Content: Cover
Title Page
Copyright Page
Dedication
Acknowledgments
Preface
Table of Contents
1: RANDOM PROCESSES
STOCHASTIC PROCESSES IN THE ENVIRONMENT
STRUCTURE OF BOOK
2: THEORY OF PROBABILITY
PROBABILITY CONCEPTS
PROBABILITY LAWS
CONDITIONAL PROBABILITY AND BAYES' THEOREM
Bayes' Theorem
SUMMARY
PROBLEMS
3: PROBABILITY MODELS
DISCRETE PROBABILITY MODELS
Geometric Distribution
CONTINUOUS RANDOM VARIABLES
Uniform Distribution
Computer Simulation
Exponential Distribution
MOMENTS, EXPECTED VALUE, AND CENTRAL TENDENCY
VARIANCE, KURTOSIS, AND SKEWNESS
ANALYSIS OF OBSERVED DATA Computing Statistics from DataHistograms and Frequency Plots
Fitting Probability Models to Environmental Data
Tail Exponential Method
SUMMARY
PROBLEMS
4: BERNOULLI PROCESSES
CONDITIONS FOR BERNOULLI PROCESS
DEVELOPMENT OF MODEL
Example: Number of Persons Engaged in Cigarette Smoking
Development of Model by Inductive Reasoning
BINOMIAL DISTRIBUTION
APPLICATIONS TO ENVIRONMENTAL PROBLEMS
Probability Distribution for the Number of Exceedances
Robustness of Statistical Assumptions
COMPUTATION OF B(n, p)
PROBLEMS
5: POISSON PROCESSES
CONDITIONS FOR POISSON PROCESS APPLICATIONS TO ENVIRONMENTAL PHENOMENAAir Quality
Indoor Air Quality
Water Quality
Concentrations in Soils, Plants, and Animals
Concentrations in Foods and Human Tissue
Ore Deposits
SUMMARY AND CONCLUSIONS
PROBLEMS
9: LOGNORMAL PROCESSES
CONDITIONS FOR LOGNORMAL PROCESS
DEVELOPMENT OF MODEL
LOGNORMAL PROBABILITY MODEL
Parameters of the Lognormal Distribution
Plotting the Lognormal Distribution
ESTIMATING PARAMETERS OF THE LOGNORMAL DISTRIBUTION FROM DATA
Visual Estimation
Method of Moments
Method of Quantiles
Maximum Likelihood Estimation (MLE)