Problem 4 Dipanjoy Saha

[shreyam202236]

---

title: "Problem 4" author: "Dipanjoy Saha" date: "2022-11-17" output: html_document

knitr::opts_chunk$set(echo = TRUE)

knitr::opts_chunk$set(echo = TRUE)
knitr::opts_chunk$set(fig.align = 'center')
knitr::opts_chunk$set(fig = TRUE)
knitr::opts_chunk$set(warning = FALSE)
knitr::opts_chunk$set(tidy.opts = list(width.cutoff = 60), tidy = TRUE)

library(tidyverse)

Problem 4

gaussian <- function(vec)
{
  b0 <- vec[1]
  b1 <- vec[2]
  sigma <- vec[3]
  loglike <- 0
  for (i in 1:n row(Insurance))
  {
    loglike <- loglike + dnorm(Insurance$Claims[i],mean=avg, sd=sigma, log=TRUE)
    avg <- b0 + b1*Insurance$Holders[i] 
  }
  return(-1*loglike)
}
bic <- function(mle, parameters, data)
{
  N <- length(data)
  return((length(parameters))log(N)-2(mle$value))
}
gauss.est <- optim(c(0,1/5,1), gaussian)
gauss.bic <- bic(gauss.est, gauss.est$par, Insurance)
cat("The Gaussian BIC is:", gauss.bic)

loglap <- function(x, mu, b)
{
  deno <- 2*b
  num <- exp(-abs(x-mu)/b)
  laplace <- num/deno
  return(log(laplace))
}
laplacian <- function(vec)
{
  b0 <- vec[1]
  b1 <- vec[2]
  sigma <- vec[3]
  loglike <- 0
  for (i in 1:nrow(Insurance))
  {
    avg <- b0 + b1*Insurance$Holders[i]
    loglike <- loglike + loglap(Insurance$Claims[i],mu=avg, b=sigma)
  }
  return(-1*loglike)
}
laplac.est <- optim(c(0, 0, 1), laplacian)
laplace.bic <- bic(laplac.est, laplac.est$par, Insurance)
cat("The Laplacian BIC is:", laplac.bic)

lognorm <- function(vec)
{
  b0 <- vec[1]
  b1 <- vec[2]
  sigma <- vec[3]
  loglike <- 0
  for (i in 1:nrow(Insurance))
  {
    if (Insurance$Claims[i] > 0)
    {
      avg <- b0 + b1*Insurance$Holders[i]
      loglike <- loglike + dlnorm(Insurance$Claims[i], meanlog=avg, sdlog=sigma, log=TRUE)
    }
  }
  return(-1*loglike)
}
lognorm.est <- optim(c(0, 0, 1), lognormal)
lognorm.bic <- bic(lognorm.est, lognorm.est$par, Insurance)
cat("The Lognormal BIC is:", lognorm.bic)

gamma.mod <- function(vec)
{
  b0 <- vec[1]
  b1 <- vec[2]
  sigma <- vec[3]
  loglike <- 0
  for (i in 1:nrow(Insurance))
  {
    if (Insurance$Claims[i] > 0)
    {
      avg <- b0 + b1*Insurance$Holders[i]
      loglike <- loglike + dgamma(Insurance$Claims[i], shape=avg, scale=sigma, log=TRUE)
    }
  }
  return(-1*loglike)
}
gamma.est <- optim(c(0,1/5,1), gamma.mod)
gamma.bic <- bic(gamma.est, gamma.est$par, Insurance)
cat("The Gamma BIC is:", gamma.bic)

[sourish-cmi]

Checked but there were no review by other ream member