**'org.apache.commons.math3.random.EmpiricalDistribution'**Java class

## Class EmpiricalDistribution

- java.lang.Object
- org.apache.commons.math3.distribution.AbstractRealDistribution
- org.apache.commons.math3.random.EmpiricalDistribution

- All Implemented Interfaces:
- Serializable, RealDistribution

public class EmpiricalDistributionextends AbstractRealDistribution

Represents an empirical probability distribution -- a probability distribution derived from observed data without making any assumptions about the functional form of the population distribution that the data come from.

An

`EmpiricalDistribution`

maintains data structures, called*distribution digests*, that describe empirical distributions and support the following operations:- loading the distribution from a file of observed data values
- dividing the input data into "bin ranges" and reporting bin frequency counts (data for histogram)
- reporting univariate statistics describing the full set of data values as well as the observations within each bin
- generating random values from the distribution

`EmpiricalDistribution`

to build grouped frequency histograms representing the input data or to generate random values "like" those in the input file -- i.e., the values generated will follow the distribution of the values in the file.The implementation uses what amounts to the Variable Kernel Method with Gaussian smoothing:

**Digesting the input file**- Pass the file once to compute min and max.
- Divide the range from min-max into
`binCount`

"bins." - Pass the data file again, computing bin counts and univariate statistics (mean, std dev.) for each of the bins
- Divide the interval (0,1) into subintervals associated with the bins, with the length of a bin's subinterval proportional to its count.

**Generating random values from the distribution**- Generate a uniformly distributed value in (0,1)
- Select the subinterval to which the value belongs.
- Generate a random Gaussian value with mean = mean of the associated bin and std dev = std dev of associated bin.

EmpiricalDistribution implements the

`RealDistribution`

interface as follows. Given x within the range of values in the dataset, let B be the bin containing x and let K be the within-bin kernel for B. Let P(B-) be the sum of the probabilities of the bins below B and let K(B) be the mass of B under K (i.e., the integral of the kernel density over B). Then set P(X < x) = P(B-) + P(B) * K(x) / K(B) where K(x) is the kernel distribution evaluated at x. This results in a cdf that matches the grouped frequency distribution at the bin endpoints and interpolates within bins using within-bin kernels.**USAGE NOTES:**- The
`binCount`

is set by default to 1000. A good rule of thumb is to set the bin count to approximately the length of the input file divided by 10. - The input file
*must*be a plain text file containing one valid numeric entry per line.

- See Also:
- Serialized Form

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