Course detail

Stochastic Modelling

FSI-S2M Acad. year: 2024/2025 Winter semester

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

Czech

Number of ECTS credits

3

Entry knowledge

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

Rules for evaluation and completion of the course

Graded course-unit credit requirements: active participation in seminars, mastering the subject matter, assignments elaboration; evaluation is based on the semester assignment results.
Attendance at seminars is controlled and the teacher decides on the compensation for absences.

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.
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.

The study programmes with the given course

Programme N-MAI-P: Mathematical Engineering, Master's, elective

Type of course unit

 

Exercise

26 hours, compulsory

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.