Probability: With Applications and R

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This is very often the case, but there is a growing number of packages that are under-development or completed and are made available through other repositories. Sticking momentarily to the packages available in the CRAN repository, the use of the install. For example, if you want to install the package devtools you can simply write:.

Once a package is installed it is not directly usable within your R session. For example, after having installed the devtools package, in order to use it within your session you would write:. Once this is done, all the functions and documentation of this package are available and can be used within your current session.

However, once you close your R session, all loaded packages will be closed and you will have to load them again if you want to use them in a new R session. One of the main packages that is required for this class would be our STAT package, that contains all the necessary packages and functions that will be utilized in this book. Run the following code to install the package directly from GitHub. There are many more elements in RStudio, and we encourage you to use the RStudio Cheatsheet as a reference. The R environment provides an up-to-date and efficient programming language to develop different tools and applications.

Nevertheless, its main functionality lies in the core statistical framework and tools that consistute the basis of this language.

Indeed, this book aims at introducing and describing the methods and approaches of statistical programming which therefore require a basic knowledge of Probability and Statistics in order to grasp the logic and usefulness of the features presented in this book. For this reason, we will briefly take the reader through some of the basic functions that are available within R to obtain probabilities based on parametric distributions, compute summary statistics and understand basic data structures.

The latter is just an introduction and a more in-depth description of different data structures will be given in a future chapter. Since the R environment can serve as an advanced calculator, it is worth noting this also allows for simple calculations. In the table below we show a few examples of such calculations where the first column gives a mathematical expression calculation , the second gives the equivalent of this expression in R and finally in the third column we can find the result that is output from R.

Probability distributions can be uniquely characterized by different functions such as, for example, their density or distribution functions. Based on these it is possible to compute theoretical quantiles and also randomly sample observations from them. Replacing the R syntax for a given probability distribution with the general syntax name , all these functions and calculations are made available in R through the built-in functions:. Note that, when using these functions in practice, name is replaced with the syntax used in R to denote a specific probability distribution.

For example, if we wish to deal with a Uniform probability distribution, then the syntax name is replaced by unif and, furthering the example, to randomly generate observations from a uniform distribution the function to use will be therefore runif. R allows to make use of these functions for a wide variety of probability distributions that include, but are not limited to: Gaussian or Normal , Binomial, Chi-square, Exponential, F-distribution, Geometric, Poisson, Student-t and Uniform.

In order to get an idea of how these functions can be used, below is an example of a problem that can be solved using them. Assume that the test scores of a college entrance exam follows a Normal distribution. Furthermore, suppose that the mean test score is 70 and that the standard deviation is How would we find the percentage of students scoring 90 or more in this exam?

To find this probability we need the distribution function pname for which we therefore replace name with the R syntax for the Normal distribution: norm. The distribution function in R has various parameters to be specified in order to compute a probability which, at least for the Normal distribution, can be found by typing? Knowing these arguments, it is now possible to compute the probability we are interested in as follows:. While the previous functions deal with theoretical distributions, it is also necessary to deal with real data from which we would like to extract information.

The use of certain functions varies according to the nature of the inputs since these can be, for example, numerical or factors. A first step in analysing numerical inputs is given by computing summary statistics of the data which, in this section, we can generally denote as x we will discuss the structure of this data more in detail in the following chapters. For central tendency or spread statistics of a numerical input, we can use the following R built-in functions:.

If the data of interest is a factor with different categories or levels, then different summaries are more appropriate. For example, for a factor input we can extract counts and percentages to summarize the variable by using table. Using functions and data structures that will be described in the following chapters, below we create an example dataset with 90 observations of three different colors: 20 being Yellow , 10 being Green and 50 being Blue. We then apply the table function to it:. In many cases, when dealing with data we are actually dealing with datasets see Chapter 03 where variables of different nature are aligned together usually in columns.

For datasets there is another convenient way to get simple summary statistics which consists in applying the function summary to the dataset itself instead of simply a numerical input as seen earlier. As an example, let us explore the Iris flower dataset contained in the R built-in datasets package. The data set consists of 50 samples from each of three species of Iris Setosa, Virginica and Versicolor.

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Four features were measured from each sample consisting in the length and the width in centimeters of the both sepals and petals. This dataset is widely used as an example since it was used by Fisher to develop a linear discriminant model based on which he intended to distinguish the three species from each other using combinations of these four features. Using this dataset, let us use the summary function on it to output the minimum, first quartile and thrid quartile, median, mean and maximum statistics for the numerical variables in the dataset and frequency counts for factor inputs.

This is not the first or the last book that has been written explaining and describing statistical programming in R. Indeed, this can be seen as a book that brings together and reorganizes information and material from other sources structuring and tailoring it to a course in basic statistical programming. The main references which are far from being an exhaustive review of literature that can be used to have a more in-depth view of different aspects treated in this book are:.

Introduction to Probability with R - CRC Press Book

Wickham, Hadley. Advanced R. CRC Press. R Packages. Xie, Yihui.

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Dynamic Documents with R and Knitr. Statistical Programming Methods 1 Introduction 1. What is reproducible research? Defining the R Code in the backend of the Shiny app 7. This document is under development and it is therefore preferable to always access the text online to be sure you are using the most up-to-date version. Ask the seller a question. Collecting P. Barnum P. Collecting Children's Literature Children's books are among some of the most popular themes to build a book collection on.

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Probability: With Applications and R Probability: With Applications and R
Probability: With Applications and R Probability: With Applications and R
Probability: With Applications and R Probability: With Applications and R
Probability: With Applications and R Probability: With Applications and R
Probability: With Applications and R Probability: With Applications and R
Probability: With Applications and R Probability: With Applications and R
Probability: With Applications and R Probability: With Applications and R

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