# 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)
>>> rad
array([  1.,   1.,   1.,   1.,   1.,   1.,   1.,   1.,   1.,   1.,   1.,
1.,   2.,   2.,   2.,   2.,   2.,   3.,   3.,   3.,   4.,   4.,
5.,   5.,   6.,   7.,   8.,  10.,  13.,  21.])

>>> # Fit the logser_uptrunc to data and estimate the parameters
>>> md.logser_uptrunc.fit_mle(rad)
(0.8957385644316679, 114.0)


Methods

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