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_continuous
class,truncnorm
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 standard form of this distribution is a standard normal truncated to the range [a, b] — notice that a and b are defined over the domain of the standard normal. To convert clip values for a specific mean and standard deviation, use:
a, b = (myclip_a - my_mean) / my_std, (myclip_b - my_mean) / my_std
truncnorm
takes \(a\) and \(b\) as shape parameters.The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the
loc
andscale
parameters. Specifically,truncnorm.pdf(x, a, b, loc, scale)
is identically equivalent totruncnorm.pdf(y, a, b) / scale
withy = (x - loc) / scale
.Examples
>>> from scipy.stats import truncnorm >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate a few first moments:
>>> a, b = 0.1, 2 >>> 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
cdf
andppf
:>>> 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, normed=True, histtype='stepfilled', alpha=0.2) >>> ax.legend(loc='best', frameon=False) >>> plt.show()
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(n, a, b, loc=0, scale=1)
Non-central moment of order n 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, a, b, loc=0, scale=1)
Parameter estimates for generic data. 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(alpha, a, b, loc=0, scale=1)
Endpoints of the range that contains alpha percent of the distribution