BUILT-IN MATHEMATICA SYMBOL

# HistogramDistribution

HistogramDistribution[{x1, x2, ...}]
represents the probability distribution corresponding to a histogram of the data values .

HistogramDistribution[{{x1, y1, ...}, {x2, y2, ...}, ...}]
represents a multivariate histogram distribution based on data values .

HistogramDistribution[..., bspec]
represents a histogram distribution with bins specified by bspec.

## DetailsDetails

• HistogramDistribution returns a DataDistribution object that can be used like any other probability distribution.
• The probability density function for HistogramDistribution for a value is given by where is the number of data points in bin , is the width of bin , are bin delimiters, and is the total number of data points.
• The width of each bin is computed according to the values , the width according to the , etc.
• The following bin specifications bpsec can be given:
•  n use n bins {w} use bins of width w {min,max,w} use bins of width w from min to max {{b1,b2,...}} use bins Automatic determine bin widths automatically "name" use a named binning method fw apply fw to get an explicit bin specification {xspec,yspec,...} give different x, y, etc. specifications
• Possible named binning methods include:
•  "FreedmanDiaconis" twice the interquartile range divided by the cube root of sample size "Knuth" balance likelihood and prior probability of a piecewise uniform model "Scott" asymptotically minimize the mean square error "Sturges" compute the number of bins based on the length of data "Wand" one-level recursive approximate Wand binning
• The probability density for value in a histogram distribution is a piecewise constant function.
• HistogramDistribution can be used with such functions as Mean, CDF, and RandomVariate.

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Create a histogram distribution of univariate data:

Use the resulting distribution to perform analysis, including visualizing distribution functions:

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Compute moments and quantiles:

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Create a histogram distribution of bivariate data:

Visualize the PDF and CDF:

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Compute covariance and general moments:

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