# macroeco.models.logser¶

macroeco.models.logser = <macroeco.models._distributions.logser_gen object at 0x1086532d0>

Logseries (logarithmic) random variable.

$P(x) = - p**x / (x*log(1-p))$
Parameters: x : array_like quantiles 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 = logser(p, loc=0) : Frozen RV object with the same methods but holding the given shape and location fixed. p : float p parameter of the logseries distribution

Examples

>>> import macroeco.models as md

>>> # Define a logseries distribution by specifying the necessary parameters
>>> logser_dist = md.logser(p=0.9)

>>> # Get the pmf
>>> logser_dist.pmf(1)
0.39086503371292664

>>> # Get the cdf
>>> logser_dist.cdf(10)
0.9201603889810761

>>> # You can also use the following notation
>>> md.logser.pmf(1, 0.9)
0.39086503371292664
>>> md.logser.cdf(10, 0.9)
0.9201603889810761

>>> # Get a rank abundance distribution for 30 species

>>> # Fit the logser to data and estimate the parameters