Estimation of expected value for lognormal and gamma distributions. [Environmental pollutants]

Conference · Sun Jan 01 04:00:00 EST 1978

OSTI ID:6936261

White, G C

Concentrations of environmental pollutants tend to follow positively skewed frequency distributions. Two such density functions are the gamma and lognormal. Minimum variance unbiased estimators of the expected value for both densities are available. The small sample statistical properties of each of these estimators were compared for its own distribution, as well as the other distribution to check the robustness of the estimator. Results indicated that the arithmetic mean provides an unbiased estimator when the underlying density function of the sample is either lognormal or gamma, and that the achieved coverage of the confidence interval is greater than 75 percent for coefficients of variation less than two. Further Monte Carlo simulations were conducted to study the robustness of the above estimators by simulating a lognormal or gamma distribution with the expected value of a particular observation selected from a uniform distribution before the lognormal or gamma observation is generated. Again, the arithmetic mean provides an unbiased estimate of expected value, and the achieved coverage of the confidence interval is greater than 75 percent for coefficients of variation less than two.

• Research Organization: Los Alamos Scientific Lab., N.Mex. (USA)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 6936261
• Report Number(s): LA-UR-78-959; CONF-780212-3
• Country of Publication: United States
• Language: English

Related Subjects

500200* -- Environment
Atmospheric-- Chemicals Monitoring & Transport-- (-1989)
54 ENVIRONMENTAL SCIENCES
AIR POLLUTION
CHEMICAL EFFLUENTS
DATA ANALYSIS
DISTRIBUTION FUNCTIONS
ENVIRONMENT
ENVIRONMENTAL TRANSPORT
MASS TRANSFER
MECHANICS
MONTE CARLO METHOD
POLLUTION
PROBABILITY
SAMPLING
STATISTICAL MECHANICS
VARIATIONS