scipy.stats.logistic¶
- scipy.stats.logistic = <scipy.stats._continuous_distns.logistic_gen object at 0x2b238b46f890>[source]¶
A logistic (or Sech-squared) continuous random variable.
As an instance of the rv_continuous class, logistic 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 logistic is:
logistic.pdf(x) = exp(-x) / (1+exp(-x))**2
logistic is a special case of genlogistic with c == 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, logistic.pdf(x, loc, scale) is identically equivalent to logistic.pdf(y) / scale with y = (x - loc) / scale.
Examples
>>> from scipy.stats import logistic >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate a few first moments:
>>> mean, var, skew, kurt = logistic.stats(moments='mvsk')
Display the probability density function (pdf):
>>> x = np.linspace(logistic.ppf(0.01), ... logistic.ppf(0.99), 100) >>> ax.plot(x, logistic.pdf(x), ... 'r-', lw=5, alpha=0.6, label='logistic 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 = logistic() >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
Check accuracy of cdf and ppf:
>>> vals = logistic.ppf([0.001, 0.5, 0.999]) >>> np.allclose([0.001, 0.5, 0.999], logistic.cdf(vals)) True
Generate random numbers:
>>> r = logistic.rvs(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(loc=0, scale=1, size=1, random_state=None) Random variates. pdf(x, loc=0, scale=1) Probability density function. logpdf(x, loc=0, scale=1) Log of the probability density function. cdf(x, loc=0, scale=1) Cumulative density function. logcdf(x, loc=0, scale=1) Log of the cumulative density function. sf(x, loc=0, scale=1) Survival function (also defined as 1 - cdf, but sf is sometimes more accurate). logsf(x, loc=0, scale=1) Log of the survival function. ppf(q, loc=0, scale=1) Percent point function (inverse of cdf — percentiles). isf(q, loc=0, scale=1) Inverse survival function (inverse of sf). moment(n, loc=0, scale=1) Non-central moment of order n stats(loc=0, scale=1, moments='mv') Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). entropy(loc=0, scale=1) (Differential) entropy of the RV. fit(data, loc=0, scale=1) Parameter estimates for generic data. expect(func, args=(), 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(loc=0, scale=1) Median of the distribution. mean(loc=0, scale=1) Mean of the distribution. var(loc=0, scale=1) Variance of the distribution. std(loc=0, scale=1) Standard deviation of the distribution. interval(alpha, loc=0, scale=1) Endpoints of the range that contains alpha percent of the distribution