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DataDistribution
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DataDistribution

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DataDistribution[ddist,…]

represents a probability distribution of type ddist, estimated from a set of data.

Details

Examples

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Basic Examples  (4)Summary of the most common use cases

Create a univariate DataDistribution:

In[1]:=1
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https://wolfram.com/xid/0dqv31t55qy-c313f7

Using SmoothKernelDistribution:

In[2]:=2
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https://wolfram.com/xid/0dqv31t55qy-41od0
Out[2]=2

Using HistogramDistribution:

In[3]:=3
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https://wolfram.com/xid/0dqv31t55qy-bdse0f
Out[3]=3

Visualize the PDF of a data distribution:

In[1]:=1
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https://wolfram.com/xid/0dqv31t55qy-gexjva
In[2]:=2
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https://wolfram.com/xid/0dqv31t55qy-l4qom
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0dqv31t55qy-5ndij
Out[3]=3

Visualize the CDF of a data distribution:

In[1]:=1
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https://wolfram.com/xid/0dqv31t55qy-fk5m5p
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqv31t55qy-i0o7gr
Out[2]=2

Calculate moments of a data distribution:

In[1]:=1
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https://wolfram.com/xid/0dqv31t55qy-jnfh5t
Out[1]=1

Mean:

In[2]:=2
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https://wolfram.com/xid/0dqv31t55qy-kl9s5
Out[2]=2

Variance:

In[3]:=3
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https://wolfram.com/xid/0dqv31t55qy-ec3acp
Out[3]=3

Scope  (4)Survey of the scope of standard use cases

DataDistribution objects can be created from five data-based distributions:

In[1]:=1
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https://wolfram.com/xid/0dqv31t55qy-ds72qf
In[2]:=2
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https://wolfram.com/xid/0dqv31t55qy-eh393a
In[3]:=3
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https://wolfram.com/xid/0dqv31t55qy-jgevle

Any property that applies to a parametric distribution applies to data distributions:

In[1]:=1
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https://wolfram.com/xid/0dqv31t55qy-btgsn3
In[2]:=2
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https://wolfram.com/xid/0dqv31t55qy-bbnais

Generating functions:

In[3]:=3
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https://wolfram.com/xid/0dqv31t55qy-feoc80

Random number generation:

In[4]:=4
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https://wolfram.com/xid/0dqv31t55qy-eqd2yg
Out[4]=4

Distribution functions:

In[5]:=5
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https://wolfram.com/xid/0dqv31t55qy-pvv8y
Out[5]=5

Moments:

In[6]:=6
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https://wolfram.com/xid/0dqv31t55qy-d890d
Out[6]=6

Multivariate data distribution:

In[1]:=1
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https://wolfram.com/xid/0dqv31t55qy-nxywi3
In[2]:=2
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https://wolfram.com/xid/0dqv31t55qy-3a4ope

Mean and standard deviation:

In[3]:=3
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https://wolfram.com/xid/0dqv31t55qy-evk6wn
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0dqv31t55qy-i236wx
Out[4]=4

Scalar central moment for each marginal:

In[5]:=5
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https://wolfram.com/xid/0dqv31t55qy-hjji0s
Out[5]=5

Multivariate central joint moment:

In[6]:=6
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https://wolfram.com/xid/0dqv31t55qy-1n932z
Out[6]=6

DataDistribution created from quantity data retains information about units:

In[1]:=1
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https://wolfram.com/xid/0dqv31t55qy-khfpfe
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqv31t55qy-l2sf1n
Out[2]=2

Extract distribution of the data magnitude and the unit of the data:

In[3]:=3
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https://wolfram.com/xid/0dqv31t55qy-br4ukp
Out[3]=3

Find basic moments:

In[4]:=4
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https://wolfram.com/xid/0dqv31t55qy-y0nxue
Out[4]=4
Wolfram Research (2010), DataDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/DataDistribution.html (updated 2016).
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Wolfram Research (2010), DataDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/DataDistribution.html (updated 2016).

Text

Wolfram Research (2010), DataDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/DataDistribution.html (updated 2016).

✖
Wolfram Research (2010), DataDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/DataDistribution.html (updated 2016).

CMS

Wolfram Language. 2010. "DataDistribution." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016. https://reference.wolfram.com/language/ref/DataDistribution.html.

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Wolfram Language. 2010. "DataDistribution." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016. https://reference.wolfram.com/language/ref/DataDistribution.html.

APA

Wolfram Language. (2010). DataDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DataDistribution.html

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Wolfram Language. (2010). DataDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DataDistribution.html

BibTeX

@misc{reference.wolfram_2025_datadistribution, author="Wolfram Research", title="{DataDistribution}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/DataDistribution.html}", note=[Accessed: 29-March-2025 ]}

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@misc{reference.wolfram_2025_datadistribution, author="Wolfram Research", title="{DataDistribution}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/DataDistribution.html}", note=[Accessed: 29-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_datadistribution, organization={Wolfram Research}, title={DataDistribution}, year={2016}, url={https://reference.wolfram.com/language/ref/DataDistribution.html}, note=[Accessed: 29-March-2025 ]}

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@online{reference.wolfram_2025_datadistribution, organization={Wolfram Research}, title={DataDistribution}, year={2016}, url={https://reference.wolfram.com/language/ref/DataDistribution.html}, note=[Accessed: 29-March-2025 ]}