# Binomial and Poisson Mixtures, Maximum Likelihood, and Maple Code

## Abstract

The bias, variance, and skewness of maximum likelihoood estimators are considered for binomial and Poisson mixture distributions. The moments considered are asymptotic, and they are assessed using the Maple code. Question of existence of solutions and Karl Pearson's study are mentioned, along with the problems of valid sample space. Large samples to reduce variances are not unusual; this also applies to the size of the asymptotic skewness.

- Authors:

- ORNL
- University of Georgia, Athens, GA

- Publication Date:

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

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

- OSTI Identifier:
- 1003505

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

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Far East Journal of Theoretical Statistics; Journal Volume: 20; Journal Issue: 1

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; MAXIMUM-LIKELIHOOD FIT; ASYMMETRY; DISTRIBUTION; PROBABILITY; STATISTICS

### Citation Formats

```
Bowman, Kimiko o, and Shenton, LR.
```*Binomial and Poisson Mixtures, Maximum Likelihood, and Maple Code*. United States: N. p., 2006.
Web.

```
Bowman, Kimiko o, & Shenton, LR.
```*Binomial and Poisson Mixtures, Maximum Likelihood, and Maple Code*. United States.

```
Bowman, Kimiko o, and Shenton, LR. Sun .
"Binomial and Poisson Mixtures, Maximum Likelihood, and Maple Code". United States.
doi:.
```

```
@article{osti_1003505,
```

title = {Binomial and Poisson Mixtures, Maximum Likelihood, and Maple Code},

author = {Bowman, Kimiko o and Shenton, LR},

abstractNote = {The bias, variance, and skewness of maximum likelihoood estimators are considered for binomial and Poisson mixture distributions. The moments considered are asymptotic, and they are assessed using the Maple code. Question of existence of solutions and Karl Pearson's study are mentioned, along with the problems of valid sample space. Large samples to reduce variances are not unusual; this also applies to the size of the asymptotic skewness.},

doi = {},

journal = {Far East Journal of Theoretical Statistics},

number = 1,

volume = 20,

place = {United States},

year = {Sun Jan 01 00:00:00 EST 2006},

month = {Sun Jan 01 00:00:00 EST 2006}

}

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