- scipy.stats.genhalflogistic = <scipy.stats._continuous_distns.genhalflogistic_gen object at 0x4506a62c>¶
A generalized half-logistic continuous random variable.
As an instance of the rv_continuous class, genhalflogistic 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.
The probability density function for genhalflogistic is:
genhalflogistic.pdf(x, c) = 2 * (1-c*x)**(1/c-1) / (1+(1-c*x)**(1/c))**2
for 0 <= x <= 1/c, and c > 0.
genhalflogistic takes c as a shape parameter.
The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the loc and scale parameters. Specifically, genhalflogistic.pdf(x, c, loc, scale) is identically equivalent to genhalflogistic.pdf(y, c) / scale with y = (x - loc) / scale.
>>> from scipy.stats import genhalflogistic >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate a few first moments:
>>> c = 0.773 >>> mean, var, skew, kurt = genhalflogistic.stats(c, moments='mvsk')
Display the probability density function (pdf):
>>> x = np.linspace(genhalflogistic.ppf(0.01, c), ... genhalflogistic.ppf(0.99, c), 100) >>> ax.plot(x, genhalflogistic.pdf(x, c), ... 'r-', lw=5, alpha=0.6, label='genhalflogistic 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 = genhalflogistic(c) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
Check accuracy of cdf and ppf:
>>> vals = genhalflogistic.ppf([0.001, 0.5, 0.999], c) >>> np.allclose([0.001, 0.5, 0.999], genhalflogistic.cdf(vals, c)) True
Generate random numbers:
>>> r = genhalflogistic.rvs(c, size=1000)
And compare the histogram:
>>> ax.hist(r, normed=True, histtype='stepfilled', alpha=0.2) >>> ax.legend(loc='best', frameon=False) >>> plt.show()
rvs(c, loc=0, scale=1, size=1, random_state=None) Random variates. pdf(x, c, loc=0, scale=1) Probability density function. logpdf(x, c, loc=0, scale=1) Log of the probability density function. cdf(x, c, loc=0, scale=1) Cumulative density function. logcdf(x, c, loc=0, scale=1) Log of the cumulative density function. sf(x, c, loc=0, scale=1) Survival function (1 - cdf — sometimes more accurate). logsf(x, c, loc=0, scale=1) Log of the survival function. ppf(q, c, loc=0, scale=1) Percent point function (inverse of cdf — percentiles). isf(q, c, loc=0, scale=1) Inverse survival function (inverse of sf). moment(n, c, loc=0, scale=1) Non-central moment of order n stats(c, loc=0, scale=1, moments='mv') Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). entropy(c, loc=0, scale=1) (Differential) entropy of the RV. fit(data, c, loc=0, scale=1) Parameter estimates for generic data. expect(func, c, 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(c, loc=0, scale=1) Median of the distribution. mean(c, loc=0, scale=1) Mean of the distribution. var(c, loc=0, scale=1) Variance of the distribution. std(c, loc=0, scale=1) Standard deviation of the distribution. interval(alpha, c, loc=0, scale=1) Endpoints of the range that contains alpha percent of the distribution