Title:

Statistics, Stochastic Procesess, Operational Analysis

Code:DMA1 (FEKT DMA1)
Ac.Year:2017/2018
Term:Winter
Curriculums:
ProgrammeBranchYearDuty
CSE-PHD-4DVI4-Elective
Language:Czech
Completion:examination (verbal)
Type of
instruction:
Hour/semLecturesSem. ExercisesLab. exercisesComp. exercisesOther
Hours:390000
 ExaminationTestsExercisesLaboratoriesOther
Points:1000000
Guarantee:Baštinec Jaromír, doc. RNDr., CSc., DMAT
Lecturer:Baštinec Jaromír, doc. RNDr., CSc., DMAT
Faculty:Faculty of Electrical Engineering and Communication BUT
Department:Department of Mathematics FEEC BUT
 
Learning objectives:
  The objective of the course is to expand knowledge in the area of statistical tests and data sample processing, Markov chain and time series, including applications in economy.
Description:
  Basic statistical tests, i.e. t-test, F-test, chi-quadrant test. Regression analysis. Goodness of fit test. Nonparametric tests. Mathematical methods in economics - linear programming, the transport problem. Dynamic programming, inventory models. Markov chain and time series.
Learning outcomes and competences:
  The graduate of this course should be able to solve the optimizing and statistical problems of technical and economical practice.
Syllabus of lectures:
 
  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-quadrant 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 especially stochastic problems.
  11. Time series
  12. Note on floating averages and hidden periods
Fundamental 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.