# scipy.stats.boltzmann¶

scipy.stats.boltzmann()

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:

Methods: 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). :

Examples

```>>> 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)
```

```>>> 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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