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]
, wherea
andb
are user-provided shape parameters. The parameterloc
shifts the mean of the underlying normal distribution, andscale
controls the standard deviation of the underlying normal, buta
andb
are still defined with respect to the standard normal. Ifmyclip_a
andmyclip_b
are clip values defined with respect to a shifted and scaled normal, they can be converted the required form according to:a, b = (myclip_a - loc) / scale, (myclip_b - loc) / scale
Examples
>>> from scipy.stats import truncnorm >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate the first four 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, density=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(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.