StatQuantile(Read
Definition
Assembly: Novacta.Analytics (in Novacta.Analytics.dll) Version: 2.1.0+428f3840cfab98dda567bb0ed350b302533e273a
public static DoubleMatrix Quantile(
ReadOnlyDoubleMatrix data,
DoubleMatrix probabilities
)Public Shared Function Quantile (
data As ReadOnlyDoubleMatrix,
probabilities As DoubleMatrix
) As DoubleMatrixpublic:
static DoubleMatrix^ Quantile(
ReadOnlyDoubleMatrix^ data,
DoubleMatrix^ probabilities
)static member Quantile :
data : ReadOnlyDoubleMatrix *
probabilities : DoubleMatrix -> DoubleMatrix Parameters
- data ReadOnlyDoubleMatrix
- The data.
- probabilities DoubleMatrix
- The probabilities whose quantiles are to be computed.
Return Value
DoubleMatrixThe data quantiles corresponding to the specified probabilities.
Remarks
The quantile of a distribution 
for the probability 
can be defined as follows:
The method returns a DoubleMatrix instance which includes the quantiles of data.
It has the same dimensions of probabilities.
Let 
be
the Length of probabilities and
define
Then the k-th
linear position of the returned matrix is occupied by the quantile
corresponding to
,
say 
.
It is computed as proposed by Hyndman and Fan (1996)[1].
Let 
be
the Length of data and
let
be the values in data sorted in ascending order.
Value 
is taken as
the quantile corresponding to the probability
and quantile 
is obtained by
linear interpolation of the points
hence setting
if 
;
if 
;
if 
.
Example
In the following example, the quantiles of the values in a data matrix are computed for probabilities .005, .50, .75, and .999.
using System;
namespace Novacta.Analytics.CodeExamples
{
public class QuantileExample0
{
public void Main()
{
// Create a matrix.
var matrix = DoubleMatrix.Dense(25, 4);
for (int m = 0; m < matrix.Count; m++) {
matrix[m] = 1 + m;
}
Console.WriteLine("The data matrix:");
Console.WriteLine(matrix);
// Create the probabilities.
var probabilities = DoubleMatrix.Dense(2, 2);
probabilities[0, 0] = .005;
probabilities[1, 0] = .50;
probabilities[0, 1] = .75;
probabilities[1, 1] = .999;
// Compute the data quantiles.
var quantiles = Stat.Quantile(matrix, probabilities);
Console.WriteLine();
Console.WriteLine("Probabilities are:");
Console.WriteLine(probabilities);
Console.WriteLine();
Console.WriteLine("Corresponding data quantiles are:");
Console.WriteLine(quantiles);
// Quantile is overloaded to accept data as a read-only matrix:
// compute the quantiles using a read-only wrapper of the data matrix.
ReadOnlyDoubleMatrix readOnlyMatrix = matrix.AsReadOnly();
var quantilesOfReadOnlyData = Stat.Quantile(readOnlyMatrix, probabilities);
Console.WriteLine();
Console.WriteLine("Using read-only data. The quantiles are:");
Console.WriteLine(quantilesOfReadOnlyData);
}
}
}
// Executing method Main() produces the following output:
//
// The data matrix:
// 1 26 51 76
// 2 27 52 77
// 3 28 53 78
// 4 29 54 79
// 5 30 55 80
// 6 31 56 81
// 7 32 57 82
// 8 33 58 83
// 9 34 59 84
// 10 35 60 85
// 11 36 61 86
// 12 37 62 87
// 13 38 63 88
// 14 39 64 89
// 15 40 65 90
// 16 41 66 91
// 17 42 67 92
// 18 43 68 93
// 19 44 69 94
// 20 45 70 95
// 21 46 71 96
// 22 47 72 97
// 23 48 73 98
// 24 49 74 99
// 25 50 75 100
//
//
//
// Probabilities are:
// 0.005 0.75
// 0.5 0.999
//
//
//
// Corresponding data quantiles are:
// 1 75.5833333
// 50.5 100
//
//
//
// Using read-only data. The quantiles are:
// 1 75.5833333
// 50.5 100
//
//Exceptions
| ArgumentNullException | data is null. -or- probabilities is null. |
| ArgumentException | probabilities has entries not belonging to the closed interval [0, 1]. |