Bootstrap for Gaussian Distribution , R

Bootstrap for Gaussian Distribution

set.seed(5610)
x <- rnorm(300,10,15)

bootstrap <- function(B,data){
    sam  = B
    dat  = data
    n = length(data)
    mean.vector = c()
    
    for( i in 1:sam){
    a = sample(dat,n,replace = T)
    mean.vector[i] = mean(a)
    }
    
    m.est   = mean(mean.vector) # Mean estimate of samples 
    var.est = var(mean.vector)  # Variance estimate of samples 
    
    
    # Histogram 
    hist(mean.vector,col = 'gray50',freq = F,border = 'white', ylim = c(0,1),
    xlab = "Sample Mean",main = "Histogram of Sample Mean", cex.main = 0.8, breaks = 45)
    
    # Density estimate 
    curve(dnorm(x,m.est,var.est), add  = TRUE, lwd = 2, col = "red3")
    
    # maximum is (sigma*sqrt(2*pi))^(-1); use sigma_est = var.est 
    
    max = (var.est*sqrt(2*pi))^(-1) 
    points(m.est, max, col = "red3", pch = 19)
    
    # Line of mean estimate 
    segments(m.est,0,m.est,max,col = 'blue',lty = 2, lwd = 2, pch = 19)
    
    cat("\n The mean estimate is: ", mean(mean.vector))
    cat("\n The variance estimate is: ", var(mean.vector))
    cat("\n Standard error: ", sqrt(var(mean.vector)))
    
}

mean(x)
bootstrap(100000,x)


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