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Exercise with R
These notes are a companion material to the course 'The R language and environment for statistical computing' held by the author at Università Cattolica del Sacro Cuore, Bachelor Degree in 'Economics and management'.
The aim of the course is to make participants able to implement statistical procedures in order to properly solve business and economic problems by means of the open source software R (R Core Team, 2019).
The reader is assumed to possess a basic understanding of statistics with regard to data analysis, probability and inference, at the level of the combined courses 'Statistica (Analisi dei dati e probabilità)'/Statistics and 'Statistica applicata'/'Applied statistics and big data' teached at Università Cattolica del Sacro Cuore.
Notes are organized as follows.
Sections from 1 to 3 consider the basics of R and deal with problems of descriptive statistics, according to the methodological presentation available e.g. in Boari, Cantaluppi (2018).
Section 4 considers the generation of pseudo-random numbers, introduces some simulation problems and gives the basics on how to work with parallel architectures.
Section 5 explains how to read/import data in R by also considering social network and open data sources.
Section 6 illustrates how to solve some basic mathematical problems. In particular, graphical representations of functions in one and two variables, optimization problems and solution to system of equations and system of inequalities are considered.
Section 7 proposes a short analysis of the survey on households wealth administered by the Bank of Italy (2014).
Section 8 describes how to solve some basic inferential problems (fitting distributions, testing population proportions, testing mean and variances in one and two sample instances, fitting linear and generalized linear (logit) models).
Finally, Appendix A gives a brief introduction to packages dplyr, ggplot2 and ggmap that are frequently used in data science applications.
Sections from 1 to 7 are accompanied by exercises. Verzani (2002), Wickman, Grolemund (2016) and Williams (2017) are useful references for further methods/exercises/problems.
Companion material to these notes (files, data sources and codes) can be requested to the author.
These notes were produced with R (version 3.5.3), knitr 1.22 and MiKTeX 2.9
« Degli amori. parte seconda. Gabriello Symeoni alle donne d'ingegno et più gentili salute » , P. 74 r°
Simeoni Gabriele. « Degli amori. parte seconda. Gabriello Symeoni alle donne d'ingegno et più gentili salute » , P. 74 r° . In: Seizième Siècle, N°7, 2011. pp. 67-83
Conchiglie, pesci e fossili. Il lungo cammino della natura per Oronzio Gabriele Costa.
Oronzio Gabriele Costa svolse un'imponente opera di ricerca scientifica e di insegnamento nella prima metà dell'Ottocento nel Regno di Napoli, delineando un'immagine della natura in continuo mutamento
Gabriele Rossetti, from a portrait by Dante Gabriel Rossetti, 1848
1 carte de visiteCarte de visite of oil painting by D. G. Rossetti (Surtees No. 442) of Gabriele Rossetti. On verso: note in unknown hand "Gabriele Rossetti in 1848.
Gabriele Rossetti, from a portrait by Dante Gabriel Rossetti, 1848
1 carte de visiteCarte de visite of oil painting by D. G. Rossetti (Surtees No. 442) of Gabriele Rossetti. On verso: note in unknown hand "Gabriele Rossetti in 1848.
Carte de visite of drawing of Gabriele Rossetti, c. 1822
1 carte de visiteCarte de visite of drawing of Gabriele Rossetti (father of Dante Gabriel Rossetti) by "C.E.L."(?), dated "1822"(?), "London." Fratelli Alinari, Firenze. On reverse: note in unknown hand "with Seymour Kirkup's best regards.
Carte de visite of drawing of Gabriele Rossetti, c. 1822
1 carte de visiteCarte de visite of drawing of Gabriele Rossetti (father of Dante Gabriel Rossetti) by "C.E.L."(?), dated "1822"(?), "London." Fratelli Alinari, Firenze. On reverse: note in unknown hand "with Seymour Kirkup's best regards.
Pisa crocevia di uomini, lingue e culture. L'età medievale. Atti del Convegno (Pisa, 25-27 ottobre 2007), éd. L. Battaglia Ricci et R. Cella, Rome, Aracne, 2009
Giannini Gabriele. Pisa crocevia di uomini, lingue e culture. L'età medievale. Atti del Convegno (Pisa, 25-27 ottobre 2007), éd. L. Battaglia Ricci et R. Cella, Rome, Aracne, 2009. In: Romania, tome 129 n°515-516, 2011. pp. 512-515
Pisa crocevia di uomini, lingue e culture. L'età medievale. Atti del Convegno (Pisa, 25-27 ottobre 2007), éd. L. Battaglia Ricci et R. Cella, Rome, Aracne, 2009
Giannini Gabriele. Pisa crocevia di uomini, lingue e culture. L'età medievale. Atti del Convegno (Pisa, 25-27 ottobre 2007), éd. L. Battaglia Ricci et R. Cella, Rome, Aracne, 2009. In: Romania, tome 129 n°515-516, 2011. pp. 512-515
A consistent use of the Gurson-Tvergaard-Needleman damage model for the R-curve calculation
The scope of the present work is to point out a consistent simulation procedure for the quasi-static fracture processes, starting from the micro-structural characteristics of the material. To this aim, a local nine-parameters Gurson-Tvergaard-Needleman (GTN) damage law has been used. The damage parameters depend on the micro-structural characteristics and must be calculated, measured or opportunely tuned. This can be done, as proposed by the author, by using an opportunely tuned GTN model for the representative volume element simulations, in order to enrich the original damage model by considering also the defect size distribution. Once determined all the material parameters, an MT fracture test has been simulated by a FE code, to calculate the R-curve in an aeronautical Al-based alloy. The simulation procedure produced results in a very good agreement with the experimental data
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