorm.pdf(y, s) / scale`` with
``y = (x - loc) / scale``. Note that shifting the location of a distribution
does not make it a "noncentral" distribution; noncentral generalizations of
some distributions are available in separate classes.
Suppose a normally distributed random variable ``X`` has mean ``mu`` and
standard deviation ``sigma``. Then ``Y = exp(X)`` is lognormally
distributed with ``s = sigma`` and ``scale = exp(mu)``.
Examples
--------
>>> import numpy as np
>>> from scipy.stats import lognorm
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)
Calculate the first four moments:
>>> s = 0.954
>>> mean, var, skew, kurt = lognorm.stats(s, moments='mvsk')
Display the probability density function (``pdf``):
>>> x = np.linspace(lognorm.ppf(0.01, s),
... lognorm.ppf(0.99, s), 100)
>>> ax.plot(x, lognorm.pdf(x, s),
... 'r-', lw=5, alpha=0.6, label='lognorm pdf')
Alternatively, the distribution object can be called (as a function)
to fix the shape, location and scale parameters. This returns a "frozen"
RV object holding the given parameters fixed.
Freeze the distribution and display the frozen ``pdf``:
>>> rv = lognorm(s)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
Check accuracy of ``cdf`` and ``ppf``:
>>> vals = lognorm.ppf([0.001, 0.5, 0.999], s)
>>> np.allclose([0.001, 0.5, 0.999], lognorm.cdf(vals, s))
True
Generate random numbers:
>>> r = lognorm.rvs(s, size=1000)
And compare the histogram:
>>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
>>> ax.set_xlim([x[0], x[-1]])
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()
The logarithm of a log-normally distributed random variable is
normally distributed:
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from scipy import stats
>>> fig, ax = plt.subplots(1, 1)
>>> mu, sigma = 2, 0.5
>>> X = stats.norm(loc=mu, scale=sigma)
>>> Y = stats.lognorm(s=sigma, scale=np.exp(mu))
>>> x = np.linspace(*X.interval(0.999))
>>> y = Y.rvs(size=10000)
>>> ax.plot(x, X.pdf(x), label='X (pdf)')
>>> ax.hist(np.log(y), density=True, bins=x, label='log(Y) (histogram)')
>>> ax.legend()
>>> plt.show()
u = <pint.registry.UnitRegistry object>
FILE
/opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/particula/util/distribution_discretization.py
