# Parameter estimation for censored samples from delta-ized distributions with application to air quality monitoring data

## Abstract

The concentration of a contaminant measured in a particular medium might be distributed as a positive random variable when it is present, but it may not always be present. Suppose that in the underlying population, the value zero occurs with probability delta, and that the conditional distribution given the value is nonzero, is that of a positive random variable. If there is a level below which the concentration cannot be distinguished from zero by the analytical apparatus, a sample from such a population will be censored on the left. The presence of both zeros and positive values in the censored portion of such samples complicates the problem of estimating the parameters of the underlying positive random variable and the probability of a zero observation. Using the method of maximum likelihood, it is shown that the solution to this estimation problem reduces largely to that of estimating the parameters of the distribution truncated at the point of censorship. The maximum likelihood estimate of the proportion of zero values follows directly. The derivation of the maximum likelihood estimates for a lognormal population with zeros is given in detail, and the asymptotic properties of the estimates are examined. Simulation studies were performed tomore »

- Authors:

- Publication Date:

- Research Org.:
- Polytechnic Inst. of Brooklyn, NY (USA)

- OSTI Identifier:
- 5464893

- Resource Type:
- Thesis/Dissertation

- Resource Relation:
- Other Information: Thesis (Ph. D.)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 54 ENVIRONMENTAL SCIENCES; KRYPTON 85; AIR POLLUTION MONITORING; RADIOECOLOGICAL CONCENTRATION; SAVANNAH RIVER PLANT; AIR QUALITY; AIR POLLUTION; PROBABILITY; SAMPLING; SIMULATION; SPATIAL DISTRIBUTION; BETA DECAY RADIOISOTOPES; BETA-MINUS DECAY RADIOISOTOPES; DISTRIBUTION; ECOLOGICAL CONCENTRATION; ENVIRONMENTAL QUALITY; EVEN-ODD NUCLEI; HOURS LIVING RADIOISOTOPES; INTERMEDIATE MASS NUCLEI; ISOMERIC TRANSITION ISOTOPES; ISOTOPES; KRYPTON ISOTOPES; NATIONAL ORGANIZATIONS; NUCLEI; POLLUTION; RADIOISOTOPES; US AEC; US DOE; US ERDA; US ORGANIZATIONS; YEARS LIVING RADIOISOTOPES; 500300* - Environment, Atmospheric- Radioactive Materials Monitoring & Transport- (-1989)

### Citation Formats

```
Gogolak, C V.
```*Parameter estimation for censored samples from delta-ized distributions with application to air quality monitoring data*. United States: N. p., 1986.
Web.

```
Gogolak, C V.
```*Parameter estimation for censored samples from delta-ized distributions with application to air quality monitoring data*. United States.

```
Gogolak, C V. Wed .
"Parameter estimation for censored samples from delta-ized distributions with application to air quality monitoring data". United States.
```

```
@article{osti_5464893,
```

title = {Parameter estimation for censored samples from delta-ized distributions with application to air quality monitoring data},

author = {Gogolak, C V},

abstractNote = {The concentration of a contaminant measured in a particular medium might be distributed as a positive random variable when it is present, but it may not always be present. Suppose that in the underlying population, the value zero occurs with probability delta, and that the conditional distribution given the value is nonzero, is that of a positive random variable. If there is a level below which the concentration cannot be distinguished from zero by the analytical apparatus, a sample from such a population will be censored on the left. The presence of both zeros and positive values in the censored portion of such samples complicates the problem of estimating the parameters of the underlying positive random variable and the probability of a zero observation. Using the method of maximum likelihood, it is shown that the solution to this estimation problem reduces largely to that of estimating the parameters of the distribution truncated at the point of censorship. The maximum likelihood estimate of the proportion of zero values follows directly. The derivation of the maximum likelihood estimates for a lognormal population with zeros is given in detail, and the asymptotic properties of the estimates are examined. Simulation studies were performed to study the small sample behavior of the estimates, and to compare them to previously suggested methods for handling such data. The estimation method was used to fit several different distributions to a set of severely censored /sup 85/Kr monitoring data from six locations at the Savannah River Plant chemical separations facilities. The results for lognormal, exponential, gamma, Weibull, and inverse Gaussian distributions with zeros are discussed and compared.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1986},

month = {1}

}