mathnet-numerics/src/Numerics/Statistics/Percentile.cs

// <copyright file="Percentile.cs" company="Math.NET">
// Math.NET Numerics, part of the Math.NET Project
// http://numerics.mathdotnet.com
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namespace MathNet.Numerics.Statistics
{
    using System;
    using System.Collections.Generic;
    using System.Linq;

    /// <summary>
    /// Methods to calculate the percentiles.
    /// </summary>
    public enum PercentileMethod
    {
        /// <summary>
        /// Using the method recommened my NIST,
        /// http://www.itl.nist.gov/div898/handbook/prc/section2/prc252.htm
        /// </summary>
        Nist = 0, 

        /// <summary>
        /// Using the nearest rank, http://en.wikipedia.org/wiki/Percentile#Nearest_Rank
        /// </summary>
        Nearest, 

        /// <summary>
        /// Using the same method as Excel does, 
        /// http://www.itl.nist.gov/div898/handbook/prc/section2/prc252.htm
        /// </summary>
        Excel, 

        /// <summary>
        /// Use linear interpolation between the two nearest ranks,
        /// http://en.wikipedia.org/wiki/Percentile#Linear_Interpolation_Between_Closest_Ranks
        /// </summary>
        Interpolation
    }

    /// <summary>
    /// Class to calculate percentiles.
    /// </summary>
    public class Percentile
    {
        /// <summary>
        /// Holds the data.
        /// </summary>
        private readonly List<double> _data;

        /// <summary>
        /// Gets or sets the method used to calculate the percentiles.
        /// </summary>
        /// <value>The calculation method.</value>
        /// <remarks>defaults to <see cref="PercentileMethod.Nist"/>.</remarks>
        public PercentileMethod Method
        {
            get;
            set;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="Percentile"/> class.
        /// </summary>
        /// <param name="data">The data to calculate the percentiles of.</param>
        public Percentile(IEnumerable<double> data)
        {
            if (data == null)
            {
                throw new ArgumentNullException("data");
            }
            
            if (data.Count() < 3)
            {
                throw new ArgumentException(string.Format(Properties.Resources.MustContainAtLeast, 3), "data");
            }

            _data = new List<double>(data);
            _data.Sort();
        }

        /// <summary>
        /// Computes the percentile.
        /// </summary>
        /// <param name="percentile">The percentile, must be between 0.0 and 1.0 (inclusive).</param>
        /// <returns>the requested percentile.</returns>
        public double Compute(double percentile)
        {
            if (percentile < 0 || percentile > 100)
            {
                throw new ArgumentException("Percentile value must be between 0 and 100.");
            }

            if (percentile == 0.0)
            {
                return _data[0];
            }

            if (percentile == 1.0)
            {
                return _data[_data.Count - 1];
            }

            var result = double.NaN;
            switch (Method)
            {
                case PercentileMethod.Nist:
                    result = Nist(percentile);
                    break;
                case PercentileMethod.Nearest:
                    result = Nearest(percentile);
                    break;
                case PercentileMethod.Interpolation:
                    result = Interpolation(percentile);
                    break;
                case PercentileMethod.Excel:
                    result = Excel(percentile);
                    break;
            }

            return result;
        }

        /// <summary>
        /// Computes the percentiles for the given list.
        /// </summary>
        /// <param name="percentiles">The percentiles, must be between 0.0 and 1.0 (inclusive)</param>
        /// <returns>the values that correspond to the given percentiles.</returns>
        public IList<double> Compute(IEnumerable<double> percentiles)
        {
            if (percentiles == null)
            {
                throw new ArgumentNullException("percentiles");
            }

            return percentiles.Select(Compute).ToList();
        }

        /// <summary>
        /// Computes the percentile using the nearest value.
        /// </summary>
        /// <param name="percentile">The percentile.</param>
        /// <returns>the percentile using the nearest value.</returns>
        private double Nearest(double percentile)
        {
            var n = (int)Math.Round((_data.Count * percentile) + 0.5, 0);
            return _data[n - 1];
        }

        /// <summary>
        /// Computes the percentile using Excel's method.
        /// </summary>
        /// <param name="percentile">The percentile.</param>
        /// <returns>the percentile using Excel's method.</returns>
        private double Excel(double percentile)
        {
            var tmp = 1 + (percentile * (_data.Count - 1.0));
            var k = (int)tmp;
            var d = tmp - k;

            return _data[k - 1] + (d * (_data[k] - _data[k - 1]));
        }

        /// <summary>
        /// Computes the percentile using interpolation.
        /// </summary>
        /// <param name="percentile">The percentile.</param>
        /// <returns>the percentile using the interpolation.</returns>
        private double Interpolation(double percentile)
        {
            var k = (int)(_data.Count * percentile);
            var pk = (k - 0.5) / _data.Count;
            return _data[k - 1] + (_data.Count * (percentile - pk) * (_data[k] - _data[k - 1]));
        }

        /// <summary>
        /// Computes the percentile using NIST's method.
        /// </summary>
        /// <param name="percentile">The percentile.</param>
        /// <returns>the percentile using NIST's method.</returns>
        private double Nist(double percentile)
        {
            var tmp = percentile * (_data.Count + 1.0);
            var k = (int)tmp;
            var d = tmp - k;

            return _data[k - 1] + (d * (_data[k] - _data[k - 1]));
        }
    }
}