StatUtils (Hipparchus 1.3 API)

java.lang.Object
- org.hipparchus.stat.StatUtils

```
public final class StatUtils
extends Object
```
StatUtils provides static methods for computing statistics based on data stored in double[] arrays.

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method	Description
`static double`	`geometricMean(double... values)`	Returns the geometric mean of the entries in the input array, or `Double.NaN` if the array is empty.
`static double`	`geometricMean(double[] values, int begin, int length)`	Returns the geometric mean of the entries in the specified portion of the input array, or `Double.NaN` if the designated subarray is empty.
`static double`	`max(double... values)`	Returns the maximum of the entries in the input array, or `Double.NaN` if the array is empty.
`static double`	`max(double[] values, int begin, int length)`	Returns the maximum of the entries in the specified portion of the input array, or `Double.NaN` if the designated subarray is empty.
`static double`	`mean(double... values)`	Returns the arithmetic mean of the entries in the input array, or `Double.NaN` if the array is empty.
`static double`	`mean(double[] values, int begin, int length)`	Returns the arithmetic mean of the entries in the specified portion of the input array, or `Double.NaN` if the designated subarray is empty.
`static double`	`meanDifference(double[] sample1, double[] sample2)`	Returns the mean of the (signed) differences between corresponding elements of the input arrays -- i.e., sum(sample1[i] - sample2[i]) / sample1.length.
`static double`	`min(double... values)`	Returns the minimum of the entries in the input array, or `Double.NaN` if the array is empty.
`static double`	`min(double[] values, int begin, int length)`	Returns the minimum of the entries in the specified portion of the input array, or `Double.NaN` if the designated subarray is empty.
`static double[]`	`mode(double... sample)`	Returns the sample mode(s).
`static double[]`	`mode(double[] sample, int begin, int length)`	Returns the sample mode(s).
`static double[]`	`normalize(double... sample)`	Normalize (standardize) the sample, so it is has a mean of 0 and a standard deviation of 1.
`static double`	`percentile(double[] values, double p)`	Returns an estimate of the `p`th percentile of the values in the `values` array.
`static double`	`percentile(double[] values, int begin, int length, double p)`	Returns an estimate of the `p`th percentile of the values in the `values` array, starting with the element in (0-based) position `begin` in the array and including `length` values.
`static double`	`populationVariance(double... values)`	Returns the population variance of the entries in the input array, or `Double.NaN` if the array is empty.
`static double`	`populationVariance(double[] values, double mean)`	Returns the population variance of the entries in the input array, using the precomputed mean value.
`static double`	`populationVariance(double[] values, double mean, int begin, int length)`	Returns the population variance of the entries in the specified portion of the input array, using the precomputed mean value.
`static double`	`populationVariance(double[] values, int begin, int length)`	Returns the population variance of the entries in the specified portion of the input array, or `Double.NaN` if the designated subarray is empty.
`static double`	`product(double... values)`	Returns the product of the entries in the input array, or `Double.NaN` if the array is empty.
`static double`	`product(double[] values, int begin, int length)`	Returns the product of the entries in the specified portion of the input array, or `Double.NaN` if the designated subarray is empty.
`static double`	`sum(double... values)`	Returns the sum of the values in the input array, or `Double.NaN` if the array is empty.
`static double`	`sum(double[] values, int begin, int length)`	Returns the sum of the entries in the specified portion of the input array, or `Double.NaN` if the designated subarray is empty.
`static double`	`sumDifference(double[] sample1, double[] sample2)`	Returns the sum of the (signed) differences between corresponding elements of the input arrays -- i.e., sum(sample1[i] - sample2[i]).
`static double`	`sumLog(double... values)`	Returns the sum of the natural logs of the entries in the input array, or `Double.NaN` if the array is empty.
`static double`	`sumLog(double[] values, int begin, int length)`	Returns the sum of the natural logs of the entries in the specified portion of the input array, or `Double.NaN` if the designated subarray is empty.
`static double`	`sumSq(double... values)`	Returns the sum of the squares of the entries in the input array, or `Double.NaN` if the array is empty.
`static double`	`sumSq(double[] values, int begin, int length)`	Returns the sum of the squares of the entries in the specified portion of the input array, or `Double.NaN` if the designated subarray is empty.
`static double`	`variance(double... values)`	Returns the variance of the entries in the input array, or `Double.NaN` if the array is empty.
`static double`	`variance(double[] values, double mean)`	Returns the variance of the entries in the input array, using the precomputed mean value.
`static double`	`variance(double[] values, double mean, int begin, int length)`	Returns the variance of the entries in the specified portion of the input array, using the precomputed mean value.
`static double`	`variance(double[] values, int begin, int length)`	Returns the variance of the entries in the specified portion of the input array, or `Double.NaN` if the designated subarray is empty.
`static double`	`varianceDifference(double[] sample1, double[] sample2, double meanDifference)`	Returns the variance of the (signed) differences between corresponding elements of the input arrays -- i.e., var(sample1[i] - sample2[i]).

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Method Detail
  - sum
```
public static double sum(double... values)
                  throws MathIllegalArgumentException
```
    Returns the sum of the values in the input array, or Double.NaN if the array is empty.
    Throws IllegalArgumentException if the input array is null.
    
    Parameters:
    
    values - array of values to sum
    
    Returns:
    
    the sum of the values or Double.NaN if the array is empty
    
    Throws:
    
    MathIllegalArgumentException - if the array is null
  - sum
```
public static double sum(double[] values,
                         int begin,
                         int length)
                  throws MathIllegalArgumentException
```
    Returns the sum of the entries in the specified portion of the input array, or Double.NaN if the designated subarray is empty.
    Throws IllegalArgumentException if the array is null.
    
    Parameters:
    
    values - the input array
    
    begin - index of the first array element to include
    
    length - the number of elements to include
    
    Returns:
    
    the sum of the values or Double.NaN if length = 0
    
    Throws:
    
    MathIllegalArgumentException - if the array is null or the array index parameters are not valid
  - sumSq
```
public static double sumSq(double... values)
                    throws MathIllegalArgumentException
```
    Returns the sum of the squares of the entries in the input array, or Double.NaN if the array is empty.
    Throws IllegalArgumentException if the array is null.
    
    Parameters:
    
    values - input array
    
    Returns:
    
    the sum of the squared values or Double.NaN if the array is empty
    
    Throws:
    
    MathIllegalArgumentException - if the array is null
  - sumSq
```
public static double sumSq(double[] values,
                           int begin,
                           int length)
                    throws MathIllegalArgumentException
```
    Returns the sum of the squares of the entries in the specified portion of the input array, or Double.NaN if the designated subarray is empty.
    Throws IllegalArgumentException if the array is null.
    
    Parameters:
    
    values - the input array
    
    begin - index of the first array element to include
    
    length - the number of elements to include
    
    Returns:
    
    the sum of the squares of the values or Double.NaN if length = 0
    
    Throws:
    
    MathIllegalArgumentException - if the array is null or the array index parameters are not valid
  - product
```
public static double product(double... values)
                      throws MathIllegalArgumentException
```
    Returns the product of the entries in the input array, or Double.NaN if the array is empty.
    Throws IllegalArgumentException if the array is null.
    
    Parameters:
    
    values - the input array
    
    Returns:
    
    the product of the values or Double.NaN if the array is empty
    
    Throws:
    
    MathIllegalArgumentException - if the array is null
  - product
```
public static double product(double[] values,
                             int begin,
                             int length)
                      throws MathIllegalArgumentException
```
    Returns the product of the entries in the specified portion of the input array, or Double.NaN if the designated subarray is empty.
    Throws IllegalArgumentException if the array is null.
    
    Parameters:
    
    values - the input array
    
    begin - index of the first array element to include
    
    length - the number of elements to include
    
    Returns:
    
    the product of the values or Double.NaN if length = 0
    
    Throws:
    
    MathIllegalArgumentException - if the array is null or the array index parameters are not valid
  - sumLog
```
public static double sumLog(double... values)
                     throws MathIllegalArgumentException
```
    Returns the sum of the natural logs of the entries in the input array, or Double.NaN if the array is empty.
    Throws IllegalArgumentException if the array is null.
    See SumOfLogs.
    
    Parameters:
    
    values - the input array
    
    Returns:
    
    the sum of the natural logs of the values or Double.NaN if the array is empty
    
    Throws:
    
    MathIllegalArgumentException - if the array is null
  - sumLog
```
public static double sumLog(double[] values,
                            int begin,
                            int length)
                     throws MathIllegalArgumentException
```
    Returns the sum of the natural logs of the entries in the specified portion of the input array, or Double.NaN if the designated subarray is empty.
    Throws IllegalArgumentException if the array is null.
    See SumOfLogs.
    
    Parameters:
    
    values - the input array
    
    begin - index of the first array element to include
    
    length - the number of elements to include
    
    Returns:
    
    the sum of the natural logs of the values or Double.NaN if length = 0
    
    Throws:
    
    MathIllegalArgumentException - if the array is null or the array index parameters are not valid
  - mean
```
public static double mean(double... values)
                   throws MathIllegalArgumentException
```
    Returns the arithmetic mean of the entries in the input array, or Double.NaN if the array is empty.
    Throws IllegalArgumentException if the array is null.
    See Mean for details on the computing algorithm.
    
    Parameters:
    
    values - the input array
    
    Returns:
    
    the mean of the values or Double.NaN if the array is empty
    
    Throws:
    
    MathIllegalArgumentException - if the array is null
  - mean
```
public static double mean(double[] values,
                          int begin,
                          int length)
                   throws MathIllegalArgumentException
```
    Returns the arithmetic mean of the entries in the specified portion of the input array, or Double.NaN if the designated subarray is empty.
    Throws IllegalArgumentException if the array is null.
    See Mean for details on the computing algorithm.
    
    Parameters:
    
    values - the input array
    
    begin - index of the first array element to include
    
    length - the number of elements to include
    
    Returns:
    
    the mean of the values or Double.NaN if length = 0
    
    Throws:
    
    MathIllegalArgumentException - if the array is null or the array index parameters are not valid
  - geometricMean
```
public static double geometricMean(double... values)
                            throws MathIllegalArgumentException
```
    Returns the geometric mean of the entries in the input array, or Double.NaN if the array is empty.
    Throws IllegalArgumentException if the array is null.
    See GeometricMean for details on the computing algorithm.
    
    Parameters:
    
    values - the input array
    
    Returns:
    
    the geometric mean of the values or Double.NaN if the array is empty
    
    Throws:
    
    MathIllegalArgumentException - if the array is null
  - geometricMean
```
public static double geometricMean(double[] values,
                                   int begin,
                                   int length)
                            throws MathIllegalArgumentException
```
    Returns the geometric mean of the entries in the specified portion of the input array, or Double.NaN if the designated subarray is empty.
    Throws IllegalArgumentException if the array is null.
    See GeometricMean for details on the computing algorithm.
    
    Parameters:
    
    values - the input array
    
    begin - index of the first array element to include
    
    length - the number of elements to include
    
    Returns:
    
    the geometric mean of the values or Double.NaN if length = 0
    
    Throws:
    
    MathIllegalArgumentException - if the array is null or the array index parameters are not valid
  - variance
```
public static double variance(double... values)
                       throws MathIllegalArgumentException
```
    Returns the variance of the entries in the input array, or Double.NaN if the array is empty.
    This method returns the bias-corrected sample variance (using n - 1 in the denominator). Use populationVariance(double[]) for the non-bias-corrected population variance.
    See Variance for details on the computing algorithm.
    Returns 0 for a single-value (i.e. length = 1) sample.
    Throws MathIllegalArgumentException if the array is null.
    
    Parameters:
    
    values - the input array
    
    Returns:
    
    the variance of the values or Double.NaN if the array is empty
    
    Throws:
    
    MathIllegalArgumentException - if the array is null
  - variance
```
public static double variance(double[] values,
                              int begin,
                              int length)
                       throws MathIllegalArgumentException
```
    Returns the variance of the entries in the specified portion of the input array, or Double.NaN if the designated subarray is empty.
    This method returns the bias-corrected sample variance (using n - 1 in the denominator). Use populationVariance(double[], int, int) for the non-bias-corrected population variance.
    See Variance for details on the computing algorithm.
    Returns 0 for a single-value (i.e. length = 1) sample.
    Throws MathIllegalArgumentException if the array is null or the array index parameters are not valid.
    
    Parameters:
    
    values - the input array
    
    begin - index of the first array element to include
    
    length - the number of elements to include
    
    Returns:
    
    the variance of the values or Double.NaN if length = 0
    
    Throws:
    
    MathIllegalArgumentException - if the array is null or the array index parameters are not valid
  - variance
```
public static double variance(double[] values,
                              double mean,
                              int begin,
                              int length)
                       throws MathIllegalArgumentException
```
    Returns the variance of the entries in the specified portion of the input array, using the precomputed mean value. Returns Double.NaN if the designated subarray is empty.
    This method returns the bias-corrected sample variance (using n - 1 in the denominator). Use populationVariance(double[], double, int, int) for the non-bias-corrected population variance.
    See Variance for details on the computing algorithm.
    The formula used assumes that the supplied mean value is the arithmetic mean of the sample data, not a known population parameter. This method is supplied only to save computation when the mean has already been computed.
    Returns 0 for a single-value (i.e. length = 1) sample.
    Throws MathIllegalArgumentException if the array is null or the array index parameters are not valid.
    
    Parameters:
    
    values - the input array
    
    mean - the precomputed mean value
    
    begin - index of the first array element to include
    
    length - the number of elements to include
    
    Returns:
    
    the variance of the values or Double.NaN if length = 0
    
    Throws:
    
    MathIllegalArgumentException - if the array is null or the array index parameters are not valid
  - variance
```
public static double variance(double[] values,
                              double mean)
                       throws MathIllegalArgumentException
```
    Returns the variance of the entries in the input array, using the precomputed mean value. Returns Double.NaN if the array is empty.
    This method returns the bias-corrected sample variance (using n - 1 in the denominator). Use populationVariance(double[], double) for the non-bias-corrected population variance.
    See Variance for details on the computing algorithm.
    The formula used assumes that the supplied mean value is the arithmetic mean of the sample data, not a known population parameter. This method is supplied only to save computation when the mean has already been computed.
    Returns 0 for a single-value (i.e. length = 1) sample.
    Throws MathIllegalArgumentException if the array is null.
    
    Parameters:
    
    values - the input array
    
    mean - the precomputed mean value
    
    Returns:
    
    the variance of the values or Double.NaN if the array is empty
    
    Throws:
    
    MathIllegalArgumentException - if the array is null
  - populationVariance
```
public static double populationVariance(double... values)
                                 throws MathIllegalArgumentException
```
    Returns the population variance of the entries in the input array, or Double.NaN if the array is empty.
    See Variance for details on the formula and computing algorithm.
    Returns 0 for a single-value (i.e. length = 1) sample.
    Throws MathIllegalArgumentException if the array is null.
    
    Parameters:
    
    values - the input array
    
    Returns:
    
    the population variance of the values or Double.NaN if the array is empty
    
    Throws:
    
    MathIllegalArgumentException - if the array is null
  - populationVariance
```
public static double populationVariance(double[] values,
                                        int begin,
                                        int length)
                                 throws MathIllegalArgumentException
```
    Returns the population variance of the entries in the specified portion of the input array, or Double.NaN if the designated subarray is empty.
    See Variance for details on the computing algorithm.
    Returns 0 for a single-value (i.e. length = 1) sample.
    Throws MathIllegalArgumentException if the array is null or the array index parameters are not valid.
    
    Parameters:
    
    values - the input array
    
    begin - index of the first array element to include
    
    length - the number of elements to include
    
    Returns:
    
    the population variance of the values or Double.NaN if length = 0
    
    Throws:
    
    MathIllegalArgumentException - if the array is null or the array index parameters are not valid
  - populationVariance
```
public static double populationVariance(double[] values,
                                        double mean,
                                        int begin,
                                        int length)
                                 throws MathIllegalArgumentException
```
    Returns the population variance of the entries in the specified portion of the input array, using the precomputed mean value. Returns Double.NaN if the designated subarray is empty.
    See Variance for details on the computing algorithm.
    The formula used assumes that the supplied mean value is the arithmetic mean of the sample data, not a known population parameter. This method is supplied only to save computation when the mean has already been computed.
    Returns 0 for a single-value (i.e. length = 1) sample.
    Throws MathIllegalArgumentException if the array is null or the array index parameters are not valid.
    
    Parameters:
    
    values - the input array
    
    mean - the precomputed mean value
    
    begin - index of the first array element to include
    
    length - the number of elements to include
    
    Returns:
    
    the population variance of the values or Double.NaN if length = 0
    
    Throws:
    
    MathIllegalArgumentException - if the array is null or the array index parameters are not valid
  - populationVariance
```
public static double populationVariance(double[] values,
                                        double mean)
                                 throws MathIllegalArgumentException
```
    Returns the population variance of the entries in the input array, using the precomputed mean value. Returns Double.NaN if the array is empty.
    See Variance for details on the computing algorithm.
    The formula used assumes that the supplied mean value is the arithmetic mean of the sample data, not a known population parameter. This method is supplied only to save computation when the mean has already been computed.
    Returns 0 for a single-value (i.e. length = 1) sample.
    Throws MathIllegalArgumentException if the array is null.
    
    Parameters:
    
    values - the input array
    
    mean - the precomputed mean value
    
    Returns:
    
    the population variance of the values or Double.NaN if the array is empty
    
    Throws:
    
    MathIllegalArgumentException - if the array is null
  - max
```
public static double max(double... values)
                  throws MathIllegalArgumentException
```
    Returns the maximum of the entries in the input array, or Double.NaN if the array is empty.
    Throws MathIllegalArgumentException if the array is null.
    - The result is NaN iff all values are NaN (i.e. NaN values have no impact on the value of the statistic).
    - If any of the values equals Double.POSITIVE_INFINITY, the result is Double.POSITIVE_INFINITY.
    Parameters:
    
    values - the input array
    
    Returns:
    
    the maximum of the values or Double.NaN if the array is empty
    
    Throws:
    
    MathIllegalArgumentException - if the array is null
  - max
```
public static double max(double[] values,
                         int begin,
                         int length)
                  throws MathIllegalArgumentException
```
    Returns the maximum of the entries in the specified portion of the input array, or Double.NaN if the designated subarray is empty.
    Throws MathIllegalArgumentException if the array is null or the array index parameters are not valid.
    - The result is NaN iff all values are NaN (i.e. NaN values have no impact on the value of the statistic).
    - If any of the values equals Double.POSITIVE_INFINITY, the result is Double.POSITIVE_INFINITY.
    Parameters:
    
    values - the input array
    
    begin - index of the first array element to include
    
    length - the number of elements to include
    
    Returns:
    
    the maximum of the values or Double.NaN if length = 0
    
    Throws:
    
    MathIllegalArgumentException - if the array is null or the array index parameters are not valid
  - min
```
public static double min(double... values)
                  throws MathIllegalArgumentException
```
    Returns the minimum of the entries in the input array, or Double.NaN if the array is empty.
    Throws MathIllegalArgumentException if the array is null.
    - The result is NaN iff all values are NaN (i.e. NaN values have no impact on the value of the statistic).
    - If any of the values equals Double.NEGATIVE_INFINITY, the result is Double.NEGATIVE_INFINITY.
    Parameters:
    
    values - the input array
    
    Returns:
    
    the minimum of the values or Double.NaN if the array is empty
    
    Throws:
    
    MathIllegalArgumentException - if the array is null
  - min
```
public static double min(double[] values,
                         int begin,
                         int length)
                  throws MathIllegalArgumentException
```
    Returns the minimum of the entries in the specified portion of the input array, or Double.NaN if the designated subarray is empty.
    Throws MathIllegalArgumentException if the array is null or the array index parameters are not valid.
    - The result is NaN iff all values are NaN (i.e. NaN values have no impact on the value of the statistic).
    - If any of the values equals Double.NEGATIVE_INFINITY, the result is Double.NEGATIVE_INFINITY.
    Parameters:
    
    values - the input array
    
    begin - index of the first array element to include
    
    length - the number of elements to include
    
    Returns:
    
    the minimum of the values or Double.NaN if length = 0
    
    Throws:
    
    MathIllegalArgumentException - if the array is null or the array index parameters are not valid
  - percentile
```
public static double percentile(double[] values,
                                double p)
                         throws MathIllegalArgumentException
```
    Returns an estimate of the pth percentile of the values in the values array.
    - Returns Double.NaN if values has length 0
    - Returns (for any value of p) values[0] if values has length 1
    - Throws IllegalArgumentException if values is null or p is not a valid quantile value (p must be greater than 0 and less than or equal to 100)
    See Percentile for a description of the percentile estimation algorithm used.
    Parameters:
    
    values - input array of values
    
    p - the percentile value to compute
    
    Returns:
    
    the percentile value or Double.NaN if the array is empty
    
    Throws:
    
    MathIllegalArgumentException - if values is null or p is invalid
  - percentile
```
public static double percentile(double[] values,
                                int begin,
                                int length,
                                double p)
                         throws MathIllegalArgumentException
```
    Returns an estimate of the pth percentile of the values in the values array, starting with the element in (0-based) position begin in the array and including length values.
    - Returns Double.NaN if length = 0
    - Returns (for any value of p) values[begin] if length = 1
    - Throws MathIllegalArgumentException if values is null, begin or length is invalid, or p is not a valid quantile value (p must be greater than 0 and less than or equal to 100)
    See Percentile for a description of the percentile estimation algorithm used.
    Parameters:
    
    values - array of input values
    
    p - the percentile to compute
    
    begin - the first (0-based) element to include in the computation
    
    length - the number of array elements to include
    
    Returns:
    
    the percentile value
    
    Throws:
    
    MathIllegalArgumentException - if the parameters are not valid or the input array is null
  - sumDifference
```
public static double sumDifference(double[] sample1,
                                   double[] sample2)
                            throws MathIllegalArgumentException
```
    Returns the sum of the (signed) differences between corresponding elements of the input arrays -- i.e., sum(sample1[i] - sample2[i]).
    
    Parameters:
    
    sample1 - the first array
    
    sample2 - the second array
    
    Returns:
    
    sum of paired differences
    
    Throws:
    
    MathIllegalArgumentException - if the arrays do not have the same (positive) length.
    
    MathIllegalArgumentException - if the sample arrays are empty.
  - meanDifference
```
public static double meanDifference(double[] sample1,
                                    double[] sample2)
                             throws MathIllegalArgumentException
```
    Returns the mean of the (signed) differences between corresponding elements of the input arrays -- i.e., sum(sample1[i] - sample2[i]) / sample1.length.
    
    Parameters:
    
    sample1 - the first array
    
    sample2 - the second array
    
    Returns:
    
    mean of paired differences
    
    Throws:
    
    MathIllegalArgumentException - if the arrays do not have the same (positive) length.
    
    MathIllegalArgumentException - if the sample arrays are empty.
  - varianceDifference
```
public static double varianceDifference(double[] sample1,
                                        double[] sample2,
                                        double meanDifference)
                                 throws MathIllegalArgumentException
```
    Returns the variance of the (signed) differences between corresponding elements of the input arrays -- i.e., var(sample1[i] - sample2[i]).
    
    Parameters:
    
    sample1 - the first array
    
    sample2 - the second array
    
    meanDifference - the mean difference between corresponding entries
    
    Returns:
    
    variance of paired differences
    
    Throws:
    
    MathIllegalArgumentException - if the arrays do not have the same length.
    
    MathIllegalArgumentException - if the arrays length is less than 2.
    
    See Also:
    
    meanDifference(double[],double[])
  - normalize
```
public static double[] normalize(double... sample)
```
    Normalize (standardize) the sample, so it is has a mean of 0 and a standard deviation of 1.
    
    Parameters:
    
    sample - Sample to normalize.
    
    Returns:
    
    normalized (standardized) sample.
  - mode
```
public static double[] mode(double... sample)
                     throws MathIllegalArgumentException
```
    Returns the sample mode(s).
    The mode is the most frequently occurring value in the sample. If there is a unique value with maximum frequency, this value is returned as the only element of the output array. Otherwise, the returned array contains the maximum frequency elements in increasing order.
    For example, if sample is {0, 12, 5, 6, 0, 13, 5, 17}, the returned array will have length two, with 0 in the first element and 5 in the second.
    NaN values are ignored when computing the mode - i.e., NaNs will never appear in the output array. If the sample includes only NaNs or has length 0, an empty array is returned.
    
    Parameters:
    
    sample - input data
    
    Returns:
    
    array of array of the most frequently occurring element(s) sorted in ascending order.
    
    Throws:
    
    MathIllegalArgumentException - if the indices are invalid or the array is null
  - mode
```
public static double[] mode(double[] sample,
                            int begin,
                            int length)
```
    Returns the sample mode(s).
    The mode is the most frequently occurring value in the sample. If there is a unique value with maximum frequency, this value is returned as the only element of the output array. Otherwise, the returned array contains the maximum frequency elements in increasing order.
    For example, if sample is {0, 12, 5, 6, 0, 13, 5, 17}, the returned array will have length two, with 0 in the first element and 5 in the second.
    NaN values are ignored when computing the mode - i.e., NaNs will never appear in the output array. If the sample includes only NaNs or has length 0, an empty array is returned.
    
    Parameters:
    
    sample - input data
    
    begin - index (0-based) of the first array element to include
    
    length - the number of elements to include
    
    Returns:
    
    array of array of the most frequently occurring element(s) sorted in ascending order.
    
    Throws:
    
    MathIllegalArgumentException - if the indices are invalid or the array is null

Class StatUtils

Method Summary

Methods inherited from class java.lang.Object

Method Detail

sum

sum

sumSq

sumSq

product

product

sumLog

sumLog

mean

mean

geometricMean

geometricMean

variance

variance

variance

variance

populationVariance

populationVariance

populationVariance

populationVariance

max

max

min

min

percentile

percentile

sumDifference

meanDifference

varianceDifference

normalize

mode

mode