NAG CL Interface
g07gbc (outlier_​peirce_​2var)

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1 Purpose

g07gbc returns a flag indicating whether a single data point is an outlier as defined by Peirce's criterion.

2 Specification

#include <nag.h>
Nag_Boolean  g07gbc (Integer n, double e, double var1, double var2, double *x, double *lx, double *ux, NagError *fail)
The function may be called by the names: g07gbc, nag_univar_outlier_peirce_2var or nag_outlier_peirce_two_var.

3 Description

g07gbc tests a potential outlying value using Peirce's criterion. Let
Peirce's method flags e~ as a potential outlier if |e~|x, where x=σ2z and z is obtained from the solution of
R = λ 1-n (n-1) n-1 nn (1)
R = 2 exp(( z2 - 1 2 )(1-Φ(z))) (2)
and Φ is the cumulative distribution function for the standard Normal distribution.
Unlike g07gac, both σ2 and σ~2 must be supplied and, therefore, no assumptions are made about the nature of the relationship between these two quantities. Only a single potential outlier is tested for at a time.
This function uses an algorithm described in e04abc to refine a lower, l, and upper, u, limit for x. This refinement stops when |e~|<l or |e~|>u.

4 References

Gould B A (1855) On Peirce's criterion for the rejection of doubtful observations, with tables for facilitating its application The Astronomical Journal 45
Peirce B (1852) Criterion for the rejection of doubtful observations The Astronomical Journal 45

5 Arguments

1: n Integer Input
On entry: n, the number of observations.
Constraint: n3.
2: e double Input
On entry: e~, the value being tested.
3: var1 double Input
On entry: σ2, the residual variance on fitting model M to y.
Constraint: var1>0.0.
4: var2 double Input
On entry: σ~2, the residual variance on fitting model M to y~.
  • var2>0.0;
  • var2<var1.
5: x double * Output
On exit: an estimated value of x, the cutoff that indicates an outlier.
6: lx double * Output
On exit: l, the lower limit for x.
7: ux double * Output
On exit: u, the upper limit for x.
8: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument value had an illegal value.
On entry, n=value.
Constraint: n3.
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
On entry, var1=value.
Constraint: var1>0.0.
On entry, var2=value.
Constraint: var2>0.0.
On entry, var1=value, var2=value.
Constraint: var2<var1.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
g07gbc is not threaded in any implementation.

9 Further Comments


10 Example

This example reads in a series of values and variances and checks whether each is a potential outlier.
The dataset used is from Peirce's original paper and consists of fifteen observations on the vertical semidiameter of Venus. Each subsequent line in the dataset, after the first, is the result of dropping the observation with the highest absolute value from the previous data and recalculating the variance.

10.1 Program Text

Program Text (g07gbce.c)

10.2 Program Data

Program Data (g07gbce.d)

10.3 Program Results

Program Results (g07gbce.r)