A truncated discrete exponential discrete random variable.

Discrete random variables are defined from a standard form and may require some shape parameters to complete its specification. Any optional keyword parameters can be passed to the methods of the RV object as given below:


boltzmann.rvs(lambda_,N,loc=0,size=1) :

  • random variates

boltzmann.pmf(x,lambda_,N,loc=0) :

  • probability mass function

boltzmann.cdf(x,lambda_,N,loc=0) :

  • cumulative density function

boltzmann.sf(x,lambda_,N,loc=0) :

  • survival function (1-cdf — sometimes more accurate)

boltzmann.ppf(q,lambda_,N,loc=0) :

  • percent point function (inverse of cdf — percentiles)

boltzmann.isf(q,lambda_,N,loc=0) :

  • inverse survival function (inverse of sf)

boltzmann.stats(lambda_,N,loc=0,moments=’mv’) :

  • mean(‘m’,axis=0), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’)

boltzmann.entropy(lambda_,N,loc=0) :

  • entropy of the RV

Alternatively, the object may be called (as a function) to fix :

the shape and location parameters returning a :

“frozen” discrete RV object: :

myrv = boltzmann(lambda_,N,loc=0) :

  • frozen RV object with the same methods but holding the given shape and location fixed.

You can construct an aribtrary discrete rv where P{X=xk} = pk :

by passing to the rv_discrete initialization method (through the values= :

keyword) a tuple of sequences (xk,pk) which describes only those values of :

X (xk) that occur with nonzero probability (pk). :


>>> import matplotlib.pyplot as plt
>>> numargs = boltzmann.numargs
>>> [ lambda_,N ] = ['Replace with resonable value',]*numargs

Display frozen pmf:

>>> rv = boltzmann(lambda_,N)
>>> x = np.arange(0,np.min(rv.dist.b,3)+1)
>>> h = plt.plot(x,rv.pmf(x))

Check accuracy of cdf and ppf:

>>> prb = boltzmann.cdf(x,lambda_,N)
>>> h = plt.semilogy(np.abs(x-boltzmann.ppf(prb,lambda_,N))+1e-20)

Random number generation:

>>> R = boltzmann.rvs(lambda_,N,size=100)

Custom made discrete distribution:

>>> vals = [arange(7),(0.1,0.2,0.3,0.1,0.1,0.1,0.1)]
>>> custm = rv_discrete(name='custm',values=vals)
>>> h = plt.plot(vals[0],custm.pmf(vals[0]))

Boltzmann (Truncated Discrete Exponential)

boltzmann.pmf(k,b,N) = (1-exp(-b))*exp(-b*k)/(1-exp(-b*N)) for k=0,..,N-1

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