Course detail

Statistics, Stochastic Procesess, Operational Analysis

FIT-DMA1Acad. year: 2010/2011

Basic statistical tests, i.e. t-test, F-test, chi-kvadrat test. Regression analyssis. Goodnessw of fit test. Nonparametric tests. Mathematical methods in economics - linear programming, the transport problem. Dynamic programming, inventory models. Markov chain and time series.

Language of instruction

Czech

Number of ECTS credits

0

Mode of study

Not applicable.

Guarantor

doc. RNDr. Jaromír Baštinec, CSc.

Department

Department of Mathematics (UMAT)

Learning outcomes of the course unit

The graduate of this course should be able to solve the optimising and statistical problems of technical and economical practice.

Prerequisites

There are no prerequisites

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Study evaluation is based on marks obtained for specified items. Minimimum number of marks to pass is 50.

Course curriculum

  1. Basic concepts of probability theory
  2. Statistical samples
  3. Point and interval estimates
  4. Testing hypotheses of given parameters (not only normal distribution)
  5. Distribution tests (chi-quadrat test, Kolmogorov-Smirnov test, etc.)
  6. Operational analysis methods, linear and non-linear programming
  7. Dynamical programming, Bellman principle
  8. Markov chain, M/M/s systems
  9. Inventory models, especially random issues
  10. Replicate theory, deterministic and especcially stochastic problems.
  11. Time series
  12. Note on floating averages and hidden periods

Work placements

Not applicable.

Aims

The objecive of the course is to expand knowledge in the area of statistical tests and data sample processing, Markow chain and time series, including applications in economy.

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

There are no checked study.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

  • Zapletal, J.: Úvod do analýzy ekonomických časových řad. PC-DIR, VUT, Brno 2000.
  • Zapletal, J.: Základy počtu pravděpodobnosti a matematrické statistiky. PC-DIR,VUT, Brno, 1995
  • Anděl, J.: Statistické metody. Matfyzpress, MFF UK Praha, 1993.
  • Taha, H.A.: Operations research. An Introduction. Fourth Edition, Macmillan Publishing Company, New York 1989.
  • Miller, I., Miller, M.: John E. Freund's Mathematical Statistics. Sixth Edition. Prentice Hall, Inc., New Jersey 1999. Předchozí vydání publikováno pod názvem Freund, J.E.: Mathematical Statistics, Fifth Edition.
  • Montgomery, D.C., Runger, G.C.: Applied Statistics and Probability for Engineers. Third Edition. John Wiley & Sons, Inc., New York 2003.
  • Loftus, J., Loftus, E.: Essence of Statistics. Second Edition, A. A. Knopf, New York, 1988
  • Aramanovič, J. G., Lunc, G. L., Elsgolc, L. C., Funkcie komplexnej premennej, operátorový počet, teória stability, Alfa, SNTL, 1973.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme VTI-DR-4 Doctoral

    branch DVI4 , any year of study, winter semester, elective

  • Programme VTI-DR-4 Doctoral

    branch DVI4 , any year of study, winter semester, elective

Type of course unit

 

Lecture

39 hours, optionally

Teacher / Lecturer

doc. RNDr. Jaromír Baštinec, CSc.

Syllabus

  1. Basic concepts of probability theory
  2. Statistical samples
  3. Point and interval estimates
  4. Testing hypotheses of given parameters (not only normal distribution)
  5. Distribution tests (chi-quadrat test, Kolmogorov-Smirnov test, etc.)
  6. Operational analysis methods, linear and non-linear programming
  7. Dynamical programming, Bellman principle
  8. Markov chain, M/M/s systems
  9. Inventory models, especially random issues
  10. Replicate theory, deterministic and especcially stochastic problems.
  11. Time series
  12. Note on floating averages and hidden periods