scipy.stats.boltzmann¶
-
scipy.stats.
boltzmann
= <scipy.stats._discrete_distns.boltzmann_gen object>[source]¶ A Boltzmann (Truncated Discrete Exponential) random variable.
As an instance of the
rv_discrete
class,boltzmann
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 mass function for
boltzmann
is:boltzmann.pmf(k) = (1-exp(-lambda_)*exp(-lambda_*k)/(1-exp(-lambda_*N))
for
k = 0,..., N-1
.boltzmann
takeslambda_
andN
as shape parameters.The probability mass function above is defined in the “standardized” form. To shift distribution use the
loc
parameter. Specifically,boltzmann.pmf(k, lambda_, N, loc)
is identically equivalent toboltzmann.pmf(k - loc, lambda_, N)
.Examples
>>> from scipy.stats import boltzmann >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate a few first moments:
>>> lambda_, N = 1.4, 19 >>> mean, var, skew, kurt = boltzmann.stats(lambda_, N, moments='mvsk')
Display the probability mass function (
pmf
):>>> x = np.arange(boltzmann.ppf(0.01, lambda_, N), ... boltzmann.ppf(0.99, lambda_, N)) >>> ax.plot(x, boltzmann.pmf(x, lambda_, N), 'bo', ms=8, label='boltzmann pmf') >>> ax.vlines(x, 0, boltzmann.pmf(x, lambda_, N), 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 = boltzmann(lambda_, N) >>> 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 = boltzmann.cdf(x, lambda_, N) >>> np.allclose(x, boltzmann.ppf(prob, lambda_, N)) True
Generate random numbers:
>>> r = boltzmann.rvs(lambda_, N, size=1000)
Methods
rvs(lambda_, N, loc=0, size=1, random_state=None)
Random variates. pmf(k, lambda_, N, loc=0)
Probability mass function. logpmf(k, lambda_, N, loc=0)
Log of the probability mass function. cdf(k, lambda_, N, loc=0)
Cumulative distribution function. logcdf(k, lambda_, N, loc=0)
Log of the cumulative distribution function. sf(k, lambda_, N, loc=0)
Survival function (also defined as 1 - cdf
, but sf is sometimes more accurate).logsf(k, lambda_, N, loc=0)
Log of the survival function. ppf(q, lambda_, N, loc=0)
Percent point function (inverse of cdf
— percentiles).isf(q, lambda_, N, loc=0)
Inverse survival function (inverse of sf
).stats(lambda_, N, loc=0, moments='mv')
Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). entropy(lambda_, N, loc=0)
(Differential) entropy of the RV. expect(func, args=(lambda_, N), loc=0, lb=None, ub=None, conditional=False)
Expected value of a function (of one argument) with respect to the distribution. median(lambda_, N, loc=0)
Median of the distribution. mean(lambda_, N, loc=0)
Mean of the distribution. var(lambda_, N, loc=0)
Variance of the distribution. std(lambda_, N, loc=0)
Standard deviation of the distribution. interval(alpha, lambda_, N, loc=0)
Endpoints of the range that contains alpha percent of the distribution