Package org.hipparchus.stat.descriptive.rank

Class RandomPercentile

  • All Implemented Interfaces:
    Serializable, DoubleConsumer, AggregatableStatistic<RandomPercentile>, StorelessUnivariateStatistic, UnivariateStatistic, MathArrays.Function
    public class RandomPercentile
extends AbstractStorelessUnivariateStatistic
implements StorelessUnivariateStatistic, AggregatableStatistic<RandomPercentile>, Serializable
    A StorelessUnivariateStatistic estimating percentiles using the RANDOM Algorithm.

    Storage requirements for the RANDOM algorithm depend on the desired accuracy of quantile estimates. Quantile estimate accuracy is defined as follows.

    Let \(X\) be the set of all data values consumed from the stream and let \(q\) be a quantile (measured between 0 and 1) to be estimated. If

    • \(\epsilon\) is the configured accuracy
    • \(\hat{q}\) is a RandomPercentile estimate for \(q\) (what is returned by getResult() or getResult(double)) with \(100q\) as actual parameter)
    • \(rank(\hat{q}) = |\{x \in X : x < \hat{q}\}|\) is the actual rank of \(\hat{q}\) in the full data stream
    • \(n = |X|\) is the number of observations
    then we can expect \((q - \epsilon)n < rank(\hat{q}) < (q + \epsilon)n\).

    The algorithm maintains \(\left\lceil {log_{2}(1/\epsilon)}\right\rceil + 1\) buffers of size \(\left\lceil {1/\epsilon \sqrt{log_2(1/\epsilon)}}\right\rceil\). When epsilon is set to the default value of \(10^{-4}\), this makes 15 buffers of size 36,453.

    The algorithm uses the buffers to maintain samples of data from the stream. Until all buffers are full, the entire sample is stored in the buffers. If one of the getResult methods is called when all data are available in memory and there is room to make a copy of the data (meaning the combined set of buffers is less than half full), the getResult method delegates to a Percentile instance to compute and return the exact value for the desired quantile. For default epsilon, this means exact values will be returned whenever fewer than \(\left\lceil {15 \times 36453 / 2} \right\rceil = 273,398\) values have been consumed from the data stream.

    When buffers become full, the algorithm merges buffers so that they effectively represent a larger set of values than they can hold. Subsequently, data values are sampled from the stream to fill buffers freed by merge operations. Both the merging and the sampling require random selection, which is done using a RandomGenerator. To get repeatable results for large data streams, users should provide RandomGenerator instances with fixed seeds. RandomPercentile itself does not reseed or otherwise initialize the RandomGenerator provided to it. By default, it uses a Well19937c generator with the default seed.

    Note: This implementation is not thread-safe.

    See Also:
    Serialized Form

    • Field Detail

      • DEFAULT_EPSILON

        public static final double DEFAULT_EPSILON
        Default quantile estimation error setting
        See Also:
        Constant Field Values

    • Constructor Detail

      • RandomPercentile

        public RandomPercentile​(double epsilon,
                        RandomGenerator randomGenerator)
        Constructs a RandomPercentile with quantile estimation error epsilon using randomGenerator as its source of random data.
        Parameters:
        epsilon - bound on quantile estimation error (see class javadoc)
        randomGenerator - PRNG used in sampling and merge operations
        Throws:
        MathIllegalArgumentException - if percentile is not in the range [0, 100]

      • RandomPercentile

        public RandomPercentile​(RandomGenerator randomGenerator)
        Constructs a RandomPercentile with default estimation error using randomGenerator as its source of random data.
        Parameters:
        randomGenerator - PRNG used in sampling and merge operations
        Throws:
        MathIllegalArgumentException - if percentile is not in the range [0, 100]

      • RandomPercentile

        public RandomPercentile​(double epsilon)
        Constructs a RandomPercentile with quantile estimation error epsilon using the default PRNG as source of random data.
        Parameters:
        epsilon - bound on quantile estimation error (see class javadoc)
        Throws:
        MathIllegalArgumentException - if percentile is not in the range [0, 100]

      • RandomPercentile

        public RandomPercentile()
        Constructs a RandomPercentile with quantile estimation error set to the default (DEFAULT_EPSILON), using the default PRNG as source of random data.

      • RandomPercentile

        public RandomPercentile​(RandomPercentile original)
        Copy constructor, creates a new RandomPercentile identical to the original. Note: the RandomGenerator used by the new instance is referenced, not copied - i.e., the new instance shares a generator with the original.
        Parameters:
        original - the PSquarePercentile instance to copy

    • Method Detail

      • evaluate

        public double evaluate​(double percentile,
                       double[] values,
                       int begin,
                       int length)
                throws MathIllegalArgumentException
        Returns an estimate of the given percentile, computed using the designated array segment as input data.
        Parameters:
        values - source of input data
        begin - position of the first element of the values array to include
        length - number of array elements to include
        percentile - desired percentile (scaled 0 - 100)
        Returns:
        estimated percentile
        Throws:
        MathIllegalArgumentException - if percentile is out of the range [0, 100]

      • evaluate

        public double evaluate​(double percentile,
                       double[] values)
        Returns an estimate of percentile over the given array.
        Parameters:
        values - source of input data
        percentile - desired percentile (scaled 0 - 100)
        Returns:
        estimated percentile
        Throws:
        MathIllegalArgumentException - if percentile is out of the range [0, 100]

      • getResult

        public double getResult​(double percentile)
        Returns an estimate of the given percentile.
        Parameters:
        percentile - desired percentile (scaled 0 - 100)
        Returns:
        estimated percentile
        Throws:
        MathIllegalArgumentException - if percentile is out of the range [0, 100]

      • getRank

        public double getRank​(double value)
        Gets the estimated rank of value, i.e. \(|\{x \in X : x < value\}|\) where \(X\) is the set of values that have been consumed from the stream.
        Parameters:
        value - value whose overall rank is sought
        Returns:
        estimated number of sample values that are strictly less than value

      • getQuantileRank

        public double getQuantileRank​(double value)
        Returns the estimated quantile position of value in the dataset. Specifically, what is returned is an estimate of \(|\{x \in X : x < value\}| / |X|\) where \(X\) is the set of values that have been consumed from the stream.
        Parameters:
        value - value whose quantile rank is sought.
        Returns:
        estimated proportion of sample values that are strictly less than value

      • reduce

        public double reduce​(double percentile,
                     Collection<RandomPercentile> aggregates)
        Computes the given percentile by combining the data from the collection of aggregates. The result describes the combined sample of all data added to any of the aggregates.
        Parameters:
        percentile - desired percentile (scaled 0-100)
        aggregates - RandomPercentile instances to combine data from
        Returns:
        estimate of the given percentile using combined data from the aggregates
        Throws:
        MathIllegalArgumentException - if percentile is out of the range [0, 100]

      • getAggregateRank

        public double getAggregateRank​(double value,
                               Collection<RandomPercentile> aggregates)
        Computes the estimated rank of value in the combined dataset of the aggregates. Sums the values from getRank(double).
        Parameters:
        value - value whose rank is sought
        aggregates - collection to aggregate rank over
        Returns:
        estimated number of elements in the combined dataset that are less than value

      • getAggregateQuantileRank

        public double getAggregateQuantileRank​(double value,
                                       Collection<RandomPercentile> aggregates)
        Returns the estimated quantile position of value in the combined dataset of the aggregates. Specifically, what is returned is an estimate of \(|\{x \in X : x < value\}| / |X|\) where \(X\) is the set of values that have been consumed from all of the datastreams feeding the aggregates.
        Parameters:
        value - value whose quantile rank is sought.
        aggregates - collection of RandomPercentile instances being combined
        Returns:
        estimated proportion of combined sample values that are strictly less than value

      • getAggregateN

        public double getAggregateN​(Collection<RandomPercentile> aggregates)
        Returns the total number of values that have been consumed by the aggregates.
        Parameters:
        aggregates - collection of RandomPercentile instances whose combined sample size is sought
        Returns:
        total number of values that have been consumed by the aggregates

      • maxValuesRetained

        public static long maxValuesRetained​(double epsilon)
        Returns the maximum number of double values that a RandomPercentile instance created with the given epsilon value will retain in memory.

        If the number of values that have been consumed from the stream is less than 1/2 of this value, reported statistics are exact.

        Parameters:
        epsilon - bound on the relative quantile error (see class javadoc)
        Returns:
        upper bound on the total number of primitive double values retained in memory
        Throws:
        MathIllegalArgumentException - if epsilon is not in the interval (0,1)