EmpiricalQuantiles Class

Computes empirical quantiles.

For a list of all members of this type, see EmpiricalQuantiles Members.

System.Object
Imsl.Stat.EmpiricalQuantiles

public class EmpiricalQuantiles

Thread Safety

Public static (Shared in Visual Basic) members of this type are safe for multithreaded operations. Instance members are not guaranteed to be thread-safe.

Remarks

The class EmpiricalQuantiles determines the empirical quantiles, as indicated in the array qProp, from the data in x. The algorithm first checks to see if x is sorted; if x is not sorted, the algorithm does either a complete or partial sort, depending on how many order statistics are required to compute the quantiles requested. The algorithm returns the empirical quantiles and, for each quantile, the two order statistics from the sample that are at least as large and at least as small as the quantile. For a sample of size n, the quantile corresponding to the proportion p is defined as

$Q(p) = (1 - f)x_{(j)} + fx_{(j+1)}$

where $j = \lfloor p(n+1) \rfloor$ ,

, and $x_{(j)}$ , is the j-th order statistic, if $1 \leq j \le n$ ; otherwise, the empirical quantile is the smallest or largest order statistic.

Requirements

Namespace: Imsl.Stat

Assembly: ImslCS (in ImslCS.dll)

EmpiricalQuantiles Class

Thread Safety

Remarks

Requirements

See Also