Course detail

Stochastic Modelling

FSI-S2M-AAcad. year: 2022/2023

The following topics are dealt with: characteristic functions of random variables and vectors, functions of random vector and their statistical analyses, multiple normal distribution, fitting of probability distributions by means of classical statistical methods, kernel estimates and quasinorms.

Language of instruction

English

Number of ECTS credits

3

Mode of study

Not applicable.

Guarantor

Ing. Josef Bednář, Ph.D.

Department

Institute of Mathematics (ÚM)

Learning outcomes of the course unit

Students acquire needed knowledge from important parts of the probability theory and mathematical statistics, which will enable them to use PC model and optimize responsible characteristics and properties of technical systems and processes.

Prerequisites

Methods of mathematical analysis of real and complex functions, probability theory and mathematical statistics.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The course is taught through exercises which are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

Graded course-unit credit requirements: active participation in seminars, mastering the subject matter, assignments elaboration; evaluation is based on the semester assignment results.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The course objective is to make students familiar with selected parts from probability theory and mathematical statistics, which extend students` knowledge acquired in previous courses. In addition other methods for modelling technical processes on PC are introduced.

Specification of controlled education, way of implementation and compensation for absences

Attendance at seminars is controlled and the teacher decides on the compensation for absences.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Gallant, A. R.: Nonlinear Statistical Models. New York : John Wiley, 2003.
MONTGOMERY, Douglas C. a George C RUNGER. Applied statistics and probability for engineers. 5th ed. Hoboken: John Wiley, 2011, xv, 768 s. : il. ; 27 cm. ISBN 978-0-470-05304-1.
Pitman, E. J. G.: Some Basic Theory for Statistical Inference. New York :John Wiley & Sons, 1978.
Silverman, B.W.: Density Estimation for Statistics and Data Analysis. London : Chapman & Hall, 1999.

Recommended reading

Anděl, J.: Statistické metody. Praha : Matfyzpress, 1993.
Likeš, J. - Machek, J.: Matematická statistika. Praha : SNTL, 1983.
Potocký, R. a kol.: Zbierka úloh z pravdepodobnosti a matematickej štatistiky. Bratislava/Praha : Alfa/SNTL, 1986.

Classification of course in study plans

  • Programme N-MAI-A Master's 1 year of study, winter semester, elective

Type of course unit

 

Exercise

26 hod., compulsory

Teacher / Lecturer

Ing. Josef Bednář, Ph.D.

Syllabus

Characteristic function of random variable, properties.
Calculating characteristic function of random variables.
Moments of random variables by the help of characteristic function.
Characteristic function of random vector, properties.
Function of random variable and random vector, convolution.
Estimates for function of random variable and random vector.
Multiple normal probability distribution, properties.
Gram - Charlier models A and B.
Pearson curves, Edgeworth and Johnson model.
Kernel estimates of probability density.
Entropy of probability distribution.
Estimates of distribution by the help of minimum Shannon quasinorm.
Estimates of distribution by the help of minimum Hellinger quasinorm.