# scipy.stats.probplot

scipy.stats.probplot(x, sparams=(), dist='norm', fit=True, plot=None, rvalue=False)

  Calculate quantiles for a probability plot, and optionally show the plot.

  Generates a probability plot of sample data against the quantiles of a specified theoretical distribution (the normal distribution by default). `probplot` optionally calculates a best-fit line for the data and plots the results using Matplotlib or a given plot function.

  Parameters:
    x array_like

      Sample/response data from which `probplot` creates the plot.

    sparams tuple, optional

      Distribution-specific shape parameters (shape parameters plus location and scale).

    dist str or stats.distributions instance, optional

      Distribution or distribution function name. The default is ‘norm’ for a normal probability plot. Objects that look enough like a stats.distributions instance (i.e. they have a `ppf` method) are also accepted.

    fit bool, optional

      Fit a least-squares regression (best-fit) line to the sample data if True (default).

    plot object, optional

      If given, plots the quantiles. If given and `fit` is True, also plots the least squares fit. plot is an object that has to have methods “plot” and “text”. The `matplotlib.pyplot` module or a Matplotlib Axes object can be used, or a custom object with the same methods. Default is None, which means that no plot is created.

    rvalue bool, optional

      If plot is provided and `fit` is True, setting rvalue to True includes the coefficient of determination on the plot. Default is False.

  Returns:
    (osm, osr)tuple of ndarrays

      Tuple of theoretical quantiles (osm, or order statistic medians) and ordered responses (osr). osr is simply sorted input x. For details on how osm is calculated see the Notes section.

    (slope, intercept, r)tuple of floats, optional

      Tuple containing the result of the least-squares fit, if that is performed by `probplot`. r is the square root of the coefficient of determination. If `fit=False` and `plot=None`, this tuple is not returned.

  Notes

  Even if plot is given, the figure is not shown or saved by `probplot`; `plt.show()` or `plt.savefig('figname.png')` should be used after calling `probplot`.

  `probplot` generates a probability plot, which should not be confused with a Q-Q or a P-P plot. Statsmodels has more extensive functionality of this type, see `statsmodels.api.ProbPlot`.

  The formula used for the theoretical quantiles (horizontal axis of the probability plot) is Filliben’s estimate:

      quantiles = dist.ppf(val), for

              0.5**(1/n),                  for i = n
        val = (i - 0.3175) / (n + 0.365),  for i = 2, ..., n-1
              1 - 0.5**(1/n),              for i = 1

  where `i` indicates the i-th ordered value and `n` is the total number of values.

  Examples

      >>> import numpy as np
      >>> from scipy import stats
      >>> import matplotlib.pyplot as plt
      >>> nsample = 100
      >>> rng = np.random.default_rng()

  A t distribution with small degrees of freedom:

      >>> ax1 = plt.subplot(221)
      >>> x = stats.t.rvs(3, size=nsample, random_state=rng)
      >>> res = stats.probplot(x, plot=plt)

  A t distribution with larger degrees of freedom:

      >>> ax2 = plt.subplot(222)
      >>> x = stats.t.rvs(25, size=nsample, random_state=rng)
      >>> res = stats.probplot(x, plot=plt)

  A mixture of two normal distributions with broadcasting:

      >>> ax3 = plt.subplot(223)
      >>> x = stats.norm.rvs(loc=[0,5], scale=[1,1.5],
      ...                    size=(nsample//2,2), random_state=rng).ravel()
      >>> res = stats.probplot(x, plot=plt)

  A standard normal distribution:

      >>> ax4 = plt.subplot(224)
      >>> x = stats.norm.rvs(loc=0, scale=1, size=nsample, random_state=rng)
      >>> res = stats.probplot(x, plot=plt)

  Produce a new figure with a loggamma distribution, using the `dist` and `sparams` keywords:

      >>> fig = plt.figure()
      >>> ax = fig.add_subplot(111)
      >>> x = stats.loggamma.rvs(c=2.5, size=500, random_state=rng)
      >>> res = stats.probplot(x, dist=stats.loggamma, sparams=(2.5,), plot=ax)
      >>> ax.set_title("Probplot for loggamma dist with shape parameter 2.5")

  Show the results with Matplotlib:

      >>> plt.show()