scipy.stats.truncweibull_min#
- scipy.stats.truncweibull_min = <scipy.stats._continuous_distns.truncweibull_min_gen object>[source]#
- A doubly truncated Weibull minimum continuous random variable. - As an instance of the - rv_continuousclass,- truncweibull_minobject inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.- Methods - rvs(c, a, b, loc=0, scale=1, size=1, random_state=None) - Random variates. - pdf(x, c, a, b, loc=0, scale=1) - Probability density function. - logpdf(x, c, a, b, loc=0, scale=1) - Log of the probability density function. - cdf(x, c, a, b, loc=0, scale=1) - Cumulative distribution function. - logcdf(x, c, a, b, loc=0, scale=1) - Log of the cumulative distribution function. - sf(x, c, a, b, loc=0, scale=1) - Survival function (also defined as - 1 - cdf, but sf is sometimes more accurate).- logsf(x, c, a, b, loc=0, scale=1) - Log of the survival function. - ppf(q, c, a, b, loc=0, scale=1) - Percent point function (inverse of - cdf— percentiles).- isf(q, c, a, b, loc=0, scale=1) - Inverse survival function (inverse of - sf).- moment(order, c, a, b, loc=0, scale=1) - Non-central moment of the specified order. - stats(c, a, b, loc=0, scale=1, moments=’mv’) - Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). - entropy(c, a, b, 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=(c, a, 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(c, a, b, loc=0, scale=1) - Median of the distribution. - mean(c, a, b, loc=0, scale=1) - Mean of the distribution. - var(c, a, b, loc=0, scale=1) - Variance of the distribution. - std(c, a, b, loc=0, scale=1) - Standard deviation of the distribution. - interval(confidence, c, a, b, loc=0, scale=1) - Confidence interval with equal areas around the median. - See also - Notes - The probability density function for - truncweibull_minis:\[f(x, a, b, c) = \frac{c x^{c-1} \exp(-x^c)}{\exp(-a^c) - \exp(-b^c)}\]- for \(a < x <= b\), \(0 \le a < b\) and \(c > 0\). - truncweibull_mintakes \(a\), \(b\), and \(c\) as shape parameters.- Notice that the truncation values, \(a\) and \(b\), are defined in standardized form: \[a = (u_l - loc)/scale b = (u_r - loc)/scale\]- where \(u_l\) and \(u_r\) are the specific left and right truncation values, respectively. In other words, the support of the distribution becomes \((a*scale + loc) < x <= (b*scale + loc)\) when \(loc\) and/or \(scale\) are provided. - The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the - locand- scaleparameters. Specifically,- truncweibull_min.pdf(x, c, a, b, loc, scale)is identically equivalent to- truncweibull_min.pdf(y, c, a, b) / 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]- Rinne, H. “The Weibull Distribution: A Handbook”. CRC Press (2009). - Examples - >>> import numpy as np >>> from scipy.stats import truncweibull_min >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Get the support: - >>> c, a, b = 2.5, 0.25, 1.75 >>> lb, ub = truncweibull_min.support(c, a, b) - Calculate the first four moments: - >>> mean, var, skew, kurt = truncweibull_min.stats(c, a, b, moments='mvsk') - Display the probability density function ( - pdf):- >>> x = np.linspace(truncweibull_min.ppf(0.01, c, a, b), ... truncweibull_min.ppf(0.99, c, a, b), 100) >>> ax.plot(x, truncweibull_min.pdf(x, c, a, b), ... 'r-', lw=5, alpha=0.6, label='truncweibull_min 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 = truncweibull_min(c, a, b) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') - Check accuracy of - cdfand- ppf:- >>> vals = truncweibull_min.ppf([0.001, 0.5, 0.999], c, a, b) >>> np.allclose([0.001, 0.5, 0.999], truncweibull_min.cdf(vals, c, a, b)) True - Generate random numbers: - >>> r = truncweibull_min.rvs(c, a, b, 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() 