# macroeco.models.logser_uptrunc¶

macroeco.models.logser_uptrunc = <macroeco.models._distributions.logser_uptrunc_gen object at 0x1086537d0>

Upper truncated logseries random variable.

This distribution was described by Harte (2011) [1]

$p(x) = \frac{1}{Z} \frac{p^n}{n}$

where Z is the normalizing factor

Parameters: x : array_like quantiles q : array_like lower or upper tail probability p, b : 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_uptrunc(p, b, 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 b : float Upper bound of the distribution

Notes

Code adapted from Ethan White’s macroecology_tools and version 0.1 of macroeco

References

 [1] Harte, J. (2011). Maximum Entropy and Ecology: A Theory of Abundance, Distribution, and Energetics. Oxford, United Kingdom: Oxford University Press.

Examples

>>> import macroeco.models as md

>>> # Define a logseries distribution by specifying the necessary parameters
>>> logser_dist = md.logser_uptrunc(p=0.9, b=1000)

>>> # 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_uptrunc.pmf(1, 0.9, 1000)
0.39086503371292664
>>> md.logser_uptrunc.cdf(10, 0.9, 1000)
0.9201603889810761

>>> # Get a rank abundance distribution for 30 species
>>> rad = md.logser_uptrunc.rank(30, 0.9, 1000)

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