Implement CDF, CCDF, LCDF, LCCDF for Normal distribution.

pymc3/distributions/continuous.py

@@ -15,7 +15,7 @@
 from pymc3.theanof import floatX
 from . import transforms
 
-from .dist_math import bound, logpow, gammaln, betaln, std_cdf, i0, i1, alltrue_elemwise
+from .dist_math import bound, logpow, gammaln, betaln, std_cdf, i0, i1, alltrue_elemwise, zvalue
 from .distribution import Continuous, draw_values, generate_samples, Bound
 
 __all__ = ['Uniform', 'Flat', 'Normal', 'Beta', 'Exponential', 'Laplace',
@@ -231,6 +231,44 @@ def logp(self, value):
         return bound((-tau * (value - mu)**2 + tt.log(tau / np.pi / 2.)) / 2.,
                      sd > 0)
 
+    def cdf(self, value):
+        mu = self.mu
+        sd = self.sd
+        z = zvalue(value, mu=mu, sd=sd)
+
+        return tt.erfc(-z / tt.sqrt(2.))/2.
+
+    def ccdf(self, value):
+        mu = self.mu
+        sd = self.sd
+        z = zvalue(value, mu=mu, sd=sd)
+
+        return tt.erfc(z / tt.sqrt(2.))/2.
+
+    def lcdf(self, value):
+        mu = self.mu
+        sd = self.sd
+        z = zvalue(value, mu=mu, sd=sd)
+
+        return tt.switch(
+            tt.lt(z, -1.0),
+            tt.log(tt.erfcx(-z / tt.sqrt(2.)) / 2.) -
+            tt.sqr(tt.abs_(z)) / 2,
+            tt.log1p(-tt.erfc(z / tt.sqrt(2.)) / 2.)
+        )
+
+    def lccdf(self, value):
+        mu = self.mu
+        sd = self.sd
+        z = zvalue(value, mu=mu, sd=sd)
+
+        return tt.switch(
+            tt.gt(z, 1.0),
+            tt.log(tt.erfcx(z / tt.sqrt(2.)) / 2) -
+            tt.sqr(tt.abs_(z)) / 2.,
+            tt.log1p(-tt.erfc(-z / tt.sqrt(2.)) / 2.)
+        )
+
 
 class HalfNormal(PositiveContinuous):
     R"""

pymc3/distributions/dist_math.py

@@ -96,3 +96,9 @@ def i1(x):
                      x**9 / 1474560 + x**11 / 176947200 + x**13 / 29727129600,
                      np.e**x / (2 * np.pi * x)**0.5 * (1 - 3 / (8 * x) + 15 / (128 * x**2) + 315 / (3072 * x**3)
                                                        + 14175 / (98304 * x**4)))
+
+def zvalue(value, sd=1, mu=0):
+    """
+    Calculate the z-value for a normal distribution. By default standard normal.
+    """
+    return (value - mu) / tt.sqrt(2. * sd ** 2.)