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# scipy.stats.truncnorm

scipy.stats.truncnorm = <scipy.stats._continuous_distns.truncnorm_gen object>

  A truncated normal continuous random variable.

  As an instance of the `rv_continuous` class, `truncnorm` 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.

  Methods

  rvs(a, b, loc=0, scale=1, size=1, random_state=None) | Random variates.
  pdf(x, a, b, loc=0, scale=1) | Probability density function.
  logpdf(x, a, b, loc=0, scale=1) | Log of the probability density function.
  cdf(x, a, b, loc=0, scale=1) | Cumulative distribution function.
  logcdf(x, a, b, loc=0, scale=1) | Log of the cumulative distribution function.
  sf(x, a, b, loc=0, scale=1) | Survival function (also defined as `1 - cdf`, but sf is sometimes more accurate).
  logsf(x, a, b, loc=0, scale=1) | Log of the survival function.
  ppf(q, a, b, loc=0, scale=1) | Percent point function (inverse of `cdf` — percentiles).
  isf(q, a, b, loc=0, scale=1) | Inverse survival function (inverse of `sf`).
  moment(order, a, b, loc=0, scale=1) | Non-central moment of the specified order.
  stats(a, b, loc=0, scale=1, moments=’mv’) | Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
  entropy(a, b, loc=0, scale=1) | (Differential) entropy of the RV.
  fit(data) | Parameter estimates for generic data. See scipy.stats.rv_continuous.fit for detailed documentation of the keyword arguments.
  expect(func, args=(a, b), 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(a, b, loc=0, scale=1) | Median of the distribution.
  mean(a, b, loc=0, scale=1) | Mean of the distribution.
  var(a, b, loc=0, scale=1) | Variance of the distribution.
  std(a, b, loc=0, scale=1) | Standard deviation of the distribution.
  interval(confidence, a, b, loc=0, scale=1) | Confidence interval with equal areas around the median.

  Notes

  This distribution is the normal distribution centered on `loc` (default 0), with standard deviation `scale` (default 1), and truncated at `a` and `b` standard deviations from `loc`. For arbitrary `loc` and `scale`, `a` and `b` are not the abscissae at which the shifted and scaled distribution is truncated.

  Note

  If `a_trunc` and `b_trunc` are the abscissae at which we wish to truncate the distribution (as opposed to the number of standard deviations from `loc`), then we can calculate the distribution parameters `a` and `b` as follows:

      a, b = (a_trunc - loc) / scale, (b_trunc - loc) / scale

  This is a common point of confusion. For additional clarification, please see the example below.

  Examples

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

  Get the support:

      >>> a, b = 0.1, 2
      >>> lb, ub = truncnorm.support(a, b)

  Calculate the first four moments:

      >>> mean, var, skew, kurt = truncnorm.stats(a, b, moments='mvsk')

  Display the probability density function (`pdf`):

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

  Check accuracy of `cdf` and `ppf`:

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

  Generate random numbers:

      >>> r = truncnorm.rvs(a, b, size=1000)

  And compare the histogram:

      >>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
      >>> ax.set_xlim([x[0], x[-1]])
      >>> ax.legend(loc='best', frameon=False)
      >>> plt.show()

  In the examples above, `loc=0` and `scale=1`, so the plot is truncated at `a` on the left and `b` on the right. However, suppose we were to produce the same histogram with `loc = 1` and `scale=0.5`.

      >>> loc, scale = 1, 0.5
      >>> rv = truncnorm(a, b, loc=loc, scale=scale)
      >>> x = np.linspace(truncnorm.ppf(0.01, a, b),
      ...                 truncnorm.ppf(0.99, a, b), 100)
      >>> r = rv.rvs(size=1000)

      >>> fig, ax = plt.subplots(1, 1)
      >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
      >>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
      >>> ax.set_xlim(a, b)
      >>> ax.legend(loc='best', frameon=False)
      >>> plt.show()

  Note that the distribution is no longer appears to be truncated at abscissae `a` and `b`. That is because the standard normal distribution is first truncated at `a` and `b`, then the resulting distribution is scaled by `scale` and shifted by `loc`. If we instead want the shifted and scaled distribution to be truncated at `a` and `b`, we need to transform these values before passing them as the distribution parameters.

      >>> a_transformed, b_transformed = (a - loc) / scale, (b - loc) / scale
      >>> rv = truncnorm(a_transformed, b_transformed, loc=loc, scale=scale)
      >>> x = np.linspace(truncnorm.ppf(0.01, a, b),
      ...                 truncnorm.ppf(0.99, a, b), 100)
      >>> r = rv.rvs(size=10000)

      >>> fig, ax = plt.subplots(1, 1)
      >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
      >>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
      >>> ax.set_xlim(a-0.1, b+0.1)
      >>> ax.legend(loc='best', frameon=False)
      >>> plt.show()