scipy.stats.trapezoid#
- scipy.stats.trapezoid = <scipy.stats._continuous_distns.trapezoid_gen object>[source]#
- A trapezoidal continuous random variable. - As an instance of the - rv_continuousclass,- trapezoidobject inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.- Notes - The trapezoidal distribution can be represented with an up-sloping line from - locto- (loc + c*scale), then constant to- (loc + d*scale)and then downsloping from- (loc + d*scale)to- (loc+scale). This defines the trapezoid base from- locto- (loc+scale)and the flat top from- cto- dproportional to the position along the base with- 0 <= c <= d <= 1. When- c=d, this is equivalent to- triangwith the same values for loc, scale and c. The method of [1] is used for computing moments.- trapezoidtakes \(c\) and \(d\) as shape parameters.- The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the - locand- scaleparameters. Specifically,- trapezoid.pdf(x, c, d, loc, scale)is identically equivalent to- trapezoid.pdf(y, c, d) / 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.- The standard form is in the range [0, 1] with c the mode. The location parameter shifts the start to loc. The scale parameter changes the width from 1 to scale. - References [1]- Kacker, R.N. and Lawrence, J.F. (2007). Trapezoidal and triangular distributions for Type B evaluation of standard uncertainty. Metrologia 44, 117-127. DOI:10.1088/0026-1394/44/2/003 - Examples - >>> import numpy as np >>> from scipy.stats import trapezoid >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Calculate the first four moments: - >>> c, d = 0.2, 0.8 >>> mean, var, skew, kurt = trapezoid.stats(c, d, moments='mvsk') - Display the probability density function ( - pdf):- >>> x = np.linspace(trapezoid.ppf(0.01, c, d), ... trapezoid.ppf(0.99, c, d), 100) >>> ax.plot(x, trapezoid.pdf(x, c, d), ... 'r-', lw=5, alpha=0.6, label='trapezoid 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 = trapezoid(c, d) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') - Check accuracy of - cdfand- ppf:- >>> vals = trapezoid.ppf([0.001, 0.5, 0.999], c, d) >>> np.allclose([0.001, 0.5, 0.999], trapezoid.cdf(vals, c, d)) True - Generate random numbers: - >>> r = trapezoid.rvs(c, d, 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(c, d, loc=0, scale=1, size=1, random_state=None) - Random variates. - pdf(x, c, d, loc=0, scale=1) - Probability density function. - logpdf(x, c, d, loc=0, scale=1) - Log of the probability density function. - cdf(x, c, d, loc=0, scale=1) - Cumulative distribution function. - logcdf(x, c, d, loc=0, scale=1) - Log of the cumulative distribution function. - sf(x, c, d, loc=0, scale=1) - Survival function (also defined as - 1 - cdf, but sf is sometimes more accurate).- logsf(x, c, d, loc=0, scale=1) - Log of the survival function. - ppf(q, c, d, loc=0, scale=1) - Percent point function (inverse of - cdf— percentiles).- isf(q, c, d, loc=0, scale=1) - Inverse survival function (inverse of - sf).- moment(order, c, d, loc=0, scale=1) - Non-central moment of the specified order. - stats(c, d, loc=0, scale=1, moments=’mv’) - Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). - entropy(c, d, 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, d), 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, d, loc=0, scale=1) - Median of the distribution. - mean(c, d, loc=0, scale=1) - Mean of the distribution. - var(c, d, loc=0, scale=1) - Variance of the distribution. - std(c, d, loc=0, scale=1) - Standard deviation of the distribution. - interval(confidence, c, d, loc=0, scale=1) - Confidence interval with equal areas around the median.