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### IMSL_TIE_STATS

IMSL_TIE_STATS

The IMSL_TIE_STATS function computes tie statistics for a sample of observations.

The IMSL_TIE_STATS function 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.

## Example

This example will compute tie statistics for a sample of length 7.

`fuzz	=	0.001`
`x	=	[1.0, 1.0001, 1.0002, 2.0, 3.0, 3.0, 4.0]`
`tstat	=	IMSL_TIE_STATS(x, FUZZ = fuzz) PRINT, tstat`
` `
`4.00000	2.50000	84.0000	6.00000`

## Syntax

Result = IMSL_TIE_STATS(X [, /DOUBLE] [, FUZZ=value])

## Return Value

One-dimensional 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.

## Arguments

### X

One-dimensional array containing the observations. X must be ordered monotonically increasing with all missing values removed.

## Keywords

### DOUBLE (optional)

If present and nonzero, double precision is used.

### FUZZ (optional)

Nonnegative constant 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. Default: 0.0

## Version History

 6.4 Introduced

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