Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2015/2016
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Insegnamento 093575 - APPLIED STATISTICS
Docente Barchielli Alberto
Cfu 6.00 Tipo insegnamento Monodisciplinare

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento

Programma dettagliato e risultati di apprendimento attesi

This course aims at providing students with a set of probabilistic and statistical tools to perform: Estimation and Hypothesis Testing, Survival Data Analysis and Multiple Regression.  The statistical software "R" will be introduced as a tool for data analysis and to help solving some exercises. 


ELEMENTS OF PROBABILITY THEORY.  Random variables and random vectors: distribution functions,  joint and marginal probability density functions, moment generating function; moments and fractiles: mode, quantiles, median, expected value, variance, coefficient of variation, skewness, kurtosis and covariance.  Functions of random variables. Normal random vectors. Independent random variables, sum of independent random variables. Weak Law of Large Numbers, Central Limit Theorem. 

ESTIMATION AND HYPOTHESIS TESTING. Moments estimators, Maximum Likelihood Estimators; interval estimation. Tests of hypotheses: type I and type II errors, critical region, test statistics, size and level of significance of the test, power function, p-value. Inference for the differences between two means, between two proportions and for the ratio between two variances of normal populations. Analysis of variance (ANOVA).

MULTIPLE REGRESSION.  Least squared estimation, confidence interval and hypothesis testing concerning the regression coefficients, prediction of  a future response, coefficient of determination and adjusted R^2, analysis of residuals: assessing the model.

LIFETIME DISTRIBUTIONS and DATA ANALYSIS. Survival function, hazard function, cumulative hazard function, mean residual life function.  Parametric Lifetime Models: Exponential, Weibull, Gamma;  Log-normal, Inverse Gaussian, Pareto, Gompertz, exponential power (normal of order p) (short review). Right censoring: time -or Type I- censoring, order statistic -or Type II- censoring and random censoring: sequential and simultaneous  testing.  Weibull parameters estimation, Weibull quantiles estimation.    

NONPARAMETRIC STATISTICS. Empirical distribution functions, Kaplan-Meier estimator, Kolmogoorv-Smirnov Goodness of Fit Test, Lilliefors test for normal and exponential data.  Comparison of two survival functions (Log-Rank Tests).


The student is supposed to have already used univariate probability distributions and to have received preliminary notions of statistical inference (confidence intervals and hypothesis testing). These notions will be recalled and deepened in the lectures and can be found in the recommended texts.

Note Sulla Modalità di valutazione

Student preparation will be evaluated by a written examination and a data analysis project.

Risorsa bibliografica obbligatoriaLecture Notes by Dr. Ilenia Epifani http://beep.metid.polimi.it
Risorsa bibliografica obbligatoriaSheldon Ross, Introduction to probability and statistics for engineers and scientists, Editore: Elsevier Academic Press, Anno edizione: 2009, ISBN: 9780123704832
Risorsa bibliografica obbligatoriaPeter Dalgaard, Introductory Statistics with R, Editore: Springer, Anno edizione: 2008, ISBN: 978-0-387-79054-1
Risorsa bibliografica facoltativaDavid G. Kleinbaum, Mitchel Klein, Survival Analysis : A Self-Learning Text, Editore: Springer, Anno edizione: 2005, ISBN: 9780387291505

reperibile a http://risorseelettroniche.biblio.polimi.it

Risorsa bibliografica facoltativaMontgomery D. C., Runger G. C., Hubele N., Engineering Statistics, 5th Edition, Editore: John Wiley & Sons Inc, Anno edizione: 2010, ISBN: 978-0470631478

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Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua Inglese
schedaincarico v. 1.6.5 / 1.6.5
Area Servizi ICT