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HighestDensityInterval (1.0.0) current version: 1.1.0 »

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Compute the shortest interval that contains a give amount of probability mass

Contributed by: Sjoerd Smit

ResourceFunction["HighestDensityInterval"][dist, p]

returns the shortest Interval for distribution dist that contains probability mass p.

ResourceFunction["HighestDensityInterval"][vec, p]

returns the shortest Interval that contains at least fraction p of the values in numerical vector vec.

Details

ResourceFunction["HighestDensityInterval"] only works for univariate distributions that can be numerically sampled.

The probability p has to be a number between 0 and 1.

Examples

Basic Examples (5)

Find the shortest interval that contains 90% of the probability mass of a GammaDistribution:

In[1]:=

Out[1]=

Verify that the interval contains 90% of the probability mass:

In[2]:=

$Probability[Between[x, First[iv]], x \[Distributed] GammaDistribution[4, 2]]$

Out[2]=

Check the length of the interval:

In[3]:=

Out[3]=

Show the probability contained in the interval:

In[4]:=

Show[
Plot[
PDF[GammaDistribution[4, 2], x], {x, 0, 20}
],
Plot[
PDF[GammaDistribution[4, 2], x], {x, iv[[1, 1]], iv[[1, 2]]},
Filling -> Axis,
PlotRange -> {0, Automatic}
]
]

Out[4]=

Compute the interval using samples from the distribution:

In[5]:=

Out[5]=

Applications (3)

The HighestDensityInterval can be used to detect and remove outliers:

In[6]:=

Out[7]=

Remove the outliers:

In[8]:=

Out[8]=

Compute the mean of the data without the outlier:

In[9]:=

Out[9]=

Publisher

Sjoerd Smit

Requirements

Wolfram Language 14.0 (January 2024) or above

Version History

1.1.0 – 23 September 2024
1.0.0 – 20 September 2024

Related Resources

License Information

This work is licensed under a Creative Commons Attribution 4.0 International License