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# scipy.stats.cosine

`scipy.stats.``cosine` = <scipy.stats._continuous_distns.cosine_gen object at 0x45035f8c>

  A cosine continuous random variable.

  As an instance of the `rv_continuous` class, `cosine` 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 cosine distribution is an approximation to the normal distribution. The probability density function for `cosine` is:

      cosine.pdf(x) = 1/(2*pi) * (1+cos(x))

  for `-pi <= x <= pi`.

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

  Examples

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

  Calculate a few first moments:

      >>> mean, var, skew, kurt = cosine.stats(moments='mvsk')

  Display the probability density function (`pdf`):

      >>> x = np.linspace(cosine.ppf(0.01),
      ...                 cosine.ppf(0.99), 100)
      >>> ax.plot(x, cosine.pdf(x),
      ...        'r-', lw=5, alpha=0.6, label='cosine 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 = cosine()
      >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

  Check accuracy of `cdf` and `ppf`:

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

  Generate random numbers:

      >>> r = cosine.rvs(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(loc=0, scale=1, size=1, random_state=None)` | Random variates.
  `pdf(x, loc=0, scale=1)` | Probability density function.
  `logpdf(x, loc=0, scale=1)` | Log of the probability density function.
  `cdf(x, loc=0, scale=1)` | Cumulative density function.
  `logcdf(x, loc=0, scale=1)` | Log of the cumulative density function.
  `sf(x, loc=0, scale=1)` | Survival function (`1 - cdf` — sometimes more accurate).
  `logsf(x, loc=0, scale=1)` | Log of the survival function.
  `ppf(q, loc=0, scale=1)` | Percent point function (inverse of `cdf` — percentiles).
  `isf(q, loc=0, scale=1)` | Inverse survival function (inverse of `sf`).
  `moment(n, loc=0, scale=1)` | Non-central moment of order n
  `stats(loc=0, scale=1, moments='mv')` | Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
  `entropy(loc=0, scale=1)` | (Differential) entropy of the RV.
  `fit(data, loc=0, scale=1)` | Parameter estimates for generic data.
  `expect(func, 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(loc=0, scale=1)` | Median of the distribution.
  `mean(loc=0, scale=1)` | Mean of the distribution.
  `var(loc=0, scale=1)` | Variance of the distribution.
  `std(loc=0, scale=1)` | Standard deviation of the distribution.
  `interval(alpha, loc=0, scale=1)` | Endpoints of the range that contains alpha percent of the distribution