# Binomial test statistics using Psi functions

## Abstract

For the negative binomial model (probability generating function (p + 1 - pt){sup -k}) a logarithmic derivative is the Psi function difference {psi}(k + x) - {psi}(k); this and its derivatives lead to a test statistic to decide on the validity of a specified model. The test statistic uses a data base so there exists a comparison available between theory and application. Note that the test function is not dominated by outliers. Applications to (i) Fisher's tick data, (ii) accidents data, (iii) Weldon's dice data are included.

- Authors:

- ORNL

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- Work for Others (WFO)

- OSTI Identifier:
- 932030

- DOE Contract Number:
- DE-AC05-00OR22725

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Far East Journal of Theoretical Statistics; Journal Volume: 23; Journal Issue: 1

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; PROBABILITY; STATISTICS; MATHEMATICAL MODELS; CALCULATION METHODS; USES

### Citation Formats

```
Bowman, Kimiko o.
```*Binomial test statistics using Psi functions*. United States: N. p., 2007.
Web.

```
Bowman, Kimiko o.
```*Binomial test statistics using Psi functions*. United States.

```
Bowman, Kimiko o. Mon .
"Binomial test statistics using Psi functions". United States.
doi:.
```

```
@article{osti_932030,
```

title = {Binomial test statistics using Psi functions},

author = {Bowman, Kimiko o},

abstractNote = {For the negative binomial model (probability generating function (p + 1 - pt){sup -k}) a logarithmic derivative is the Psi function difference {psi}(k + x) - {psi}(k); this and its derivatives lead to a test statistic to decide on the validity of a specified model. The test statistic uses a data base so there exists a comparison available between theory and application. Note that the test function is not dominated by outliers. Applications to (i) Fisher's tick data, (ii) accidents data, (iii) Weldon's dice data are included.},

doi = {},

journal = {Far East Journal of Theoretical Statistics},

number = 1,

volume = 23,

place = {United States},

year = {Mon Jan 01 00:00:00 EST 2007},

month = {Mon Jan 01 00:00:00 EST 2007}

}

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