scipy.stats.truncnorm#
- scipy.stats.truncnorm = <scipy.stats._continuous_distns.truncnorm_gen object>[source]#
- A truncated normal continuous random variable. - As an instance of the - rv_continuousclass,- truncnormobject 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(a, b, loc=0, scale=1, size=1, random_state=None) - Random variates. - pdf(x, a, b, loc=0, scale=1) - Probability density function. - logpdf(x, a, b, loc=0, scale=1) - Log of the probability density function. - cdf(x, a, b, loc=0, scale=1) - Cumulative distribution function. - logcdf(x, a, b, loc=0, scale=1) - Log of the cumulative distribution function. - sf(x, a, b, loc=0, scale=1) - Survival function (also defined as - 1 - cdf, but sf is sometimes more accurate).- logsf(x, a, b, loc=0, scale=1) - Log of the survival function. - ppf(q, a, b, loc=0, scale=1) - Percent point function (inverse of - cdf— percentiles).- isf(q, a, b, loc=0, scale=1) - Inverse survival function (inverse of - sf).- moment(order, a, b, loc=0, scale=1) - Non-central moment of the specified order. - stats(a, b, loc=0, scale=1, moments=’mv’) - Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). - entropy(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=(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(a, b, loc=0, scale=1) - Median of the distribution. - mean(a, b, loc=0, scale=1) - Mean of the distribution. - var(a, b, loc=0, scale=1) - Variance of the distribution. - std(a, b, loc=0, scale=1) - Standard deviation of the distribution. - interval(confidence, a, b, loc=0, scale=1) - Confidence interval with equal areas around the median. - Notes - This distribution is the normal distribution centered on - loc(default 0), with standard deviation- scale(default 1), and truncated at- aand- bstandard deviations from- loc. For arbitrary- locand- scale,- aand- bare not the abscissae at which the shifted and scaled distribution is truncated.- Note - If - a_truncand- b_truncare the abscissae at which we wish to truncate the distribution (as opposed to the number of standard deviations from- loc), then we can calculate the distribution parameters- aand- bas follows:- a, b = (a_trunc - loc) / scale, (b_trunc - loc) / scale - This is a common point of confusion. For additional clarification, please see the example below. - Examples - >>> import numpy as np >>> from scipy.stats import truncnorm >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Get the support: - >>> a, b = 0.1, 2 >>> lb, ub = truncnorm.support(a, b) - Calculate the first four moments: - >>> mean, var, skew, kurt = truncnorm.stats(a, b, moments='mvsk') - Display the probability density function ( - pdf):- >>> x = np.linspace(truncnorm.ppf(0.01, a, b), ... truncnorm.ppf(0.99, a, b), 100) >>> ax.plot(x, truncnorm.pdf(x, a, b), ... 'r-', lw=5, alpha=0.6, label='truncnorm 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 = truncnorm(a, b) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') - Check accuracy of - cdfand- ppf:- >>> vals = truncnorm.ppf([0.001, 0.5, 0.999], a, b) >>> np.allclose([0.001, 0.5, 0.999], truncnorm.cdf(vals, a, b)) True - Generate random numbers: - >>> r = truncnorm.rvs(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()   - In the examples above, - loc=0and- scale=1, so the plot is truncated at- aon the left and- bon the right. However, suppose we were to produce the same histogram with- loc = 1and- scale=0.5.- >>> loc, scale = 1, 0.5 >>> rv = truncnorm(a, b, loc=loc, scale=scale) >>> x = np.linspace(truncnorm.ppf(0.01, a, b), ... truncnorm.ppf(0.99, a, b), 100) >>> r = rv.rvs(size=1000) - >>> fig, ax = plt.subplots(1, 1) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') >>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2) >>> ax.set_xlim(a, b) >>> ax.legend(loc='best', frameon=False) >>> plt.show()   - Note that the distribution is no longer appears to be truncated at abscissae - aand- b. That is because the standard normal distribution is first truncated at- aand- b, then the resulting distribution is scaled by- scaleand shifted by- loc. If we instead want the shifted and scaled distribution to be truncated at- aand- b, we need to transform these values before passing them as the distribution parameters.- >>> a_transformed, b_transformed = (a - loc) / scale, (b - loc) / scale >>> rv = truncnorm(a_transformed, b_transformed, loc=loc, scale=scale) >>> x = np.linspace(truncnorm.ppf(0.01, a, b), ... truncnorm.ppf(0.99, a, b), 100) >>> r = rv.rvs(size=10000) - >>> fig, ax = plt.subplots(1, 1) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') >>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2) >>> ax.set_xlim(a-0.1, b+0.1) >>> ax.legend(loc='best', frameon=False) >>> plt.show() 