In ddarmon/confdist: confdist, a package for creating confidence functions

var.conf <- function (x, plot = TRUE) {

  n <- length(x)
  s.sq <- sd(x)^2



    var.dist.func <- function(var) 1-pchisq(((n-1)*s.sq)/var, df = (n-1))

    var.dens.func <- function(var) (((n-1)*s.sq)/(var^2))*dchisq(((n-1)*s.sq)/var, df = (n-1))

    var.conf.curv.func <- function(var) abs(2*(1-pchisq(((n-1)*s.sq)/var, df = (n-1)))-1)

    var.quantile.func <- function(p) ((n-1)*s.sq)/qchisq(1-p, df = n-1)



    x.list <- list(pconf = var.dist.func, dconf = var.dens.func, cconf = var.conf.curv.func, qconf = var.quantile.func)

    if (plot){
      crit.left <- ((n-1)*s.sq)/qchisq(0.9995, df = n-1)
      crit.right <- ((n-1)*s.sq)/qchisq(0.0005, df = n-1)
      exp.dist <- curve(var.dist.func, from = crit.left, to = crit.right)
      exp.dens <- curve(var.dens.func, from = crit.left, to = crit.right)
      exp.cc <- curve(var.conf.curv.func, from = crit.left, to = crit.right)
      }

}

gauss.rand.samp.1 <- rnorm(n=100)

var.conf(gauss.rand.samp.1)

gauss.rand.samp.2 <- rnorm(n=1000, mean = 10, sd = 3)

var.conf(gauss.rand.samp.2)

sd(weightchange$weightchange[weightchange$diet=="Low Carb"])^2
var.conf(weightchange$weightchange[weightchange$diet=="Low Carb"])

sd(weightchange$weightchange[weightchange$diet=="Low Fat"])^2
var.conf(weightchange$weightchange[weightchange$diet=="Low Fat"])

n <- 100
s.sq = 1

integrate(var.dens.func, lower = -Inf, upper = 1.000000001)

    var.dist.func <- function(var) 1-pchisq(((n-1)*s.sq)/var, df = (n-1))

    var.dens.func <- function(var) (((n-1)*s.sq)/(var^2))*dchisq(((n-1)*s.sq)/var, df = (n-1))

    area.var.dens <- function(u) integrate(var.dens.func, lower = -Inf, upper = u)

var.dist.func(1)
area.var.dens(1.0000000001)

var.quantile.func <- function(p) ((n-1)*s.sq)/qchisq(1-p, df = n-1)


var.quantile.func(.95)
var.dist.func(1.284941)

x <- c(1,2,3,4,5)
s.sq <- 2
n <-5


var.conf.curv.func <- function(var) abs(2*(1-pchisq(((n-1)*s.sq)/var, df = (n-1)))-1)

curve(var.conf.curv.func, from = 0, to = 5)