Parameter estimation for censored samples from delta-ized distributions with application to air quality monitoring data
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.
- Research Organization:
- Polytechnic Inst. of Brooklyn, NY (USA)
- OSTI ID:
- 5464893
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
Atmospheric-- Radioactive Materials Monitoring & Transport-- (-1989)
54 ENVIRONMENTAL SCIENCES
AIR POLLUTION
AIR POLLUTION MONITORING
AIR QUALITY
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 85
KRYPTON ISOTOPES
NATIONAL ORGANIZATIONS
NUCLEI
POLLUTION
PROBABILITY
RADIOECOLOGICAL CONCENTRATION
RADIOISOTOPES
SAMPLING
SAVANNAH RIVER PLANT
SIMULATION
SPATIAL DISTRIBUTION
US AEC
US DOE
US ERDA
US ORGANIZATIONS
YEARS LIVING RADIOISOTOPES