COURSE UNIT TITLE

: ORDERED RANDOM VARIABLES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
STA 5108 ORDERED RANDOM VARIABLES ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASISTANT PROFESSOR TUĞBA YILDIZ

Offered to

Statistics
STATISTICS

Course Objective

This course aimed introducing students to the basic theory of ordered random variables. A prime objective of this introduction to order statistics to make students to learn fundemantal elements and practices of order statistics, to form distributions of order statistics and to obtain probability distributions for both discrete and continuous ordered statistical data sets. Also, students will learn how to use order statistics in estimation procedures, confidence-tolerance intervals and goodness-of-fit test. In addition, students will learn mathematical properties of progressive type II censored order statistics.

Learning Outcomes of the Course Unit

1   Obtaining probability distribution for order statistics
2   To gain an understanding of the dependence structure of order statistics
3   Classifying order statistics data according to different properties
4   Understanding how to use order statistics in estimation, hypothesis testing and goodness-of-fit tests
5   Understanding the theory behind distribution free confidence and tolerance intervals
6   Demonstrate the ability to solve problems related to order statistics
7   Understanding mathematical properties of progressive type II censored order statistics

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Review of Probability
2 Review of Statistics
3 Distributions of Order Statistics
4 Joint Distribution of Two Order Statistics, Conditional Distributions of Order Statistics
5 Some Properties of Order Statistics, Distribution of the Median and Range
6 Order Statistics from Bernoulli, Binomial, Poisson, Exponential, Uniform, Logistic and Normal Distribution
7 Types of Order Statistics Data, Order Statistics and Sufficiency
8 Maximum Likelihood Estimation, Linear Estimation of Location and Scale Parameters
9 Prediction of Order Statistics, Distribution Free Confidence and Tolerance Intervals
10 Progressive Type II Censored Order Statistics, Censoring Distributions
11 Mathematical Properties of Progressive Type II Censored Order Statistics
12 Simulational Algorithms

Recomended or Required Reading

1. B. C. Arnold, N. Balakrishnan, H. N. Nagaraja, A First Course in Order Statistics, Wiley, 1992.
2. M. Ahsanullah and V. B. Nevzorov, Order Statistics: Examples and Exercises, Nova Science, NewYork, 2005.
3. N. Balakrishnan, R. Aggarwala, Progressive Censoring, Birkhauser, Boston, 2000.

Supplementary Book(s):
H. A. David, H. N. Nagaraja, Order Statistics, Wiley, 2003

Planned Learning Activities and Teaching Methods

Lecture, homework assignments, presentation

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 ASG ASSIGNMENT
3 PRS PRESENTATION
4 FIN FINAL EXAM
5 FCG FINAL COURSE GRADE MTE* 0.30 + ASG * 0.20 + PRS * 0.10 + FIN * 0.40
6 RST RESIT
7 FCGR FINAL COURSE GRADE (RESIT) MTE* 0.30 + ASG * 0.20 + PRS * 0.10 + RST * 0.40

Further Notes About Assessment Methods

None

Assessment Criteria

Evaluation of homework assignments, presentation, class participation and examinations.

Language of Instruction

English

Course Policies and Rules

Attendance to at least 70% for the lectures is an essential requirement of this course and is the responsibility of the student. It is necessary that attendance to the lecture and homework delivery must be on time. Any unethical behavior that occurs either in presentations or in exams will be dealt with as outlined in school policy. You can find the undergraduate policy at http://web.deu.edu.tr/fen

Contact Details for the Lecturer(s)

Assist. Prof. Dr. Tuğba YILDIZ
DEU, Faculty of Sciences, Department of Statistics
e-mail: tugba.ozkal@deu.edu.tr
Tel: 0232 301 85 96

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparations before/after weekly lectures 14 1 14
Preparation for midterm exam 1 24 24
Preparation for final exam 1 36 36
Preparing assignments 2 12 24
Preparing presentations 2 18 36
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 180

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10
LO.1455
LO.2455
LO.3455
LO.4455
LO.5455
LO.6455
LO.7455