scipy.stats.planck#
- scipy.stats.planck = <scipy.stats._discrete_distns.planck_gen object>[source]#
A Planck discrete exponential random variable.
As an instance of the
rv_discrete
class,planck
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.See also
Notes
The probability mass function for
planck
is:\[f(k) = (1-\exp(-\lambda)) \exp(-\lambda k)\]for \(k \ge 0\) and \(\lambda > 0\).
planck
takes \(\lambda\) as shape parameter. The Planck distribution can be written as a geometric distribution (geom
) with \(p = 1 - \exp(-\lambda)\) shifted byloc = -1
.The probability mass function above is defined in the “standardized” form. To shift distribution use the
loc
parameter. Specifically,planck.pmf(k, lambda_, loc)
is identically equivalent toplanck.pmf(k - loc, lambda_)
.Examples
>>> from scipy.stats import planck >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate the first four moments:
>>> lambda_ = 0.51 >>> mean, var, skew, kurt = planck.stats(lambda_, moments='mvsk')
Display the probability mass function (
pmf
):>>> x = np.arange(planck.ppf(0.01, lambda_), ... planck.ppf(0.99, lambda_)) >>> ax.plot(x, planck.pmf(x, lambda_), 'bo', ms=8, label='planck pmf') >>> ax.vlines(x, 0, planck.pmf(x, lambda_), colors='b', lw=5, alpha=0.5)
Alternatively, the distribution object can be called (as a function) to fix the shape and location. This returns a “frozen” RV object holding the given parameters fixed.
Freeze the distribution and display the frozen
pmf
:>>> rv = planck(lambda_) >>> ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1, ... label='frozen pmf') >>> ax.legend(loc='best', frameon=False) >>> plt.show()
Check accuracy of
cdf
andppf
:>>> prob = planck.cdf(x, lambda_) >>> np.allclose(x, planck.ppf(prob, lambda_)) True
Generate random numbers:
>>> r = planck.rvs(lambda_, size=1000)
Methods
rvs(lambda_, loc=0, size=1, random_state=None)
Random variates.
pmf(k, lambda_, loc=0)
Probability mass function.
logpmf(k, lambda_, loc=0)
Log of the probability mass function.
cdf(k, lambda_, loc=0)
Cumulative distribution function.
logcdf(k, lambda_, loc=0)
Log of the cumulative distribution function.
sf(k, lambda_, loc=0)
Survival function (also defined as
1 - cdf
, but sf is sometimes more accurate).logsf(k, lambda_, loc=0)
Log of the survival function.
ppf(q, lambda_, loc=0)
Percent point function (inverse of
cdf
— percentiles).isf(q, lambda_, loc=0)
Inverse survival function (inverse of
sf
).stats(lambda_, loc=0, moments=’mv’)
Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
entropy(lambda_, loc=0)
(Differential) entropy of the RV.
expect(func, args=(lambda_,), loc=0, lb=None, ub=None, conditional=False)
Expected value of a function (of one argument) with respect to the distribution.
median(lambda_, loc=0)
Median of the distribution.
mean(lambda_, loc=0)
Mean of the distribution.
var(lambda_, loc=0)
Variance of the distribution.
std(lambda_, loc=0)
Standard deviation of the distribution.
interval(confidence, lambda_, loc=0)
Confidence interval with equal areas around the median.