Package org.hipparchus.stat.descriptive.rank

Class Percentile

  • All Implemented Interfaces:
    Serializable, UnivariateStatistic, MathArrays.Function
    public class Percentile
extends AbstractUnivariateStatistic
implements Serializable
    Provides percentile computation.

    There are several commonly used methods for estimating percentiles (a.k.a. quantiles) based on sample data. For large samples, the different methods agree closely, but when sample sizes are small, different methods will give significantly different results. The algorithm implemented here works as follows:

    1. Let n be the length of the (sorted) array and 0 < p <= 100 be the desired percentile.
    2. If n = 1 return the unique array element (regardless of the value of p); otherwise
    3. Compute the estimated percentile position pos = p * (n + 1) / 100 and the difference, d between pos and floor(pos) (i.e. the fractional part of pos).
    4. If pos < 1 return the smallest element in the array.
    5. Else if pos >= n return the largest element in the array.
    6. Else let lower be the element in position floor(pos) in the array and let upper be the next element in the array. Return lower + d * (upper - lower)

    To compute percentiles, the data must be at least partially ordered. Input arrays are copied and recursively partitioned using an ordering definition. The ordering used by Arrays.sort(double[]) is the one determined by Double.compareTo(Double). This ordering makes Double.NaN larger than any other value (including Double.POSITIVE_INFINITY). Therefore, for example, the median (50th percentile) of {0, 1, 2, 3, 4, Double.NaN} evaluates to 2.5.

    Since percentile estimation usually involves interpolation between array elements, arrays containing NaN or infinite values will often result in NaN or infinite values returned.

    Further, to include different estimation types such as R1, R2 as mentioned in Quantile page(wikipedia), a type specific NaN handling strategy is used to closely match with the typically observed results from popular tools like R(R1-R9), Excel(R7).

    Percentile uses only selection instead of complete sorting and caches selection algorithm state between calls to the various evaluate methods. This greatly improves efficiency, both for a single percentile and multiple percentile computations. To maximize performance when multiple percentiles are computed based on the same data, users should set the data array once using either one of the evaluate(double[], double) or setData(double[]) methods and thereafter evaluate(double) with just the percentile provided.

    Note that this implementation is not synchronized. If multiple threads access an instance of this class concurrently, and at least one of the threads invokes the increment() or clear() method, it must be synchronized externally.

    See Also:
    Serialized Form

    • Method Detail

      • evaluate

        public double evaluate​(double p)
                throws MathIllegalArgumentException
        Returns the result of evaluating the statistic over the stored data.

        The stored array is the one which was set by previous calls to setData(double[])

        Parameters:
        p - the percentile value to compute
        Returns:
        the value of the statistic applied to the stored data
        Throws:
        MathIllegalArgumentException - if p is not a valid quantile value (p must be greater than 0 and less than or equal to 100)

      • evaluate

        public double evaluate​(double[] values,
                       int start,
                       int length)
                throws MathIllegalArgumentException
        Returns an estimate of the quantileth percentile of the designated values in the values array. The quantile estimated is determined by the quantile property.

        • Returns Double.NaN if length = 0
        • Returns (for any value of quantile) values[begin] if length = 1
        • Throws MathIllegalArgumentException if values is null, or start or length is invalid

        See Percentile for a description of the percentile estimation algorithm used.

        Specified by:
        evaluate in interface MathArrays.Function
        Specified by:
        evaluate in interface UnivariateStatistic
        Specified by:
        evaluate in class AbstractUnivariateStatistic
        Parameters:
        values - the input array
        start - index of the first array element to include
        length - the number of elements to include
        Returns:
        the percentile value
        Throws:
        MathIllegalArgumentException - if the parameters are not valid

      • evaluate

        public double evaluate​(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 MathIllegalArgumentException 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)

        The default implementation delegates to evaluate(double[], int, int, double) in the natural way.

        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

      • evaluate

        public double evaluate​(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.

        Calls to this method do not modify the internal quantile state of this statistic.

        • 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

      • getQuantile

        public double getQuantile()
        Returns the value of the quantile field (determines what percentile is computed when evaluate() is called with no quantile argument).
        Returns:
        quantile set while construction or setQuantile(double)

      • setQuantile

        public void setQuantile​(double p)
                 throws MathIllegalArgumentException
        Sets the value of the quantile field (determines what percentile is computed when evaluate() is called with no quantile argument).
        Parameters:
        p - a value between 0 < p <= 100
        Throws:
        MathIllegalArgumentException - if p is not greater than 0 and less than or equal to 100

      • getWorkArray

        protected double[] getWorkArray​(double[] values,
                                int begin,
                                int length)
        Get the work array to operate. Makes use of prior storedData if it exists or else do a check on NaNs and copy a subset of the array defined by begin and length parameters. The set nanStrategy will be used to either retain/remove/replace any NaNs present before returning the resultant array.
        Parameters:
        values - the array of numbers
        begin - index to start reading the array
        length - the length of array to be read from the begin index
        Returns:
        work array sliced from values in the range [begin,begin+length)
        Throws:
        MathIllegalArgumentException - if values or indices are invalid

      • getEstimationType

        public Percentile.EstimationType getEstimationType()
        Get the estimation type used for computation.
        Returns:
        the estimationType set

      • withEstimationType

        public Percentile withEstimationType​(Percentile.EstimationType newEstimationType)
        Build a new instance similar to the current one except for the estimation type.

        This method is intended to be used as part of a fluent-type builder pattern. Building finely tune instances should be done as follows: 

           Percentile customized = new Percentile(quantile).
                           withEstimationType(estimationType).
                           withNaNStrategy(nanStrategy).
                           withKthSelector(kthSelector);

        If any of the withXxx method is omitted, the default value for the corresponding customization parameter will be used.

        Parameters:
        newEstimationType - estimation type for the new instance
        Returns:
        a new instance, with changed estimation type
        Throws:
        NullArgumentException - when newEstimationType is null

      • getNaNStrategy

        public NaNStrategy getNaNStrategy()
        Get the NaN Handling strategy used for computation.
        Returns:
        NaN Handling strategy set during construction

      • withNaNStrategy

        public Percentile withNaNStrategy​(NaNStrategy newNaNStrategy)
        Build a new instance similar to the current one except for the NaN handling strategy.

        This method is intended to be used as part of a fluent-type builder pattern. Building finely tune instances should be done as follows: 

           Percentile customized = new Percentile(quantile).
                           withEstimationType(estimationType).
                           withNaNStrategy(nanStrategy).
                           withKthSelector(kthSelector);

        If any of the withXxx method is omitted, the default value for the corresponding customization parameter will be used.

        Parameters:
        newNaNStrategy - NaN strategy for the new instance
        Returns:
        a new instance, with changed NaN handling strategy
        Throws:
        NullArgumentException - when newNaNStrategy is null

      • getKthSelector

        public KthSelector getKthSelector()
        Get the kthSelector used for computation.
        Returns:
        the kthSelector set

      • getPivotingStrategy

        public PivotingStrategy getPivotingStrategy()
        Get the PivotingStrategy used in KthSelector for computation.
        Returns:
        the pivoting strategy set

      • withKthSelector

        public Percentile withKthSelector​(KthSelector newKthSelector)
        Build a new instance similar to the current one except for the kthSelector instance specifically set.

        This method is intended to be used as part of a fluent-type builder pattern. Building finely tune instances should be done as follows: 

           Percentile customized = new Percentile(quantile).
                           withEstimationType(estimationType).
                           withNaNStrategy(nanStrategy).
                           withKthSelector(newKthSelector);

        If any of the withXxx method is omitted, the default value for the corresponding customization parameter will be used.

        Parameters:
        newKthSelector - KthSelector for the new instance
        Returns:
        a new instance, with changed KthSelector
        Throws:
        NullArgumentException - when newKthSelector is null