# scipy.stats.boltzmann¶

scipy.stats.boltzmann = <scipy.stats.distributions.boltzmann_gen object at 0x4603e90>[source]

A Boltzmann (Truncated Discrete Exponential) 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:

Parameters : x : array_like quantiles q : array_like lower or upper tail probability lamda, N : array_like shape parameters loc : array_like, optional location parameter (default=0) scale : array_like, optional scale parameter (default=1) size : int or tuple of ints, optional shape of random variates (default computed from input arguments ) moments : str, optional composed of letters [‘mvsk’] specifying which moments to compute where ‘m’ = mean, ‘v’ = variance, ‘s’ = (Fisher’s) skew and ‘k’ = (Fisher’s) kurtosis. (default=’mv’) Alternatively, the object may be called (as a function) to fix the shape and : location parameters returning a “frozen” discrete RV object: : rv = boltzmann(lamda, N, loc=0) : Frozen RV object with the same methods but holding the given shape and location fixed.

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 takes lambda and N as shape parameters.

Examples

```>>> from scipy.stats import boltzmann
>>> [ lamda, N ] = [<Replace with reasonable values>]
>>> rv = boltzmann(lamda, N)
```

Display frozen pmf

```>>> x = np.arange(0, np.minimum(rv.dist.b, 3))
>>> h = plt.vlines(x, 0, rv.pmf(x), lw=2)
```

Here, rv.dist.b is the right endpoint of the support of rv.dist.

Check accuracy of cdf and ppf

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

Random number generation

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

Methods

 rvs(lamda, N, loc=0, size=1) Random variates. pmf(x, lamda, N, loc=0) Probability mass function. logpmf(x, lamda, N, loc=0) Log of the probability mass function. cdf(x, lamda, N, loc=0) Cumulative density function. logcdf(x, lamda, N, loc=0) Log of the cumulative density function. sf(x, lamda, N, loc=0) Survival function (1-cdf — sometimes more accurate). logsf(x, lamda, N, loc=0) Log of the survival function. ppf(q, lamda, N, loc=0) Percent point function (inverse of cdf — percentiles). isf(q, lamda, N, loc=0) Inverse survival function (inverse of sf). stats(lamda, N, loc=0, moments=’mv’) Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). entropy(lamda, N, loc=0) (Differential) entropy of the RV. expect(func, lamda, N, loc=0, lb=None, ub=None, conditional=False) Expected value of a function (of one argument) with respect to the distribution. median(lamda, N, loc=0) Median of the distribution. mean(lamda, N, loc=0) Mean of the distribution. var(lamda, N, loc=0) Variance of the distribution. std(lamda, N, loc=0) Standard deviation of the distribution. interval(alpha, lamda, N, loc=0) Endpoints of the range that contains alpha percent of the distribution

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