STAT2805
Chapter 1 Limited Fluctuation Credibility Theory
by K.C. Cheung
1.1 Introduction
1.1.1 Suppose that X is a random variable related to insurance coverage. For example, X may
represent the number of claims (i.e. frequency), or the amount of claim (
STAT2805/3908
Chapter 9 Model Selection
by K.C. Cheung
9.1 Kolmogorov-Smirnov Test
9.1.1 After obtaining the sample, we may want to test whether the observations are coming a
certain distribution F . In this case, we have
H0 : The data came from distribut
STAT2805/3908
Chapter 6 Estimation For Complete Data
by K.C. Cheung
6.1 Empirical Distribution For Complete, Individual Data
6.1.1 Suppose that a random sample x1 , x2 , . . . , xn is drawn from a certain population. The
empirical distribution is dened as
STAT2805/3908
Chapter 8 Parameter Estimation
by K.C. Cheung
8.1 Method of Moments
8.1.1 Suppose that F (x|) is a certain parametric distribution function with some unknown
parameters = (1 , . . . , p )T . Our objective is to estimate from n independent ob
say¥r2805/3908
Chapter 1 Limited Fluctuation Credibility Theory —
Worksheet
by KC. Cheung
Example 1: Suppose that X, which represents the size of an individual’s claim amount in
a given year, has as exponential distribution with mean 5. (Here, one year re
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT2805
CREDIBILITY THEORY AND LOSS DISTRIBUTIONS
December 17, 2004
Time: 2:30 p.m. - 5:30 p.m.
Candidates taking examinations that permit the use of calculators may use any calcu
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT2805
Credibility Theory and Loss Distributions
December 20, 2005
Time: 9:30 a.m. - 12:30 p.m.
Candidates taking examinations that permit the use of calculators may use any calc
.
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT2805
CREDIBILITY THEORY AND LOSS DISTRIBUTIONS
December 15, 2006
Time: 2:30 p.m. - 5:30 p.m.
Candidates taking examinations that permit the use of calculators may use any cal
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT2805
CREDIBILITY THEORY AND LOSS DISTRIBUTIONS
December 11, 2009
Time: 9:30 a.m. - 12:30 p.m.
Only approved calculators as announced by the Examinations Secretary can be used i
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT2805
CREDIBILITY THEORY AND LOSS DISTRIBUTIONS
December 19, 2008
Time: 9:30 a.m. - 12:30 p.m.
Candidates taking examinations that permit the use of calculators may use any calc
,)
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT2805
CREDIBILITY THEORY AND LOSS DISTRIBUTIONS
Time: 9:30 a.m. - 12:30 p.m.
December 13, 2010
Only approved calculators as announced by the Examinations Secretary can be use
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT2805
December
CREDIBILITY THEORY AND LOSS DISTRIBUTIONS
2007
Time: 2:30 p.m. - 5:30 p.m.
Candidates taking examinations that permit the use of clculators my use ny calculator
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT2805
CREDIBILITY THEORY AND LOSS DISTRIBUTIONS
December 20, 2012
Time: 9:30 a.m. - 12:30 p.m.
Only approved calculators as announced by the Examinations Secretary can be used
i
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT2805
CREDIBILITY THEORY AND LOSS DISTRIBUTIONS
December 12, 2011
Time: 9:30 a.m. - 12:30 p.m.
Only approved calculators as announced by the Examinations Secretary can be used
i
STAT2805/3908
Chapter 7 Estimation For Modied Data
by K.C. Cheung
7.1 Point Estimation
7.1.1 Truncation:
An observation is left truncated (aka truncated from below) at the level d when its value is
less than d and is not recorded.
An observation is right
STAT2805/3908
Chapter 5 Review of Mathematical Statistics
by K.C. Cheung
5.1 Quality of Point Estimation
5.1.1 Suppose that is some xed but unknown quantity (a parameter) we want to estimate.
We collect a random sample (i.i.d. sample) X1 , . . . , Xn from
STAT2805/3908
Chapter 2 Greatest Accuracy Credibility Theory
by K.C. Cheung
2.1 Introduction
2.1.1 According to the Greatest Accuracy Credibility Theory, the risk prole of an individual
is summarized by a parameter , which may be a scalar or a vector. Die
STAT2805
Chapter 2 Greatest Accuracy Credibility Theory
by K.C. Cheung
2.1 Introduction
2.1.1 According to the Greatest Accuracy Credibility Theory, the risk prole of an individual
is summarized by a parameter , which may be a scalar or a vector. Dierent
STAT 2805
Chapter 3 B hlmann-Straub Model
u
by K.C. Cheung
3.1 The Model
3.1.1 Bhlmann model is one of the simplest credibility models. It assumes that the conditional
u
distributions of Xi s given are independent, and that the hypothetical mean and the p
STAT 2805
Chapter 4 Empirical Bayes Parameter Estimation
by K.C. Cheung
4.1 Introduction
4.1.1 In Bhlmann or Bhlmann-Straub Model, we assume that the prior distribution () and
u
u
the conditional distribution fXi | in Bhlmann Model (or fXij | in Bhlmann-S
STAT 2805
Chapter 5 Review of Mathematical Statistics
by K.C. Cheung
5.1 Quality of Point Estimation
5.1.1 Suppose that is some xed but unknown quantity (a parameter) we want to estimate.
We collect a random sample (i.i.d. sample) X1 , . . . , Xn from som
STAT 2805
Chapter 6 Estimation For Complete Data
by K.C. Cheung
6.1 Empirical Distribution For Complete, Individual Data
6.1.1 Suppose that a random sample x1 , x2 , . . . , xn is drawn from a certain population. The
empirical distribution is dened as
Fn
STAT2805
Chapter 7 Estimation For Modied Data
by K.C. Cheung
7.1 Point Estimation
7.1.1 Truncation:
An observation is left truncated (aka truncated from below) at the level d when its value is
less than d and is not recorded.
An observation is right trunc
STAT2805
Chapter 8 Parameter Estimation
by K.C. Cheung
8.1 Method of Moments
8.1.1 Suppose that F (x| ) is a certain parametric distribution function with some unknown
parameters = (1 , . . . , p )T . Our objective is to estimate from n independent observ
STAT 2805
Chapter 9 Model Selection
by K.C. Cheung
9.1 Kolmogorov-Smirnov Test
9.1.1 After obtaining the sample, we may want to test whether the observations are coming a
certain distribution F . In this case, we have
H0 : The data came from distribution
The University of Hong Kong
Department of Statistics and Actuarial Science
STAT2805 Credibility Theory and Loss Distributions (2012-2013)
Lecturer:
Dr. Ka Chun CHEUNG, kccg@hku.hk, MW 522
Tutor:
Mr. Ambrose LO, amblo@hku.hk, MW518
Learning objectives and
STAT2805/3908
Chapter 1 Limited Fluctuation Credibility Theory Worksheet
by K.C. Cheung
Example 1: Suppose that X, which represents the size of an individuals claim amount in
a given year, has as exponential distribution with mean 5. (Here, one year repre
STAT2805/3908
Chapter 4 Empirical Bayes Parameter Estimation
by K.C. Cheung
4.1 Introduction
4.1.1 In Bhlmann or Bhlmann-Straub Model, we assume that the prior distribution () and
u
u
u
the conditional distribution fXi | in Bhlmann Model (or fXij | in Bhl
STAT2805/3908
Chapter 3 B hlmann-Straub Model
u
by K.C. Cheung
3.1 The Model
3.1.1 Bhlmann model is one of the simplest credibility models. It assumes that the conditional
u
distributions of Xi s given are independent, and that the hypothetical mean and t
STAT2805/3908
Chapter 1 Limited Fluctuation Credibility Theory
by K.C. Cheung
1.1 Introduction
1.1.1 Suppose that X is a random variable related to insurance coverage. For example, X may
represent the number of claims (i.e. frequency), or the amount of cl