Table of Contents
Fitting Distributions
and Computing Probabilities - Objectives
Probability distributions
(review)
Probability distributions
(review)
Why do we need to
know this?
Approaches to fitting
probability distributions
Process of fitting
distributions
Transformations
(review)
Particular distributions
Approach to discussion
particular distributions
Normal (Gaussian)
distribution
Normal (Gaussian)
distribution (continued)
Log Normal (2 and
3 parameter) distribution
Log Normal distribution
(continued)
Log Normal distribution
(continued)
Exponential distribution
Exponential distribution
(continued)
Gamma distribution
Gamma distribution
(continued)
Log Pearson Type
III distribution
Log Pearson Type
III distribution (continued)
Gumbel (Extreme
value type I) distribution
Gumbel (Extreme
value type I) distribution (continued)
Weibull (Extreme
value type III) distribution
Sampling distributions
Parameter estimation
methods
Method of Moments
Maximum likelihood
method
Graphical methods
Probability plots
Probability plots
(cont.)
Creating probability
plots
Estimating the probability,
P
Determining the
frequency factor, K(P)
Example: Probability
plot
Review of Hypothesis
testing
Goodness of fit
methods
Chi squared test
Probability Plot
correlation test
Anderson-Darling
test
Calculating probabilities
Special topics
Estimating parameters
and probabilities of censored data
Method detection
limit (MDL)
USEPA definition
USEPA method
Pooled sample variance
Variance ratio test
Estimating parameters
for data below the MDL
Better estimators
for censored data
Winsorized mean
and variance
Confidence interval
for the mean
Maximum Likelihood
Estimator
Parameter estimation
using a probability plot
Monte Carlo Simulation
Generation of random
numbers
Frequency analysis
Frequency factor
approach |