Module Catalogues, Xi'an Jiaotong-Liverpool University

Module Code: MTH313
Module Title: Loss Distribution
Module Level: Level 3
Module Credits: 5.00
Semester: SEM1
Originating Department: Mathematical Sciences
Pre-requisites: MTH206 MTH223

 Aims This module provides solid probabilistic and statistical tools to estimate parameters for a variety of actuarial models. Students are also required to understand the hypothesis tests and goodness of fit. Students gain the ability to design models according to different type of data.
 Learning outcomes A. Apply mathematical, statistical and probabilistic skills to solve actuarial models.B. Perform the estimation for complete and modified dataC. Estimate parameters: point estimation, moment estimation, maximum likelihood estimationD. Select models based on hypothesis testsE. Apply estimation and model selection to more complex modelsF. Analyze different actuarial models
 Method of teaching and learning This module is delivered through formal lectures and tutorial classes
 Syllabus 1. Point estimation, interval estimation, the empirical distribution for complete, individual and grouped data, estimation for modified data. 2. Maximum likelihood estimation (MLE) for loss frequency distributions ; Poisson, negative binomial , binomial and the (a,b,0), and (a,b,1).3. MLE based on complete individual and grouped data, MLE for truncated or censored data. 4. Variance and interval estimation 5. Meaning of loss function. Fundamental concepts of Bayesian statistics; Bayesian estimation calculation, 6. Model testing: chi-square goodness of fit test, the likelihood ration test, Kolmogorov-Smirnov test and Anderson-Darling test. 7. Extreme value models, copula models, applications to different actuarial data.
Delivery Hours
 Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total Hours/Semester 39 13 98 150

## Assessment

 Sequence Method % of Final Mark 1 Assignments 15.00 2 Midterm Exam 15.00 3 Final Exam 70.00
 Module Catalogue generated from SITS CUT-OFF: 12/10/2019 12:13:43 AM