# macroeco.models.expon_uptrunc¶

macroeco.models.expon_uptrunc = <macroeco.models._distributions.expon_uptrunc_gen object at 0x108661bd0>

An upper-truncated exponential continuous random variable.

$f(x) = \frac{\lambda e^{-\lambda x}}{1 - e^{-\lambda b}}$

for b >= x >= 0. The loc and scale parameters are not used.

Parameters: x : array_like quantiles q : array_like lower or upper tail probability lam, b : 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 = expon_uptrunc(lam, b, loc=0, scale=1) : Frozen RV object with the same methods but holding the given shape, location, and scale fixed. mu : float distribution mean b : float distribution upper limit, defaults to sum of data

Examples

>>> import macroeco.models as md
>>> import numpy as np

>>> # Get the rate parameter of the exponential distribution from a mean
>>> md.expon_uptrunc.translate_args(20, 100)
(array(0.04801007549722518), 100)

>>> # Get the pdf
>>> md.expon_uptrunc.pdf(np.linspace(0.1, 10, num=10), 0.05, 100)
array([ 0.05008812,  0.04740766,  0.04487064,  0.0424694 ,  0.04019665,
0.03804554,  0.03600953,  0.03408249,  0.03225857,  0.03053226])

>>> # Get the cdf
>>> md.expon_uptrunc.cdf(np.linspace(0.1, 10, num=10), 0.05, 100)
array([ 0.00502135,  0.05863052,  0.10937079,  0.15739571,  0.20285058,
0.24587294,  0.28659296,  0.32513386,  0.36161225,  0.3961385 ])

>>> # Get the ppf
>>> md.expon_uptrunc.ppf(0.8, 0.05, 100)
31.656858541834165

>>> # Draw a random sample
>>> samp = md.expon_uptrunc.rvs(0.05, 100, size=100)

>>> # Fit the model to data
>>> md.expon_uptrunc.fit_mle(samp)
(0.06080396315704938, 1644.6296393823973)


Methods

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