scipy.stats.trapezoid — SciPy v1.15.2 Manual (original) (raw)
scipy.stats.trapezoid = <scipy.stats._continuous_distns.trapezoid_gen object>[source]#
A trapezoidal continuous random variable.
As an instance of the rv_continuous class, trapezoid object 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 loc to (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 loc to (loc+scale) and the flat top from c to d proportional 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.
trapezoid takes \(c\) and \(d\) as shape parameters.
The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the loc and scale parameters. Specifically, trapezoid.pdf(x, c, d, loc, scale) is identically equivalent to trapezoid.pdf(y, c, d) / scale withy = (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 cdf and 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. |