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# scipy.stats.argus

`scipy.stats.``argus` = <scipy.stats._continuous_distns.argus_gen object>

  Argus distribution

  As an instance of the `rv_continuous` class, `argus` 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 density function for `argus` is:

      argus.pdf(x, chi) = chi**3 / (sqrt(2*pi) * Psi(chi)) * x * sqrt(1-x**2) * exp(- 0.5 * chi**2 * (1 - x**2))

      where:
               Psi(chi) = Phi(chi) - chi * phi(chi) - 1/2
               with Phi and phi being the CDF and PDF of a standard normal distribution, respectively.

  `argus` takes `chi` as shape a parameter.

  References

  [R528] | “ARGUS distribution”, https://en.wikipedia.org/wiki/ARGUS_distribution

  The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the `loc` and `scale` parameters. Specifically, `argus.pdf(x, chi, loc, scale)` is identically equivalent to `argus.pdf(y, chi) / scale` with `y = (x - loc) / scale`.

  New in version 0.19.0.

  Examples

      >>> from scipy.stats import argus
      >>> import matplotlib.pyplot as plt
      >>> fig, ax = plt.subplots(1, 1)

  Calculate a few first moments:

      >>> chi = 1
      >>> mean, var, skew, kurt = argus.stats(chi, moments='mvsk')

  Display the probability density function (`pdf`):

      >>> x = np.linspace(argus.ppf(0.01, chi),
      ...                 argus.ppf(0.99, chi), 100)
      >>> ax.plot(x, argus.pdf(x, chi),
      ...        'r-', lw=5, alpha=0.6, label='argus pdf')

  Alternatively, the distribution object can be called (as a function) to fix the shape, location and scale parameters. This returns a “frozen” RV object holding the given parameters fixed.

  Freeze the distribution and display the frozen `pdf`:

      >>> rv = argus(chi)
      >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

  Check accuracy of `cdf` and `ppf`:

      >>> vals = argus.ppf([0.001, 0.5, 0.999], chi)
      >>> np.allclose([0.001, 0.5, 0.999], argus.cdf(vals, chi))
      True

  Generate random numbers:

      >>> r = argus.rvs(chi, size=1000)

  And compare the histogram:

      >>> ax.hist(r, normed=True, histtype='stepfilled', alpha=0.2)
      >>> ax.legend(loc='best', frameon=False)
      >>> plt.show()

  (Source code)

  Methods

  `rvs(chi, loc=0, scale=1, size=1, random_state=None)` | Random variates.
  `pdf(x, chi, loc=0, scale=1)` | Probability density function.
  `logpdf(x, chi, loc=0, scale=1)` | Log of the probability density function.
  `cdf(x, chi, loc=0, scale=1)` | Cumulative distribution function.
  `logcdf(x, chi, loc=0, scale=1)` | Log of the cumulative distribution function.
  `sf(x, chi, loc=0, scale=1)` | Survival function (also defined as `1 - cdf`, but sf is sometimes more accurate).
  `logsf(x, chi, loc=0, scale=1)` | Log of the survival function.
  `ppf(q, chi, loc=0, scale=1)` | Percent point function (inverse of `cdf` — percentiles).
  `isf(q, chi, loc=0, scale=1)` | Inverse survival function (inverse of `sf`).
  `moment(n, chi, loc=0, scale=1)` | Non-central moment of order n
  `stats(chi, loc=0, scale=1, moments='mv')` | Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
  `entropy(chi, loc=0, scale=1)` | (Differential) entropy of the RV.
  `fit(data, chi, loc=0, scale=1)` | Parameter estimates for generic data.
  `expect(func, args=(chi,), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)` | Expected value of a function (of one argument) with respect to the distribution.
  `median(chi, loc=0, scale=1)` | Median of the distribution.
  `mean(chi, loc=0, scale=1)` | Mean of the distribution.
  `var(chi, loc=0, scale=1)` | Variance of the distribution.
  `std(chi, loc=0, scale=1)` | Standard deviation of the distribution.
  `interval(alpha, chi, loc=0, scale=1)` | Endpoints of the range that contains alpha percent of the distribution