Handle Discontinuities in a CDF
Define a formula distribution by a cumulative distribution function. The distribution function contains jump discontinuities, which represent a mixture of continuous and discrete components.
In[1]:=
![Click for copyable input](assets.en/handle-discontinuities-in-a-cdf/In_37.png)
cdf = CDF[
MixtureDistribution[{1/3, 2/3}, {LaplaceDistribution[0, 1],
TransformedDistribution[x - 2,
x \[Distributed] BinomialDistribution[4, 1/3]]}], z];
show complete Wolfram Language input
Out[2]=
![](assets.en/handle-discontinuities-in-a-cdf/O_32.png)
ProbabilityDistribution decomposes the distribution into absolutely continuous and discrete parts.
In[3]:=
![Click for copyable input](assets.en/handle-discontinuities-in-a-cdf/In_39.png)
ProbabilityDistribution[{CDF, cdf}, {z, -Infinity, Infinity}]
Out[3]=
![](assets.en/handle-discontinuities-in-a-cdf/O_33.png)
Handle PDF input with DiracDelta weights.
In[4]:=
![Click for copyable input](assets.en/handle-discontinuities-in-a-cdf/In_40.png)
ProbabilityDistribution[
Sum[1/7 DiracDelta[x - k], {k, -3, 3}], {x, -Infinity, Infinity}]
Out[4]=
![](assets.en/handle-discontinuities-in-a-cdf/O_34.png)