Stat 567:Statistical Reliability
Third Class (September 8, 1997)
Other Life Distributions and
Their Properties
Class Objectives:
Learn about the engineering ideas that lead to life distributions
Learn the properties of these life distributions
Learn about the different types of censoring and their statistical
properties
Homework Assignments:
Send me e-mail on what you found to be the less clear points of my
lectures so far.
Show that if T is a random variable with Weibull survivor function
Then X=logT has a Gumbel survivor function
where
Class Outline and Main Points:
Gamma distribution
Other life distributions
Guaranty parameters
Mixture models
Models derived from multiple modes of failure
Generalized Gamma distribution
Generalized Extreme Value distribution
hazard-based models
Competing risks
Censoring
Right, left, and interval censoring
Type I and Type II
Review method-of-moments estimators
Study Questions:
How is the Generalized Gamma distribution useful in model selection?
What is the relationship between the exponential and gamma distributions?
Think of one example where this relationship can be applied.
Suppose you have a light socket with five identical spare light bulbs
each with an exponential distribution. What would be the distribution of
the illumination time?
Suppose you have exponential data with no censoring. Why should the
ratio of the sample mean and standard deviation be close to one?
