Buffon: Buffon

In ExpRep: Experiment Repetitions

Description

Simulations of the experiment of Buffon.

Usage

Buffon(p = 0.5, width = 0.2, r = c(100, 500, 1000, 1500))

Arguments

p	Probability of occurrence of some event.
width	Width of the band where the probabilities are represented.
r	Array of four values, representing the numbers of repetitions of the experiment that will be carried out.

Value

Four graphics, each one is the simulation of the experiment of Buffon for the number of repetitions contained in the array r.

Note

Department of Mathematics. University of Oriente. Cuba.

Author(s)

Larisa Zamora and Jorge Diaz

References

Gnedenko, B. V. (1978). The Theory of Probability. Mir Publishers. Moscow.

Examples

Buffon(p = 0.5, width = 0.2, r = c(100, 500, 1000, 1500))

## The function is currently defined as
function (p = 0.5, width = 0.2, r = c(100, 500, 1000, 1500)) 
{
    Position <- function(k, colum) {
        PE <- k%/%colum
        Resto <- k%%colum
        if (Resto == 0) {
            fila <- PE
            columna <- colum
        }
        else {
            fila <- PE + 1
            columna <- Resto
        }
        Position <- list(fila, columna)
        return(Position)
    }
    nf <- layout(matrix(c(1, 2, 3, 4), 2, 2, byrow = TRUE), TRUE)
    k <- 0
    la <- p - width
    lb <- p + width
    if (la < 0) 
        la <- 0
    if (lb > 1) 
        lb <- 1
    for (j in 1:4) {
        k <- k + 1
        Probcara <- array(0, dim = r[j])
        for (i in 1:r[j]) {
            binomial <- rbinom(i, 1, p)
            cara <- length(binomial[binomial == 1])
            Probcara[i] <- cara/i
        }
        P <- Position(k, 2)
        fila <- P[[1]]
        colum <- P[[2]]
        mfg <- c(fila, colum, 2, 2)
        a <- as.character(r[j])
        plot(Probcara, type = "p", main = paste0("n=", a), xlab = "Repetitions", 
            ylab = "Probability", font.main = 3, col = "blue", 
            ylim = c(la, lb))
        abline(h = p, col = "red", lty = 1, lwd = 2)
    }
  }

Example output

function (p = 0.5, width = 0.2, r = c(100, 500, 1000, 1500)) 
{
    Position <- function(k, colum) {
        PE <- k%/%colum
        Resto <- k%%colum
        if (Resto == 0) {
            fila <- PE
            columna <- colum
        }
        else {
            fila <- PE + 1
            columna <- Resto
        }
        Position <- list(fila, columna)
        return(Position)
    }
    nf <- layout(matrix(c(1, 2, 3, 4), 2, 2, byrow = TRUE), TRUE)
    k <- 0
    la <- p - width
    lb <- p + width
    if (la < 0) 
        la <- 0
    if (lb > 1) 
        lb <- 1
    for (j in 1:4) {
        k <- k + 1
        Probcara <- array(0, dim = r[j])
        for (i in 1:r[j]) {
            binomial <- rbinom(i, 1, p)
            cara <- length(binomial[binomial == 1])
            Probcara[i] <- cara/i
        }
        P <- Position(k, 2)
        fila <- P[[1]]
        colum <- P[[2]]
        mfg <- c(fila, colum, 2, 2)
        a <- as.character(r[j])
        plot(Probcara, type = "p", main = paste0("n=", a), xlab = "Repetitions", 
            ylab = "Probability", font.main = 3, col = "blue", 
            ylim = c(la, lb))
        abline(h = p, col = "red", lty = 1, lwd = 2)
    }
}

ExpRep documentation built on May 2, 2019, 2:12 p.m.