* R Functions for Probability Distributions p for probability, the cumulative distribution function (c*. d. f.) q for quantile, the inverse c. d. f. d for density, the density function (p. f. or p. d. f.) r for random, a random variable having the specified distribution The rnorm function generates n observations from the Normal distribution with mean \mu and standard deviation \sigma. The syntax of the rnorm function in R is the following: rnorm(n, # Number of observations to be generated mean = 0, # Integer or vector of means sd = 1) # Integer or vector of standard deviation 2 Answers2. Active Oldest Votes. 5. So this is your function right now (hopefully you know how to write an R function; if not, check writing your own function ): f <- function (x) (pi / 2) * (1 / (1 + 0.25 * x ^ 2)) f is defined on (-Inf, Inf) so integration on this range gives an indefinite integral and plogis(x)has consequently been called the 'inverse logit'. The distribution function is a rescaled hyperbolic tangent, plogis(x) == (1+ tanh(x/2))/2, and it is called a sigmoid functionin contexts such as neural networks In the first example of this tutorial, I'll explain how to draw a density plot of the F distribution. As a first step, we need to create some input data for the df R function: x_df <- seq (0, 20, by = 0.1) # Specify x-values for df function Now, we can apply the df command to this dat

The e.c.d.f. (empirical cumulative distribution function) Fn is a step function with jumps i/n at observation values, where i is the number of tied observations at that value. Missing values are ignored. For observations x= (x1,x2, xn), Fn is the fraction of observations less or equal to t, i.e. R allows to compute the empirical cumulative distribution function by ecdf() (Fig. 3): plot(ecdf(x.norm),main= Empirical cumulative distribution function) A Quantile-Quantile (Q-Q) plot 3 is a scatter plot comparing the fitted and empirical distributions in terms o Dotplots, traditionally drawn with graphpaper and pen, used to be a popular way to display distributions of small, heavily tied, sets of values. The R code below assigns some values to a variable (y), then plots a conventional dotplot, with duplicate values arranged evenly above and below

In statistical mechanics, the radial distribution function, (or pair correlation function) g ( r ) {\displaystyle g (r)} in a system of particles (atoms, molecules, colloids, etc.), describes how density varies as a function of distance from a reference particle Histogram and density plots. The qplot function is supposed make the same graphs as ggplot, but with a simpler syntax. However, in practice, it's often easier to just use ggplot because the options for qplot can be more confusing to use. ## Basic histogram from the vector rating. Each bin is .5 wide. ## These both result in the same output: ggplot (dat, aes (x = rating)) + geom_histogram. The gamlss package for R offers the ability to try many different distributions and select the best according to the GAIC (the generalized Akaike information criterion). The main function is fitDist. An important option in this function is the type of the distributions that are tried X has the properties of a distribution function. Its value at x can be computed in R using the command pexp(x,0.1) for =1/10 and drawn using > curve(pexp(x,0.1),0,80) 0 20 40 60 80 0.0 0.2 0.4 0.6 0.8 1.0 x pexp(x, 0.1) Figure 7.3: Cumulative distribution function for an exponential random variable with =1/10. Exercise7.19. Thetimeuntilthenextbusarrivesisanexponentialrandomvariablewith =1/10minutes. Aperso This video shows to compute a simple function in R to obtain probabilities associated with a random variable. The random variable is sum of uppermost surface... The random variable is sum of.

If give.Rkern is true, the number \(R(K)\), otherwise an object with class density whose underlying structure is a list containing the following components. x. the n coordinates of the points where the density is estimated. y. the estimated density values. These will be non-negative, but can be zero. bw. the bandwidth used. If the observations are assumed to come from a continuous distribution, the function demp calls the R function density to compute the estimated density based on the values specified in the argument obs, and then uses linear interpolation to estimate the density at the values specified in the argument x To get a full list of the distributions available in R you can use the following command: help (Distributions) For every distribution there are four commands. The commands for each distribution are prepended with a letter to indicate the functionality: d. returns the height of the probability density function. p

R Language Distribution Functions. Introduction. R has many built-in functions to work with probability distributions, with official docs starting at ?Distributions. Remarks. There are generally four prefixes: d-The density function for the given distribution; p-The cumulative. ** This is referred as normal distribution in statistics**.

The binomial distribution function can be plotted in R with the plot function, setting type = s and passing the output of the pbinom function for a specific number of experiments and a probability of success. The following block of code can be used to plot the binomial cumulative distribution functions for 80 trials and different probabilities where N represents the total number of atoms, V the model volume and where g (r) is the radial distribution function.. In this notation the volume of the shell of thickness dr is approximated V shell = Ļ(r + dr) 3 - Ļr 3 4Ļ r 2 dr. When more than one chemical species are present the so-called partial radial distribution functions g Ī±Ī² (r) may be computed Thus, for the normal distribution we have the R functions dnorm(), pnorm(), qnorm() and rnorm(). The Normal Distribution. The probably most important probability distribution considered here is the normal distribution. This is not least due to the special role of the standard normal distribution and the Central Limit Theorem which is to be treated shortly. Normal distributions are symmetric. * package*. This function provides two plots (see Figure1): the left-hand plot is by default the histogram on a density scale (or density plot of both, according to values of arguments histo and demp) and the right-hand plot the empirical cumulative distribution function (CDF). R>plotdist(groundbeef$serving, histo = TRUE, demp = TRUE) Histogram Data Density 0 50 100 150 200 0.000 0.004 0.008 0.012 0 50 100 150 200 0.0 0.2 0.4 0.6 0.8 1.0 Cumulative distribution Dat The different functions of the uniform distribution can be calculated in R for any value of x. These R functions are dnorm , for the density function, pnorm , for the cumulative distribution and qnorm , for the quantile function

The Student t distribution is one of the most commonly used distribution in statistics. This tutorial explains how to work with the Student t distribution in R using the functions dt(), qt(), pt(), and rt().. dt. The function dt returns the value of the probability density function (pdf) of the Student t distribution given a certain random variable x and degrees of freedom df For most of the classical distributions, base R provides probability distribution functions (p), density functions (d), quantile functions (q), and random number generation (r). Beyond this basic functionality, many CRAN packages provide additional useful distributions. In particular, multivariate distributions as well as copula Probability density function (PDF) We actually rarely need the probability density function (PDF) of a normally distributed score. As a reminder: the probability of individual values of a continuous random variable is 0, only intervals of values have a probability greater than 0 (corresponding to the area under the curve, the integral). Individual values have a probability density, which.

- These integrals are numerically evaluated using R's function integrate. S0 parameterization [pm=0]: based on the (M) representation of Zolotarev for an alpha stable distribution with skewness beta. Unlike the Zolotarev (M) parameterization, gamma and delta are straightforward scale and shift parameters. This representation is continuous in all 4 parameters, and gives an intuitive meaning to.
- Lately, I have found myself looking up the normal distribution functions in R. They can be difficult to keep straight, so this post will give a succinct overview and show you how they can be useful in your data analysis. To start, here is a table with all four normal distribution functions and their purpose, syntax, and an example
- For each distribution, there are four functions. The random sample function: when the function begins with r, it generates (pseudo)random samples from the specified distribution. We used this in the very first lab with rnorm(). The density function: when the function begins with d, i

- d for density - probability function / probability density function p for probability - cumulative distribution function q for quantile - quantile function (inverse cumulative distribution function) r for random - random number generato
- R has four in-built functions to generate binomial distribution. They are described below. dbinom(x, size, prob) pbinom(x, size, prob) qbinom(p, size, prob) rbinom(n, size, prob) Following is the description of the parameters used ā . x is a vector of numbers. p is a vector of probabilities. n is number of observations. size is the number of trials. prob is the probability of success of each.
- g - qt() Function. 10, Jun 20. Compute Randomly Drawn F Density in R Program
- We apply the quantile function qf of the F distribution against the decimal value 0.95. > qf(.95, df1=5, df2=2) [1] 19.296 Answer. The 95 th percentile of the F distribution with (5, 2) degrees of freedom is 19.296. ā¹ Student t Distribution up Interval Estimation āŗ Tags: Elementary Statistics with R; F distribution; probability distribution; df; Search this site: R Tutorial eBook. R.
- can be done using other R functions (Ricci2005). In this paper, we present the R pack-age tdistrplus (Delignette-Muller, Pouillot, Denis, and Dutang2014) implementing several methods for tting univariate parametric distribution. A rst objective in developing this package was to provide R users a set of functions dedicated to help this overall process. The fitdistr function estimates.
- Distribution functions in R. Every distribution has four associated functions whose prefix indicates the type of function and the suffix indicates the distribution. To exemplify the use of these functions, I will limit myself to the normal (Gaussian) distribution. The four normal distribution functions are: dnorm: density function of the normal distribution; pnorm: cumulative density function.
- Introduction to R Normal Distribution. In these articles, we will learn about R Normal Distribution. Normal Distribution is one of the fundamental concepts in Statistics. It is defined by the equation of probability density function. The probability density function is defined as the normal distribution with mean and standard deviation

Normal distribution functions using R Cumulative normal distribution function. R's pnorm function calculates what proportion of a normally-distributed... Inverse normal distribution function. R's qnorm function calculates which value in a normal population (y) has a given... Normal density function.. In RcmdrMisc: R Commander Miscellaneous Functions. Description Usage Arguments Value Author(s) Examples. View source: R/plots.R. Description. This function plots a probability density, mass, or distribution function, adapting the form of the plot as appropriate. Usag Representation of such entries requires a distribution function. This is where the concept of 'Cumulative Distribution Function' comes into play. The CDF of a random variable X is defined as, Let us assume that X is a discrete random variable with range R = {x1, x2, x3.} and the range R is bounded from below (i.e. x1). The below given figure shows the general form of the resulting CDF. DISTRIBUTION FUNCTIONS 9 1.4 Distribution Functions Deļ¬nition 1.8. The probability of the event (X ā¤ x) expressed as a function of x ā R: FX(x) = PX(X ā¤ x) is called the cumulative distribution function (cdf) of the rv X. Example 1.7. The cdf of the rv deļ¬ned in Example 1.5 can be written as FX(x) = 0, for x ā (āā,0); q, for x ā [0,1); q +p = 1, for x ā [1,ā). Properties.

Eric W. Weisstein: Probability Density Function. In: MathWorld (englisch). Einzelnachweise Diese Seite wurde zuletzt am 28. Februar 2021 um 16:43 Uhr bearbeitet.. Radial distribution functions (also called RDFs or g(r)) are a metric of local structure, making them ideal for characterizing amorphous materials that, by definition, lack long-range order and therefore produce no strong diffraction peaks. Calculating a radial distribution function is conceptually very simple. You first choose an atom around which the RDF will be calculated. For every value. The dnorm function will generate the density (or point) probability for a specific value for a normal distribution. This function is very useful for creating a plot of a density function of a distribution. In the list of the random number generator functions all the functions started with an r, similarly the density functions for all the distributions all start with a d. # point.

- Probability Distributions and their Mass/Density Functions. Mar 17, 2016: R, Statistics. A probability distribution is a way to represent the possible values and the respective probabilities of a random variable. There are two types of probability distributions: discrete and continuous probability distribution. As you might have guessed, a discrete probability distribution is used when we have.
- By convention the cumulative distribution functions begin with a \p in R, as in pbinom(). Let's try it out: > pbinom(3,size=10,prob=0.513) [1] 0.1513779 We can compare this with the probability of having exactly 3 boy births > dbinom(3,size=10,prob=0.513) [1] 0.1052534 Sometimes we want to know what the probability is of having more than x events of a certain kind, in which case we need to.
- Here is a graph of the Chi-Squared distribution 7 degrees of freedom. Problem. Find the 95 th percentile of the Chi-Squared distribution with 7 degrees of freedom. Solution. We apply the quantile function qchisq of the Chi-Squared distribution against the decimal values 0.95
- The reverse/inverse of the normal distribution function in R. Ask Question Asked 7 years, 6 months ago. Active 1 year, 3 months ago. Viewed 29k times 10. 4. To plot a normal distribution curve in R we can use: (x = seq(-4,4, length=100)) y = dnorm(x) plot(x, y) If dnorm.
- Here you'll visualize the cumulative distribution function (CDF) for the logistic distribution. That is, if you have a logistically distributed variable, x, and a possible value, xval, that x could take, then the CDF gives the probability that x is less than xval. The logistic distribution's CDF is calculated with the logistic function (hence the name). The plot of this has an S-shape, known.

** Here, we present an R package, RWiener, that provides the four functions R uses to represent a distribution, implemented for the Wiener diffusion model: the density function d (Navarro and Fuss, 2009) to compute the probability density function (PDF) at a given quantile for a given parameter set; the probability function p (Blurton et al**.,2012) to compute the cumulative distribution (CDF) at a. Normal distribution is important because of Central Limit TheoremTells us that sampling distribution of other non-normal distributions approaches a normal distribution as the sample size increases. It allows us to perform hypothesis testing on all sorts of data. Normal distribution with R. The following functions support Normal distribution in R

R Normal Distribution - In a random collection of data from independent sources, it is generally observed that the distribution of data is normal. Which means, on plotting a graph with the value of the variable in the horizontal axis and the count of the values in the vertical axis we get a bell shape curve. The center of the curve represents the mean of the data set Suppose that \(T\) has probability density function \(f(t) = r e^{-r t}\) for \(0 \le t \lt \infty\), where \(r \gt 0\) is a parameter. Find the distribution function and sketch the graph. Find the reliability function and sketch the graph. Find the failure rate function and sketch the graph. Find the quantile function and sketch the graph. Compute the five-number summary. Sketch the graph of. ** For a comprehensive list, see Statistical Distributions on the R wiki**. The functions available for each distribution follow this format: name: description: dname( ) density or probability function : pname( ) cumulative density function : qname( ) quantile function : Rname( ) random deviates : For example, pnorm(0) =0.5 (the area under the standard normal curve to the left of zero). qnorm(0.9.

The auxiliary function () is known as the cavity distribution function.: Table 4.1 It has been shown that for classical fluids at a fixed density and a fixed positive temperature, the effective pair potential that generates a given g ( r ) {\displaystyle g(r)} under equilibrium is unique up to an additive constant, if it exists The Distribution Function I We have seen that the dynamics of our discrete system of Npoint masses is given by 6Nequations of motion, which allow us to compute 6Nunknowns (~x;~v)as function of time t. The system is completely speciļ¬ed by 6Ninitial conditions (~x0;~v0) We can specify these initial conditions by deļ¬ning the distribution function

- 1. R dbinom() function. R provides us with dbinom() function that enables us to calculate the probability density values at every point for the data where we expect only two possible outcomes for the event. So, we tend to understand the binomial data in terms of the probability density values. Syntax
- Placing a prefix for the distribution function changes it's behavior in the following ways: dxxx(x,) returns the density or the value on the y-axis of a probability distribution for a discrete value of x pxxx(q,) returns the cumulative density function (CDF) or the area under the curve to the left of an x value on a probability distribution curve qxxx(p,) returns the quantile value, i.e. the.
- Introduction. Continuing my recent series on exploratory data analysis (EDA), and following up on the last post on the conceptual foundations of empirical cumulative distribution functions (CDFs), this post shows how to plot them in R. (Previous posts in this series on EDA include descriptive statistics, box plots, kernel density estimation, and violin plots.

** data: The values on which density function is built**. min: Specifies the minimum value to be set for the uniform density function. max: Depicts the maximum value for the uniform density function. Example dt gives the density, pt gives the **distribution** **function**, qt gives the quantile **function**, and rt generates random deviates. Invalid arguments will result in return value NaN, with a warning. Note. Setting ncp = 0 is not equivalent to omitting ncp. **R** uses the non-centrality functionality whenever ncp is specified which provides continuous behavior at ncp=0. Source. The central dt is computed.

The F Distribution Description. Density, distribution function, quantile function and random generation for the F distribution with df1 and df2 degrees of freedom (and optional non-centrality parameter ncp). Usage df(x, df1, df2, log = FALSE) pf(q, df1, df2, ncp=0, lower.tail = TRUE, log.p = FALSE) qf(p, df1, df2, lower.tail = TRUE, log.p = FALSE) rf(n, df1, df2 This R tutorial describes how to create an ECDF plot (or Empirical Cumulative Density Function) using R software and ggplot2 package. ECDF reports for any given number the percent of individuals that are below that threshold. The function stat_ecdf() can be used

- Take a look at R's qpois function, which calculates the inverse poisson distribution, a negative binomial distribution. This is the inverse of the operation performed by ppois. You provide the function with the specific percentile within the cumulative distribution function you want to be at or below and it will generate the expected value of events associated with that cumulative.
- R's runif function is part of R's collection of built in probability distributions. Other distributions include the binomial distribution, the standard distribution (standard normal), the exponential distribution, the beta distribution, and the Poisson distribution. This random function covers uniform random numbers
- The Chi-Square Distribution in R You may use this project freely under The dchisq() function gives the density, the pchisq()function gives the distribution function, the qchisq() function gives the quantile function, and the rchisq()function generates random deviates. We use the dchisq() to calculate the density for the integer values 4 to 8 of a Ļ 2-curve with d f = 7. dchisq(4: 8, df.
- Functions in R for Probability Distributions. R distribution handles four functions to generate random numbers. There is a root name. The root name for the normal distribution is the norm. This root is prefixed by one of the following letters. The p is for probability and it is a cumulative distribution function. For example, pnorm() function. The q is for quantile, and it is an.

** Negative binomial inverse distribution function**. R's qnbinom function does the opposite of its pnbinom function - that is it returns the relevent quantile (again a count). Negative binomial random function. R's rnbinom function gives 1 (or more) counts randomly selected from the specified negative binomial distribution(s). For example, rnbinom(5, s=3, m=2) would provide 5 counts randomly. Exponential distribution is the only continuous distribution which have the memoryless property. Reference. Refer Exponential Distribution Calculator to find the probability density and cumulative probabilities for Exponential distribution with parameter $\theta$ and examples. Exponential Distribution Calculato Functions in R is a routine in R that is purposefully designed and can be implemented as a set of statements that perform a particular task by taking certain parameters, which are also known as an argument passed by the user to obtain a requisite result. In which the user can use as needed based on the context, thus enabling the user to systematically implement the program by dividing it into. R Pubs by RStudio. Sign in Register Gamma Distribution in R; by Michael Foley; Last updated over 2 years ago; Hide Comments (-) Share Hide Toolbars Ć Post on: Twitter Facebook Google+ Or copy & paste this link into an email or IM:.

Dear R Users, Does R have an inverse empirical cumulative distribution function, something one can use to invert ecdf ? Thanks in advance, Tolga Generally, this communication is for informational purposes only and it is not intended as an offer or solicitation for the purchase or sale of any financial instrument or as an official confirmation of any transaction 3.2.1 Cumulative Distribution Function. The PMF is one way to describe the distribution of a discrete random variable. As we will see later on, PMF cannot be defined for continuous random variables. The cumulative distribution function (CDF) of a random variable is another method to describe the distribution of random variables. The advantage of the CDF is that it can be defined for any kind. The probability density function for gumbel_r is: \[f(x) = \exp(-(x + e^{-x}))\] The Gumbel distribution is sometimes referred to as a type I Fisher-Tippett distribution. It is also related to the extreme value distribution, log-Weibull and Gompertz distributions. The probability density above is defined in the standardized form. To shift and/or scale the distribution use the loc and. Simulations of distributions The central limit theorem is perhaps the most important concept in statistics. For any distribution with finite mean and standard deviation, samples taken from that population will tend towards a normal distribution around the mean of the population as sample size increases. Furthermore, as sample size increases, the variation of the sample means will decrease Probability Distributions and their Mass/Density Functions. Mar 17, 2016: R, Statistics. A probability distribution is a way to represent the possible values and the respective probabilities of a random variable. There are two types of probability distributions: discrete and continuous probability distribution. As you might have guessed, a discrete probability distribution is used when we have a discrete random variable. A continuous probability distribution is used when we have a.

Density, distribution function, quantile function and random generation for mixture of distributions Usage dmixtdistr(x, phi, arg, log = FALSE, lower.tail = TRUE, log.p = FALSE) pmixtdistr(q, phi, arg, lower.tail = TRUE, log.p = FALSE) qmixtdistr(p, interval = c(0, 1000), phi, arg, lower.tail = TRUE, log.p = FALSE) rmixtdistr(n, phi, arg 1.4. DISTRIBUTION FUNCTIONS 9 1.4 Distribution Functions Deļ¬nition 1.8. The probability of the event (X ā¤ x) expressed as a function of x ā R: FX(x) = PX(X ā¤ x) is called the cumulative distribution function (cdf) of the rv X. Example 1.7. The cdf of the rv deļ¬ned in Example 1.5 can be written as FX(x) = 0, for x ā (āā,0) Statistics textbooks teach us that a more useful way to define a distribution for numeric data is to define a function that reports the proportion of the data below \(a\) for all possible values of \(a\). This function is called the cumulative distribution function (CDF). In statistics, the following notation is used IntroductionChoice of distributions to ļ¬tFit of distributionsSimulation of uncertaintyConclusion Objective Build a package that provides functions to help the whole process of speciļ¬cation of a distribution from data choose among a family of distributions the best candidates to ļ¬t a sample estimate the distribution parameters and their uncertaint Method #1: Using the ecdf () and plot () functions. I know of 2 ways to plot the empirical CDF in R. The first way is to use the ecdf () function to generate the values of the empirical CDF and to use the plot () function to plot it. (The plot.ecdf () function combines these 2 steps and directly generates the plot.

A very good (in my opinion) manual with R functions is written by Paul Hewson. Georgios Pappas from the university of Nottingham helped me construct the contour plots of the von Mises-Fisher and the Kent distribution Now, there are, of course, other useful functions in base R. For example, you can use the t() function to transpose a matrix or dataframe in R. A Simple Example of How to use replicate() in R. In this replicate in R example, we are going to simulate values from a normal distribution. This is accomplished by using the rnorm() function. In the. Eine Wahrscheinlichkeitsdichtefunktion, oft kurz Dichtefunktion, Wahrscheinlichkeitsdichte, Verteilungsdichte oder nur Dichte genannt und mit WDF oder englisch pdf von probability density function abgekĆ¼rzt, ist eine spezielle reellwertige Funktion in der Stochastik, einem Teilgebiet der Mathematik. Dort dienen die Wahrscheinlichkeitsdichtefunktionen zur Konstruktion von Wahrscheinlichkeitsverteilungen mithilfe von Integralen sowie zur Untersuchung und Klassifikation von.

Probability distributions R supports a large number of distributions. Usually, four types of functions are provided for each distribution: d*: density function p*: cumulative distribution function, P(X x) q*: quantile function r*: draw random numbers from the distribution * represents the name of a distribution A random draw of values from a particular distribution. This used to be done with statistical tables printed in the back of textbooks. Now, R has functions for obtaining density, distribution, quantile and random values. The general naming structure of the relevant R functions is: dname calculates density (pdf) at input x For a simple liquid, the pair distribution function depends only on the separation, R = | R m-R n |, so it is simply written as g (R) called the radial distribution function [17]. g ( R ) has a peak at a mean inter-particle distance a and with the distance R increasing it converges oscillatingly to the average density Ļ The distribution function for acceptors differs also because of the different possible ways to occupy the acceptor level. The neutral acceptor contains two electrons with opposite spin, the ionized acceptor still contains one electron which can have either spin, while the doubly positive state is not allowed since this would require a different energy. This restriction would yield a factor of.

The function works for each of the distributions in Table1. This particular example is the JAGS implementation of 'rnorm(10000,10,2)' in R. It is presented as minimal demonstration; for a non-trivial application, seeLeBauer et al.(2013). r.distn <- data.frame(distn = norm, parama = 10, paramb = 2) bugs.distn <- r2bugs.distributions(r.distn R Documentation: The Multivariate Normal Distribution Description. These functions provide information about the multivariate normal distribution with mean equal to mean and covariance matrix sigma. dmvnorm gives the density and rmvnorm generates random deviates. Usage dmvnorm(x, mean, sigma, log=FALSE) rmvnorm(n, mean, sigma) Arguments. x: Vector or matrix of quantiles. If x is a matrix, each. The (cumulative) distribution function of X is the function F: R ā [0, 1] defined by F(x) = P(X ā¤ x), x ā R The distribution function is important because it makes sense for any type of random variable, regardless of whether the distribution is discrete, continuous, or even mixed, and because it completely determines the distribution of X The radial distribution function gives the probability density for an electron to be found anywhere on the surface of a sphere located a distance r from the proton. Since the area of a spherical surface is 4 Ļ r 2, the radial distribution function is given by 4 Ļ r 2 R (r) ā R (r). Radial distribution functions are shown in Figure 8.2. 4 4.7.3.1. Average radial distribution functionĀ¶. InterRDF is a tool to calculate average radial distribution functions between two groups of atoms. Suppose we have two AtomGroups A and B. A contains atom A1, A2, and B contains B1, B2.Given A and B to InterRDF, the output will be the average of RDFs between A1 and B1, A1 and B2, A2 and B1, A2 and B2.A typical application is to calculate the RDF. the shift function: a powerful tool to compare two entire distributions 25 Replies The R code for this post is available on github, and is based on Rand Wilcox's WRS R package, with extra visualisation functions written using ggplot2. The R code for the 2013 percentile bootstrap version of the shift function was also covered here and here