macroeco.models.geom = <macroeco.models._distributions.geom_gen object at 0x1082d3f50>

A geometric discrete random variable.

This implementation of the geometric distribution differs from that in scipy.stats, as the distribution here has support from 0 to inf.

\[P(x) = (1-p)^{x} p\]

for x >= 0. The loc parameter is not used.


x : array_like


q : array_like

lower or upper tail probability

p : array_like

shape parameters

loc : array_like, optional

location parameter (default=0)

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 and :

location parameters returning a “frozen” discrete RV object: :

rv = geom(p, loc=0) :

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

mu : float

distribution mean


>>> import macroeco.models as md
>>> # Get the geom_parameters from a mean
>>> mu = 20
>>> p = md.geom.translate_args(mu)
>>> # Get the pmf
>>> md.geom.pmf(np.arange(0, 5), p)
array([ 0.04761905,  0.04535147,  0.04319188,  0.04113512,  0.03917631])
>>> # Generate a rank abundance distribution
>>> rad = md.geom.rank(20, p)
>>> rad
array([  0.,   1.,   2.,   3.,   5.,   6.,   8.,   9.,  11.,  13.,  15.,
    17.,  20.,  23.,  26.,  30.,  35.,  42.,  53.,  75.])
>>> # Fit the geom to data
>>> md.geom.fit_mle(rad)


rvs(p, loc=0, size=1) Random variates.
pmf(x, p, loc=0) Probability mass function.
logpmf(x, p, loc=0) Log of the probability mass function.
cdf(x, p, loc=0) Cumulative density function.
logcdf(x, p, loc=0) Log of the cumulative density function.
sf(x, p, loc=0) Survival function (1-cdf — sometimes more accurate).
logsf(x, p, loc=0) Log of the survival function.
ppf(q, p, loc=0) Percent point function (inverse of cdf — percentiles).
isf(q, p, loc=0) Inverse survival function (inverse of sf).
stats(p, loc=0, moments=’mv’) Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
entropy(p, loc=0) (Differential) entropy of the RV.
expect(func, p, loc=0, lb=None, ub=None, conditional=False) Expected value of a function (of one argument) with respect to the distribution.
median(p, loc=0) Median of the distribution.
mean(p, loc=0) Mean of the distribution.
var(p, loc=0) Variance of the distribution.
std(p, loc=0) Standard deviation of the distribution.
interval(alpha, p, loc=0) Endpoints of the range that contains alpha percent of the distribution