scipy.stats.powerlognorm

scipy.stats.powerlognorm = <scipy.stats._continuous_distns.powerlognorm_gen object at 0x7fe7c49b8860>

A power log-normal continuous random variable.

Continuous random variables are defined from a standard form and may require some shape parameters to complete its specification. Any optional keyword parameters can be passed to the methods of the RV object as given below:

scipy.stats.rvs(c, s, loc=0, scale=1, size=1)

Random variates.

scipy.stats.pdf(x, c, s, loc=0, scale=1)

Probability density function.

scipy.stats.logpdf(x, c, s, loc=0, scale=1)

Log of the probability density function.

scipy.stats.cdf(x, c, s, loc=0, scale=1)

Cumulative density function.

scipy.stats.logcdf(x, c, s, loc=0, scale=1)

Log of the cumulative density function.

scipy.stats.sf(x, c, s, loc=0, scale=1)

Survival function (1-cdf --- sometimes more accurate).

scipy.stats.logsf(x, c, s, loc=0, scale=1)

Log of the survival function.

scipy.stats.ppf(q, c, s, loc=0, scale=1)

Percent point function (inverse of cdf --- percentiles).

scipy.stats.isf(q, c, s, loc=0, scale=1)

Inverse survival function (inverse of sf).

scipy.stats.moment(n, c, s, loc=0, scale=1)

Non-central moment of order n

scipy.stats.stats(c, s, loc=0, scale=1, moments='mv')

Mean('m'), variance('v'), skew('s'), and/or kurtosis('k').

scipy.stats.entropy(c, s, loc=0, scale=1)

(Differential) entropy of the RV.

scipy.stats.fit(data, c, s, loc=0, scale=1)

Parameter estimates for generic data.

scipy.stats.expect(func, c, s, loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)

Expected value of a function (of one argument) with respect to the distribution.

scipy.stats.median(c, s, loc=0, scale=1)

Median of the distribution.

scipy.stats.mean(c, s, loc=0, scale=1)

Mean of the distribution.

scipy.stats.var(c, s, loc=0, scale=1)

Variance of the distribution.

scipy.stats.std(c, s, loc=0, scale=1)

Standard deviation of the distribution.

scipy.stats.interval(alpha, c, s, loc=0, scale=1)

Endpoints of the range that contains alpha percent of the distribution

Parameters:

• x (array_like) -- quantiles
• q (array_like) -- lower or upper tail probability
• s (c,) -- shape parameters
• loc (array_like, optional) -- location parameter (default=0)
• scale (array_like, optional) -- scale parameter (default=1)
• size (int or tuple of ints, optional) -- shape of random variates (default computed from input arguments )
• moments (str, optional) -- composed of letters ['mvsk'] specifying which moments to compute where 'm' = mean, 'v' = variance, 's' = (Fisher's) skew and 'k' = (Fisher's) kurtosis. (default='mv')
• the object may be called (as a function) to fix the shape, (Alternatively,) --
• and scale parameters returning a "frozen" continuous RV object (location,) --
• = powerlognorm(c, s, loc=0, scale=1) (rv) --
  • Frozen RV object with the same methods but holding the given shape,

  location, and scale fixed.

Notes

The probability density function for powerlognorm is:

powerlognorm.pdf(x, c, s) = c / (x*s) * phi(log(x)/s) *
                                        (Phi(-log(x)/s))**(c-1),

where phi is the normal pdf, and Phi is the normal cdf, and x > 0, s, c > 0.

Examples

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

Calculate a few first moments:

>>> c, s = 2.1413923530064087, 0.44639540782048337
>>> mean, var, skew, kurt = powerlognorm.stats(c, s, moments='mvsk')

Display the probability density function (pdf):

>>> x = np.linspace(powerlognorm.ppf(0.01, c, s),
...               powerlognorm.ppf(0.99, c, s), 100)
>>> ax.plot(x, powerlognorm.pdf(x, c, s),
...          'r-', lw=5, alpha=0.6, label='powerlognorm pdf')

Alternatively, freeze the distribution and display the frozen pdf:

>>> rv = powerlognorm(c, s)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

Check accuracy of cdf and ppf:

>>> vals = powerlognorm.ppf([0.001, 0.5, 0.999], c, s)
>>> np.allclose([0.001, 0.5, 0.999], powerlognorm.cdf(vals, c, s))
True

Generate random numbers:

>>> r = powerlognorm.rvs(c, s, size=1000)

And compare the histogram:

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