basic truncated normal dist

Author: phobson

paramnormal/dist.py

@@ -797,6 +797,7 @@ class exponential(BaseDist_Mixin):
     numpy.random.exponential
 
     """
+
     dist = stats.expon
     param_template = namedtuple('params', ['lamda', 'loc'])
     name = 'exponential'
@@ -833,7 +834,7 @@ class rice(BaseDist_Mixin):
     R : float
         The shape parameter of the distribution.
     sigma : float
-        The standard deviate of the distribution.
+        The standard deviation of the distribution.
     loc : float, optional
         Location parameter of the distribution. This defaults to, and
         should probably be left at, 0.
@@ -879,6 +880,7 @@ class rice(BaseDist_Mixin):
     numpy.random.exponential
 
     """
+
     dist = stats.rice
     param_template = namedtuple('params', ['R', 'sigma', 'loc'])
     name = 'rice'
@@ -904,6 +906,114 @@ def fit(cls, data, **guesses):
         return cls.param_template(R=b*sigma, loc=loc, sigma=sigma)
 
 
+class truncated_normal(BaseDist_Mixin):
+    """
+    Create and fit data to a truncated normal distribution.
+
+    Methods
+    -------
+    fit
+        Use scipy's maximum likelihood estimation methods to estimate
+        the parameters of the data's distribution.
+    from_params
+        Create a new distribution instances from the ``namedtuple``
+        result of the :meth:`~fit` method.
+
+    Parameters
+    ----------
+    lower, upper : float
+        The lower and upper limits of the distribution that serve as its
+        shape parameters.
+    mu : float, optional (default = 0)
+        The expected value (mean) of the underlying normal distribution.
+        Acts as the location parameter of the distribution.
+    sigma : float, optional (default = 1)
+        The standard deviation of the underlying normal distribution.
+        Also acts as the scale parameter of distribution.
+
+    Examples
+    --------
+    >>> import numpy
+    >>> import paramnormal as pn
+    >>> numpy.random.seed(0)
+    >>> pn.truncated_normal(lower=-0.5, upper=0.5).rvs(size=3)
+    array([ 0.04687082,  0.20804061,  0.09879796])
+
+    >>> # you can also use greek letters
+    >>> numpy.random.seed(0)
+    >>> pn.truncated_normal(lower=-0.5, upper=2.5, σ=2).rvs(size=3)
+    array([ 0.8902748 ,  1.37377049,  1.04012565])
+
+    >>> # silly fake data
+    >>> numpy.random.seed(0)
+    >>> data = pn.truncated_normal(lower=-0.5, upper=2.5, mu=0, sigma=2).rvs(size=37)
+    >>> # pretend `data` is unknown and we want to fit a dist. to it
+    >>> pn.truncated_normal.fit(data)
+    params(lower=1.040124, upper=1.082447, mu=-8.097877e-06, sigma=1.033405)
+
+    In scipy, the distribution is defined as
+    ``stats.truncnorm(a, b, loc, scale)`` where
+
+    .. math::
+
+        a = \frac{\mathrm{lower bound}} - \mu}{\sigma}
+
+    and
+
+    .. math::
+
+        b = \frac{x_{\mathrm{upper bound}} - \mu}{\sigma}
+
+    Since ``a`` and ``b`` are directly linked to the location and scale
+    of the distribution as well as the lower and upper limits,
+    respectively, it's difficult to use the ``fit`` method of this
+    distirbution without either knowing a lot about it `a priori` or
+    assuming just as much.
+
+    References
+    ----------
+    http://scipy.github.io/devdocs/generated/scipy.stats.truncnorm
+    https://en.wikipedia.org/wiki/Rice_distribution
+
+    See Also
+    --------
+    scipy.stats.rice
+    numpy.random.exponential
+
+    """
+
+    dist = stats.truncnorm
+    param_template = namedtuple('params', ['lower', 'upper', 'mu', 'sigma'])
+    name = 'truncated normal'
+
+    @staticmethod
+    @utils.greco_deco
+    def _process_args(lower=None, upper=None, mu=None, sigma=None, fit=False):
+        a = None
+        b = None
+        if lower is not None and mu is not None and sigma is not None:
+            a = (lower - mu) / sigma
+
+        if upper is not None and mu is not None and sigma is not None:
+            b = (upper - mu) / sigma
+
+        loc_key, scale_key = utils._get_loc_scale_keys(fit=fit)
+        if fit:
+            akey = 'f0'
+            bkey = 'f1'
+        else:
+            akey = 'a'
+            bkey = 'b'
+        return {akey: a, bkey: b, loc_key: mu, scale_key: sigma}
+
+    @classmethod
+    def fit(cls, data, **guesses):
+        a, b, mu, sigma = cls._fit(data, **guesses)
+        lower = a * sigma + mu
+        upper = b * sigma + mu
+        return cls.param_template(lower=lower, upper=upper, mu=mu, sigma=sigma)
+
+
 __all__ = [
     'normal',
     'lognormal',
@@ -915,4 +1025,5 @@ def fit(cls, data, **guesses):
     'pareto',
     'exponential',
     'rice',
+    'truncated_normal',
 ]