Positive random variables with a discrete probability mass at the origin: Parameter estimation for left-censored samples with application to air quality monitoring data

Technical Report · Sat Nov 01 04:00:00 EST 1986

OSTI ID:6078292

Gogolak, C V

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. 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. 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.

• Research Organization: USDOE Environmental Measurements Lab., New York
• OSTI ID: 6078292
• Report Number(s): EML-459; ON: DE87013826
• Country of Publication: United States
• Language: English

Related Subjects

500200 -- Environment
Atmospheric-- Chemicals Monitoring & Transport-- (-1989)
500300* -- Environment
Atmospheric-- Radioactive Materials Monitoring & Transport-- (-1989)
54 ENVIRONMENTAL SCIENCES
AIR POLLUTION
BETA DECAY RADIOISOTOPES
BETA-MINUS DECAY RADIOISOTOPES
DATA ANALYSIS
ECOLOGICAL CONCENTRATION
EVEN-ODD NUCLEI
HOURS LIVING RADIOISOTOPES
INTERMEDIATE MASS NUCLEI
ISOMERIC TRANSITION ISOTOPES
ISOTOPES
KRYPTON 85
KRYPTON ISOTOPES
MATHEMATICAL MODELS
NATIONAL ORGANIZATIONS
NUCLEI
POLLUTANTS
POLLUTION
RADIOECOLOGICAL CONCENTRATION
RADIOISOTOPES
SAVANNAH RIVER PLANT
US AEC
US DOE
US ERDA
US ORGANIZATIONS
YEARS LIVING RADIOISOTOPES