scipy.stats.truncpareto#
- scipy.stats.truncpareto = <scipy.stats._continuous_distns.truncpareto_gen object>[source]#
- An upper truncated Pareto continuous random variable. - As an instance of the - rv_continuousclass,- truncparetoobject inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.- See also - pareto
- Pareto distribution 
 - Notes - The probability density function for - truncparetois:\[f(x, b, c) = \frac{b}{1 - c^{-b}} \frac{1}{x^{b+1}}\]- for \(b > 0\), \(c > 1\) and \(1 \le x \le c\). - truncparetotakes b and c as shape parameters for \(b\) and \(c\).- Notice that the upper truncation value \(c\) is defined in standardized form so that random values of an unscaled, unshifted variable are within the range - [1, c]. If- u_ris the upper bound to a scaled and/or shifted variable, then- c = (u_r - loc) / scale. In other words, the support of the distribution becomes- (scale + loc) <= x <= (c*scale + loc)when scale and/or loc are provided.- The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the - locand- scaleparameters. Specifically,- truncpareto.pdf(x, b, c, loc, scale)is identically equivalent to- truncpareto.pdf(y, b, c) / scalewith- y = (x - loc) / scale. Note that shifting the location of a distribution does not make it a “noncentral” distribution; noncentral generalizations of some distributions are available in separate classes.- References [1]- Burroughs, S. M., and Tebbens S. F. “Upper-truncated power laws in natural systems.” Pure and Applied Geophysics 158.4 (2001): 741-757. - Examples - >>> import numpy as np >>> from scipy.stats import truncpareto >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Calculate the first four moments: - >>> b, c = 2, 5 >>> mean, var, skew, kurt = truncpareto.stats(b, c, moments='mvsk') - Display the probability density function ( - pdf):- >>> x = np.linspace(truncpareto.ppf(0.01, b, c), ... truncpareto.ppf(0.99, b, c), 100) >>> ax.plot(x, truncpareto.pdf(x, b, c), ... 'r-', lw=5, alpha=0.6, label='truncpareto pdf') - Alternatively, the distribution object can be called (as a function) to fix the shape, location and scale parameters. This returns a “frozen” RV object holding the given parameters fixed. - Freeze the distribution and display the frozen - pdf:- >>> rv = truncpareto(b, c) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') - Check accuracy of - cdfand- ppf:- >>> vals = truncpareto.ppf([0.001, 0.5, 0.999], b, c) >>> np.allclose([0.001, 0.5, 0.999], truncpareto.cdf(vals, b, c)) True - Generate random numbers: - >>> r = truncpareto.rvs(b, c, size=1000) - And compare the histogram: - >>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2) >>> ax.set_xlim([x[0], x[-1]]) >>> ax.legend(loc='best', frameon=False) >>> plt.show()   - Methods - rvs(b, c, loc=0, scale=1, size=1, random_state=None) - Random variates. - pdf(x, b, c, loc=0, scale=1) - Probability density function. - logpdf(x, b, c, loc=0, scale=1) - Log of the probability density function. - cdf(x, b, c, loc=0, scale=1) - Cumulative distribution function. - logcdf(x, b, c, loc=0, scale=1) - Log of the cumulative distribution function. - sf(x, b, c, loc=0, scale=1) - Survival function (also defined as - 1 - cdf, but sf is sometimes more accurate).- logsf(x, b, c, loc=0, scale=1) - Log of the survival function. - ppf(q, b, c, loc=0, scale=1) - Percent point function (inverse of - cdf— percentiles).- isf(q, b, c, loc=0, scale=1) - Inverse survival function (inverse of - sf).- moment(order, b, c, loc=0, scale=1) - Non-central moment of the specified order. - stats(b, c, loc=0, scale=1, moments=’mv’) - Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). - entropy(b, c, loc=0, scale=1) - (Differential) entropy of the RV. - fit(data) - Parameter estimates for generic data. See scipy.stats.rv_continuous.fit for detailed documentation of the keyword arguments. - expect(func, args=(b, c), 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(b, c, loc=0, scale=1) - Median of the distribution. - mean(b, c, loc=0, scale=1) - Mean of the distribution. - var(b, c, loc=0, scale=1) - Variance of the distribution. - std(b, c, loc=0, scale=1) - Standard deviation of the distribution. - interval(confidence, b, c, loc=0, scale=1) - Confidence interval with equal areas around the median.