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# scipy.stats.boltzmann

`scipy.stats.``boltzmann` = <scipy.stats.distributions.boltzmann_gen object at 0x4ae16d0>

  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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