Course detail
Stochastic Modelling
FSI-S2M-AAcad. year: 2023/2024
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
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
Attendance at seminars is controlled and the teacher decides on the compensation for absences.
Aims
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.
Study aids
Prerequisites and corequisites
Basic literature
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
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
Teacher / Lecturer
Syllabus
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.