Statistics

There are no prerequisites.

central limit theorem
introduction to statistics
sample statistics and estimators
confidence intervals
testing statistical hypotheses
linear regression
goodness of fit tests
nonparametric tests

1. M. Hladnik: Verjetnost in statistika , Založba FE in FRI, Ljubljana, 2002, ISBN: 961-6209-34-5, 140 str.
2. R. Jamnik: Matematična statistika,, DZS, Ljubljana, 1980, 408 str.
3. R. Jamnik: Verjetnostni račun in statistika, DMFA Slovenije, Ljubljana, 1986, 156 str.
4. G. Grimmett, D. Stirzaker: Probability and random processes, 3rd ed., Oxford : Oxford University Press, 2001, 2009, 541 str.

Introduction to applications of probability theory in statistics.

Understanding of theoretical concepts in various applications. The ability to recognize statistical concepts in other sciences (physics, economics, finance, actuarial science, medicine, biology, industrial statistics).

Lectures, exercises, homeworks.

written examination
theoretical test or oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Roman Drnovšek:
– DRNOVŠEK, Roman. Triangularizing semigroups of positive operators on an atomic normed Riesz space. Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 2000, let. 43, št. 1, str. 43-55 [COBISS-SI-ID 9480281]
– DRNOVŠEK, Roman. Common invariant subspaces for collections of operators. Integral equations and operator theory, ISSN 0378-620X, 2001, vol. 39, no. 3, str. 253-266 [COBISS-SI-ID 10597721]
– DRNOVŠEK, Roman. An infinite-dimensional generalization of Zenger's lemma. Journal of mathematical analysis and applications, ISSN 0022-247X. [Print ed.], 2012, vol. 388, iss. 2, str. 1233-1238 [COBISS-SI-ID 16214617]
Mihael Perman:
– PERMAN, Mihael, SENEGAČNIK, Andrej, TUMA, Matija. Semi-Markov models with an application to power-plant reliability analysis. IEEE transactions on reliability, ISSN 0018-9529, 1997, vol. 46, no. 4, str. 526-532 [COBISS-SI-ID 2567707]
– PERMAN, Mihael, WELLNER, Jon A. On the distribution of Brownian areas. Annals of applied probability, ISSN 1050-5164, 1996, let. 6, št. 4, str. 1091-1111 [COBISS-SI-ID 7101017]
– PERMAN, Mihael, PITMAN, Jim, YOR, Marc. Size-biased sampling of Poisson processes and excursions. Probability theory and related fields, ISSN 0178-8051, 1992, 92, no. 1, str. 21-39 [COBISS-SI-ID 12236377]
Martin Raič:
– CHEN, Louis Hsiao Yun, RAIČ, Martin, THÀNH, Lê Vǎn. On the error bound in the normal approximation for Jack measures. Bernoulli. Feb. 2021, vol. 27, no. 1, str. 442-468. ISSN 1350-7265. [COBISS-SI-ID 38707203]
– RAIČ, Martin. A multivariate Berry-Esseen theorem with explicit constants. Bernoulli. 2019, vol. 25, no. 4a, str. 2824-2853. ISSN 1350-7265. [COBISS-SI-ID 18772825]
– EICHELSBACHER, Peter, RAIČ, Martin, SCHREIBER, Tomasz. Moderate deviations for stabilizing functionals in geometric probability. Annales de l'I.H.P. Probabilités et statistiques. 2015, vol. 51, no. 1, str. 89-128. ISSN 0246-0203. [COBISS-SI-ID 17294681]
Jaka Smrekar:
– SMREKAR, Jaka. Gottlieb’s theorem for a periodic equivalence. Journal of fixed point theory and its applications. Dec. 2022, vol. 24, iss. 4, art. 73 (15 str.). ISSN 1661-7738. [COBISS-SI-ID 125772547]
– KIRALY, Peter, SMREKAR, Jaka, JAKI MEKJAVIĆ, Polona. Morphological parameters predicting subthreshold micropulse laser effectiveness in central serous chorioretinopathy. Lasers in medical science. 2022, vol. 37, may, str. 3129-3136. ISSN 0268-8921. [COBISS-SI-ID 112104963]
– BEŠIĆ, Nikola, SMREKAR, Jaka, STRAŽIŠAR, Branka. Acute pain and side effects after tramadol in breast cancer patients : results of a prospective double-blind randomized study. Scientific reports. 2020, vol. 10, no. 1, str. 1-8. ISSN 2045-2322. [COBISS-SI-ID 35176195]