scipy.stats.genhalflogistic¶

scipy.stats.
genhalflogistic
= <scipy.stats._continuous_distns.genhalflogistic_gen object>[source]¶ A generalized halflogistic 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.Notes
The probability density function for
genhalflogistic
is:\[f(x, c) = \frac{2 (1  c x)^{1/(c1)}}{[1 + (1  c x)^{1/c}]^2}\]for \(0 \le x \le 1/c\), 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
andscale
parameters. Specifically,genhalflogistic.pdf(x, c, loc, scale)
is identically equivalent togenhalflogistic.pdf(y, c) / scale
withy = (x  loc) / scale
.Examples
>>> 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
andppf
:>>> 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()
Methods
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 distribution function. logcdf(x, c, loc=0, scale=1)
Log of the cumulative distribution function. sf(x, c, loc=0, scale=1)
Survival function (also defined as 1  cdf
, but sf is 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)
Noncentral 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, args=(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