Chapter 6: Nonparametric Statistics

tie_statistics

Compute tie statistics for a sample of observations.

Synopsis

#include <imsls.h>

float *imsls_f_tie_statistics (int n_oservations, float x[], ..., 0)

The type double function is imsls_d_tie_statistics.

Required Arguments

int n_observations   (Input)
Number of observations in x.

float x[]   (Input)
Array of length n_observations containing the observations.

     x must be ordered monotonically increasing with all missing values removed.

Return Value

Array of length 4 containing the tie statistics.

                          

where tj is the number of ties in the j-th group (rank) of ties, and τ is the number of tie groups in the sample.

Synopsis with Optional Arguments

#include <imsls.h>

float *imsls_f_tie_statistics (int n_oservations, float x[],
IMSLS_FUZZ, float fuzz,
IMSLS_RETURN_USER, float ties[],
0)

Optional Arguments

IMSLS_FUZZ, float fuzz, (Input)
Value used to determine ties.
Observations i and j are tied if the successive differences
x[k + 1] – x[k]
between observations i and j, inclusive, are all
less than fuzz. fuzz must be nonnegative.  Default:  fuzz = 0.0

IMSLS_RETURN_USERfloat ties[],  (Output)
If specified ties[] returns the tie statistics.  Storage for ties[]
is provided by the user.   See Return Value.

Description

Function imsls_f_tie_statistics computes tie statistics for a monotonically increasing sample of observations. “Tie statistics” are statistics that may be used to correct a continuous distribution theory nonparametric test for tied observations in the data. Observations i and j are tied if the successive differences X(k + 1) - X(k), inclusive, are all less than fuzz. Note that if each of the monotonically increasing observations is equal to its predecessor plus a constant, if that constant is less than fuzz, then all observations are contained in one tie group. For example, if
fuzz = 0.11, then the following observations are all in one tie group.

0.0, 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1.00

Example

We want to compute tie statistics for a sample of length 7.

#include <imsls.h>

#include <stdio.h>

int main()

{

   float *ties=NULL;

   int nobs = 7;

   float fuzz = .001;

   float x[] = {1.0, 1.0001, 1.0002, 2., 3., 3., 4.};

 

   ties = imsls_f_tie_statistics(nobs, x, 

      IMSLS_FUZZ, fuzz,

      0);

   imsls_f_write_matrix("TIES\n", 1, 4, ties,

      IMSLS_WRITE_FORMAT, "%5.2f",

      0);

}

Output

TIES

0       1       2       3

4.00    2.50   84.00    6.00


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