macroeco.models.lognorm = <macroeco.models._distributions.lognorm_gen object at 0x108661a90>

A lognormal random variable.

\[f(x) = \frac{1}{\sigma x \sqrt{2 \pi}} e^{(\log{x} - \mu)^2 / 2 \sigma^2}\]

x : array_like


q : array_like

lower or upper tail probability

mu, sigma : array_like

shape parameters

loc : array_like, optional

location parameter (default=0)

scale : array_like, optional

scale parameter (default=1)

size : int or tuple of ints, optional

shape of random variates (default computed from input arguments )

moments : str, optional

composed of letters [‘mvsk’] specifying which moments to compute where ‘m’ = mean, ‘v’ = variance, ‘s’ = (Fisher’s) skew and ‘k’ = (Fisher’s) kurtosis. (default=’mv’)

Alternatively, the object may be called (as a function) to fix the shape, :

location, and scale parameters returning a “frozen” continuous RV object: :

rv = lognorm(mu, sigma, loc=0, scale=1) :

  • Frozen RV object with the same methods but holding the given shape, location, and scale fixed.

mu : float

mu parameter of lognormal distribution. Mean log(x)

sigma : float

sigma parameter of lognormal distribution. sd of log(x)


>>> import macroeco.models as md
>>> import numpy as np
>>> # Given mean = 20 and sigma = 2, get the parameters for the lognormal
>>> md.lognorm.translate_args(20, 2)
(0.99573227355399085, 2)
>>> # Define a lognormal distribution
>>> lgnorm = md.lognorm(mu=0.99573227355399085, sigma=2)
>>> # Get the PDF
>>> lgnorm.pdf(np.linspace(0.1, 100, num=10))
array([  5.12048368e-01,   1.38409265e-02,   5.13026600e-03,
     2.71233007e-03,   1.68257934e-03,   1.14517879e-03,
     8.28497146e-04,   6.26026253e-04,   4.88734158e-04,
>>> # Get the stats for the lognormal
>>> lgnorm.stats()
(array(19.99935453933589), array(21437.87621568711))
>>> # Similarly you could use
>>> md.lognorm.stats(mu=0.99573227355399085, sigma=2)
(array(20.0), array(21439.260013257688))
>>> # Draw some random numbers from the lognormal
>>> samp = md.lognorm.rvs(mu=1.5, sigma=1.3, size=100)
>>> # Fit model to data
>>> md.lognorm.fit_mle(samp)
(1.2717334369626212, 1.3032723732257057)
>>> # Get the rank abundance distribution for a lognormal for 10 species
>>> md.lognorm.rank(10, 1.5, 1.3)
array([  0.52818445,   1.16490157,   1.86481775,   2.71579138,
     3.806234  ,   5.27701054,   7.39583206,  10.77077745,
    17.24226102,  38.02750505])


rvs(mu, sigma, loc=0, scale=1, size=1) Random variates.
pdf(x, mu, sigma, loc=0, scale=1) Probability density function.
logpdf(x, mu, sigma, loc=0, scale=1) Log of the probability density function.
cdf(x, mu, sigma, loc=0, scale=1) Cumulative density function.
logcdf(x, mu, sigma, loc=0, scale=1) Log of the cumulative density function.
sf(x, mu, sigma, loc=0, scale=1) Survival function (1-cdf — sometimes more accurate).
logsf(x, mu, sigma, loc=0, scale=1) Log of the survival function.
ppf(q, mu, sigma, loc=0, scale=1) Percent point function (inverse of cdf — percentiles).
isf(q, mu, sigma, loc=0, scale=1) Inverse survival function (inverse of sf).
moment(n, mu, sigma, loc=0, scale=1) Non-central moment of order n
stats(mu, sigma, loc=0, scale=1, moments=’mv’) Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
entropy(mu, sigma, loc=0, scale=1) (Differential) entropy of the RV.
fit(data, mu, sigma, loc=0, scale=1) Parameter estimates for generic data.
expect(func, mu, sigma, 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(mu, sigma, loc=0, scale=1) Median of the distribution.
mean(mu, sigma, loc=0, scale=1) Mean of the distribution.
var(mu, sigma, loc=0, scale=1) Variance of the distribution.
std(mu, sigma, loc=0, scale=1) Standard deviation of the distribution.
interval(alpha, mu, sigma, loc=0, scale=1) Endpoints of the range that contains alpha percent of the distribution