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This is documentation for an old release of SciPy (version 0.17.1). Read this page in the documentation of the latest stable release (version 1.15.1).

scipy.stats.exponnorm

scipy.stats.exponnorm = <scipy.stats._continuous_distns.exponnorm_gen object at 0x2b238b20a710>[source]

An exponentially modified Normal continuous random variable.

As an instance of the rv_continuous class, exponnorm 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 probability density function for exponnorm is:

exponnorm.pdf(x, K) = 1/(2*K) exp(1/(2 * K**2)) exp(-x / K) * erfc(-(x - 1/K) / sqrt(2))

where the shape parameter K > 0.

It can be thought of as the sum of a normally distributed random value with mean loc and sigma scale and an exponentially distributed random number with a pdf proportional to exp(-lambda * x) where lambda = (K * scale)**(-1).

The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the loc and scale parameters. Specifically, exponnorm.pdf(x, K, loc, scale) is identically equivalent to exponnorm.pdf(y, K) / scale with y = (x - loc) / scale.

An alternative parameterization of this distribution (for example, in Wikipedia) involves three parameters, μ, λ and σ. In the present parameterization this corresponds to having loc and scale equal to μ and σ, respectively, and shape parameter K=1/σλ.

New in version 0.16.0.

Examples

>>>
>>> from scipy.stats import exponnorm
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)

Calculate a few first moments:

>>>
>>> K = 1.5
>>> mean, var, skew, kurt = exponnorm.stats(K, moments='mvsk')

Display the probability density function (pdf):

>>>
>>> x = np.linspace(exponnorm.ppf(0.01, K),
...                 exponnorm.ppf(0.99, K), 100)
>>> ax.plot(x, exponnorm.pdf(x, K),
...        'r-', lw=5, alpha=0.6, label='exponnorm 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 = exponnorm(K)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

Check accuracy of cdf and ppf:

>>>
>>> vals = exponnorm.ppf([0.001, 0.5, 0.999], K)
>>> np.allclose([0.001, 0.5, 0.999], exponnorm.cdf(vals, K))
True

Generate random numbers:

>>>
>>> r = exponnorm.rvs(K, size=1000)

And compare the histogram:

>>>
>>> ax.hist(r, normed=True, histtype='stepfilled', alpha=0.2)
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()

(Source code)

../_images/scipy-stats-exponnorm-1.png

Methods

rvs(K, loc=0, scale=1, size=1, random_state=None) Random variates.
pdf(x, K, loc=0, scale=1) Probability density function.
logpdf(x, K, loc=0, scale=1) Log of the probability density function.
cdf(x, K, loc=0, scale=1) Cumulative density function.
logcdf(x, K, loc=0, scale=1) Log of the cumulative density function.
sf(x, K, loc=0, scale=1) Survival function (also defined as 1 - cdf, but sf is sometimes more accurate).
logsf(x, K, loc=0, scale=1) Log of the survival function.
ppf(q, K, loc=0, scale=1) Percent point function (inverse of cdf — percentiles).
isf(q, K, loc=0, scale=1) Inverse survival function (inverse of sf).
moment(n, K, loc=0, scale=1) Non-central moment of order n
stats(K, loc=0, scale=1, moments='mv') Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
entropy(K, loc=0, scale=1) (Differential) entropy of the RV.
fit(data, K, loc=0, scale=1) Parameter estimates for generic data.
expect(func, args=(K,), 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(K, loc=0, scale=1) Median of the distribution.
mean(K, loc=0, scale=1) Mean of the distribution.
var(K, loc=0, scale=1) Variance of the distribution.
std(K, loc=0, scale=1) Standard deviation of the distribution.
interval(alpha, K, loc=0, scale=1) Endpoints of the range that contains alpha percent of the distribution

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