STAT 5124
Virginia Polytechnic Institute and State University
FINAL EXAM
Spring 2012
STATISTICS
Linear Model Theory
(Time allowed: 120 minutes)
NOTE:
1. The exam has 150 points (pts). Each part worths 10 pts.
2. Read the problems carefully.
3. When asked
STAT 5454
Virginia Polytechnic Institute and State University
FINAL EXAM
Fall 2010
STATISTICS
Survival Analysis
(Time allowed: 120 minutes)
NOTE:
1. The exam has 100 points (pts).
2. When asked to explain something, your explanations should be clear, but
STAT 5454 Reliability and Survival Analysis
Fall 2012
Homework 1 Solutions
1. [KM] Exercises
2.1
(a) Here = 0.001, the mean life time is 1/ = 1000.
(b) The cdf is F (t) = 1 exp(t). The median t0.5 can be solved from
0.5 = 1 exp(t0.5 ).
Thus, t0.5 = 693.1
STAT 5454 Reliability and Survival Analysis
Fall 2012
Homework 2 Solutions
1. [KM] Exercises 3.1, 3.2, 3.3, 3.4
3.1
(a) Here the censoring on the right. The censoring time is xed and is dierent for
dierent subjects. Thus it is generalized Type I right cen
STAT 5454 Reliability and Survival Analysis
Fall 2012
Homework 3 Solutions
1. Need to nd the standard error of logit[S(t0 )] rst. Because
dlogit(s)
1
=
ds
s(1 s)
by the delta method, the the standard error of log[S (t0 )] is
dlogit[S(t0 )]
dS (t0 )
V [S (
STAT 5454 Reliability and Survival Analysis
Fall 2012
Homework 4 Solutions
7.1 To do the test, we need to construct table similar to Table 7.1 of [KM, page 204].
sex age.entry age.event
HL
HT
[1,]
1
50
59 0.09268563 0.17080018 0.078114556
[2,]
1
60
66 0.1
STAT 5454 Reliability and Survival Analysis
Fall 2012
Homework 5 Solutions
1. You need to create a data frame yourself for this problem.
(a) The lognormal probability plot of the failure data is
Integrated Circuit Failure Time Data
with Nonparametric Simu
STAT 5454 Reliability and Survival Analysis
Fall 2012
Homework 6 Solutions
8.0 The partial likelihood function for the dataset is
L( ) =
1
e
11
e
4 + 4e
4 + 3e
2 + 2e
21
8.3 See Page 499 of [KM] for answers.
The R code is
> library(help=KMsurv)
> data(ton
STAT 5454
Virginia Polytechnic Institute and State University
MID-TERM EXAM
Fall, 2010
STATISTICS
Survival Analysis
(Time allowed: 75 minutes)
NOTE:
1. Try your best to answer all of the questions.
2. When asked to explain something, your explanations sho
STAT 5454
Virginia Polytechnic Institute and State University
MID-TERM EXAM
Fall, 2010
STATISTICS
Survival Analysis
(Time allowed: 75 minutes)
NOTE:
1. Try your best to answer all of the questions.
2. When asked to explain something, your explanations sho
STAT 5454: Reliability and Survival Analysis
Fall 2012
Yili Hong
KM Chapter 3: Censoring and Truncation
1/26
Introduction on Censoring
One special feature of time-to-event data is censoring
Censoring means some lifetimes are only known to have
occurred wi
STAT 5454: Reliability and Survival Analysis
Fall 2012
Yili Hong
ME Chapter 4: Location-Scale-Based Parametric
Distributions
1/32
Objectives
Explain importance of parametric models in the analysis of
reliability data.
Dene important functions of model par
STAT 5124, Spring 2013
HW5 Solutions
1. Note that
I
1
1
J = I PX A1 + PX J A2 .
n
n
A
That is A = A1 + A2 . We already know that A is idempotent. We have,
1
1
1
1
1
A1 A2 = (I PX )(PX J ) = PX PX PX J + PX ( J ) = PX PX J + J = 0.
n
n
n
n
n
1
1
Note that
STAT 5124
Virginia Polytechnic Institute and State University
MID-TERM EXAM I
Spring 2012
STATISTICS
Linear Model Theory
(Time allowed: 75 minutes)
NOTE:
1. The exam has 100 points (pts).
2. In addition, there are 20 bonus pts.
3. Show important steps to
STAT 5124
Virginia Polytechnic Institute and State University
MID-TERM EXAM II
Spring 2012
STATISTICS
Linear Model Theory
(Time allowed: 75 minutes)
NOTE:
1. The exam has 100 points (pts).
2. In addition, there are 20 bonus pts.
3. Read the problems caref
STAT 5454: Reliability and Survival Analysis
Fall 2012
Yili Hong
KM Chapter 2: Basic Quantities
1/16
Basic Quantities
Time to event is denoted by a positive random variable X
The cumulative distribution function (cdf)
F (x ) = Pr(X x ), gives the fraction
CONTINUED 2 ~ STAT 5454
(a) (5 pts) What is the appropriate time scale for this study?
Wt wgrmes 1n gram
(3% r )
(b) For four selecte units described below, what types of censoring and truncation [if any)
7 ,
that are represented? And why.
(i) (5 pts) Aun