# Estimating population sizes in a mixture of two radioactive populations

## Abstract

The event times are observed of a mixture of two kinds of radioactive atoms, each producing alpha particles. The probability of observing an event is p, 0 < p < 1, and of missing the observation is 1 - p. A maximum likelihood statistical method is given for estimating the size of the two populations. A second discussion assumes that the populations themselves are samples from parent populations. Bayesian methods are given for estimating parameters of the parent populations. An example is presented of an experiment involving the search for particle-bound polyneutron systems. 2 figures, 3 tables.

- Authors:

- Publication Date:

- Research Org.:
- Los Alamos Scientific Lab., N.Mex. (USA)

- OSTI Identifier:
- 5085924

- Report Number(s):
- LA-7197

TRN: 78-010373

- DOE Contract Number:
- W-7405-ENG-36

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; DAUGHTER PRODUCTS; POPULATION DYNAMICS; POLYNEUTRONS; RADIATION DETECTION; RADIOISOTOPES; ALPHA DECAY; BISMUTH 212; MAXIMUM-LIKELIHOOD FIT; POPULATIONS; SIZE; ALPHA DECAY RADIOISOTOPES; BARYONS; BETA DECAY RADIOISOTOPES; BETA-MINUS DECAY RADIOISOTOPES; BISMUTH ISOTOPES; DECAY; ELEMENTARY PARTICLES; FERMIONS; HADRONS; HEAVY NUCLEI; HOURS LIVING RADIOISOTOPES; ISOTOPES; NEUTRONS; NUCLEI; NUCLEONS; NUMERICAL SOLUTION; ODD-ODD NUCLEI; PARTICLE DECAY; 651912* - Nuclear Properties & Reactions, A=190-219, Theoretical- Radioactive Decay- (-1987); 645103 - High Energy Physics- Particle Interactions & Properties-Experimental- Strong Interactions & Baryon & Meson Properties

### Citation Formats

```
Beyer, W.A., and Qualls, C.
```*Estimating population sizes in a mixture of two radioactive populations*. United States: N. p., 1978.
Web. doi:10.2172/5085924.

```
Beyer, W.A., & Qualls, C.
```*Estimating population sizes in a mixture of two radioactive populations*. United States. doi:10.2172/5085924.

```
Beyer, W.A., and Qualls, C. Sat .
"Estimating population sizes in a mixture of two radioactive populations". United States.
doi:10.2172/5085924. https://www.osti.gov/servlets/purl/5085924.
```

```
@article{osti_5085924,
```

title = {Estimating population sizes in a mixture of two radioactive populations},

author = {Beyer, W.A. and Qualls, C.},

abstractNote = {The event times are observed of a mixture of two kinds of radioactive atoms, each producing alpha particles. The probability of observing an event is p, 0 < p < 1, and of missing the observation is 1 - p. A maximum likelihood statistical method is given for estimating the size of the two populations. A second discussion assumes that the populations themselves are samples from parent populations. Bayesian methods are given for estimating parameters of the parent populations. An example is presented of an experiment involving the search for particle-bound polyneutron systems. 2 figures, 3 tables.},

doi = {10.2172/5085924},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Sat Apr 01 00:00:00 EST 1978},

month = {Sat Apr 01 00:00:00 EST 1978}

}

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