HistogramList

HistogramList[{x1,x2,…}]

gives a list of bins and histogram heights of the values xi.

HistogramList[{{x1,y1,…},{x2,y2,…},…}]

gives a list of bins and histogram heights of the values {xi,yi,…}.

HistogramList[…,bspec]

gives a list of bins and histogram heights with bins specified by bspec.

HistogramList[…,bspec,hspec]

gives a list of bins and histogram heights with bin heights computed according to the specification hspec.

Details and Options

  • HistogramList is also known as quadrat counts.
  • HistogramList produces a list of bin delimiters {b1,b2,…} for each dimension and a depth- array of values for each bin.
  • For 2D data, the output has the form {{{bx1,bx2,…},{by1,…}},{{v1,1,v1,2,…},{v2,1,…},…}} where vi,j is the value corresponding to the bin [bxi,bxi+1)×[byj,byj+1).
  • HistogramList[data] by default gives equal bins chosen to approximate an assumed underlying smooth distribution of the values {xi,yi,…}.
  • The width of each bin is computed according to the values xi, the width according to the yi, etc.
  • The following bin specifications bpsec can be given:
  • nuse n bins
    {w}use bins of width w
    {min,max,w}use bins of width w from min to max
    {{b1,b2,…}}use bins [b1,b2),[b2,b3),…
    Automaticdetermine bin widths automatically
    "name"use a named binning method
    {"Log",bspec}apply binning bspec on log-transformed data
    fwapply fw to get an explicit bin specification {b1,b2,…}
    {xspec,yspec,…}give different x, y, etc. specifications
  • The binning specification "Log" is taken to use the Automatic underlying binning method.
  • Possible named binning methods include:
  • "Sturges"compute the number of bins based on the length of data
    "Scott"asymptotically minimize the mean square error
    "FreedmanDiaconis"twice the interquartile range divided by the cube root of sample size
    "Knuth"balance likelihood and prior probability of a piecewise uniform model
    "Wand"one-level recursive approximate Wand binning
  • The function fb in HistogramList[data,fb] is applied to a list of all {xi,yi,…}, and should return an explicit bin list {{bx1,bx2,…},{by1,by2,…},…}. In HistogramList[data,{fx,fy,…}], fx is applied to the list of xi, and fy to the list of yi, etc.
  • Different forms of histogram data can be obtained by giving different bin height specifications hspec in HistogramList[data,bspec,hspec]. The following forms can be used:
  • "Count"the number of values lying in each bin
    "CumulativeCount"cumulative counts
    "SurvivalCount"survival counts
    "Probability"fraction of values lying in each bin
    "PDF"probability density function
    "CDF"cumulative distribution function
    "SF"survival function
    "HF"hazard function
    "CHF"cumulative hazard function
    fhheights obtained by applying fh to bins and counts
  • Only values {xi,yi,…} that consist of real numbers are assigned to bins; others are taken to be missing.
  • The function fh in HistogramList[data,bspec,fh] is applied to two arguments: a list of bin delimiters {{bx1,bx2,…},{by1,by2,…},…} and for -dimensional data an array of depth with counts for each bin.

Examples

open allclose all

Basic Examples  (4)

Generate a list of bin delimiters and counts for a dataset:

Generate a list of bin delimiters and counts for a bivariate dataset:

Use unit width bins:

Use different height functions:

Scope  (10)

Bin Specifications  (7)

Specify the number of bins to use:

Specify the bin width:

Specify limits and bin size:

List specific bin delimiters:

Bins for discrete values are centered on the values when possible:

Specify the number of bins to use for each dimension:

Specify different bin specifications for each dimension:

Use different named binning methods:

Use logarithmically spaced bins:

Delimit bins on integer boundaries using a binning function:

Height Specifications  (3)

Use different height specifications:

Use a height function that accumulates the bin counts:

Nonreal data is taken to be missing:

Properties & Relations  (5)

Functions such as Histogram and Histogram3D use HistogramList to compute bins and heights:

BinCounts and BinLists can be used to find items in specific bins:

HistogramList also provides the actual bins:

Bivariate data is given as a list of pairs of numbers:

There is one set of bins for each variable dimension:

The array depth of the counts is the same as the number of variable dimensions:

With data consisting of 5-tuples:

For bin delimiters, there are bins in each dimension:

HistogramList ignores the times if the input is TimeSeries:

Compare to the histogram distribution of the values:

Possible Issues  (4)

Bins include the left endpoint, but not the right, which can result in unexpected bins:

The value 1 is not included in this histogram because it would be in the bin [1,1.2):

The bins obtained using the specification {min,max,w} may not include all data points:

Specify the min and max so all data points are included in the bin covering:

Alternatively, use the width-only bin specification {w}:

Results for multidimensional data can get quite large:

Most of the values are zero:

HistogramList does not recognize the path structure of multipath TemporalData input:

Find HistogramList pathwise:

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

Text

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

CMS

Wolfram Language. 2010. "HistogramList." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/HistogramList.html.

APA

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

BibTeX

@misc{reference.wolfram_2024_histogramlist, author="Wolfram Research", title="{HistogramList}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/HistogramList.html}", note=[Accessed: 18-November-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_histogramlist, organization={Wolfram Research}, title={HistogramList}, year={2010}, url={https://reference.wolfram.com/language/ref/HistogramList.html}, note=[Accessed: 18-November-2024 ]}