pois_exp=function(n,nt,theta)
{
  x=matrix(rpois(n*nt,theta),n,nt)
  theta_est=apply(x,2,cumsum)/(1:n)
  theta_emp_var=apply(theta_est,1,var)
  theta_emp_bias=apply(theta_est,1, mean)-theta
  Theo_bias=rep(0,n)
  Theo_var=theta/(1:n)
  CRLB=theta/(1:n)
  emp_MSE=theta_emp_var+(theta_emp_bias)^2
  Theo_MSE= Theo_var+(Theo_bias)^2 
  par(mfrow=c(1,3))
  plot(1:n, theta_emp_bias,type='l',ylab='Bias',xlab='n')
  lines(1:n,Theo_bias, col='blue')
  legend("topright",
         legend = c('Emp','Theo'),lty=1,
         col = c('black','blue')) 
  plot(1:n, theta_emp_var,type='l',ylab='Variance',xlab='n')
  lines(1:n,Theo_var, col='blue')
  lines(1:n,CRLB[1:n], col='red')
  legend("topright",
         legend = c('Emp','Theo','CRLB'),lty=c(1,1,2),
         col = c('black','blue','red')) 
  plot(1:n,emp_MSE,type='l',ylab='MSE',xlab='n')
  lines(1:n,Theo_MSE, col='blue')
  legend("topright",
         legend = c('Emp','Theo'),lty=1,
         col = c('black','blue')) 
  par(mfrow=c(1,1))
  return(list(theta_est,theta_emp_bias,theta_emp_var,Theo_bias, Theo_var, CRLB , emp_MSE,Theo_MSE))
}

exp_exp=function(n,nt,theta)
{
  x=matrix(rexp(n*nt,theta),n,nt)
  theta_est=1/(apply(x,2,cumsum)/(1:n))
  theta_emp_var=apply(theta_est,1,var)
  theta_emp_bias=apply(theta_est,1, mean)-theta
  Theo_bias=theta/((1:n)-1)
  Theo_var=theta^2*(1:n)^2/(((1:n)-1)^2*((1:n)-2))
  CRLB=theta^2/(1:n)
  emp_MSE=theta_emp_var+(theta_emp_bias)^2
  Theo_MSE= Theo_var+(Theo_bias)^2 
  par(mfrow=c(1,3))
  plot(3:n, theta_emp_bias[3:n],type='l',ylab='Bias',xlab='n')
  lines(3:n,Theo_bias[3:n], col='blue')
  legend("topright",
         legend = c('Emp','Theo'),lty=1,
         col = c('black','blue')) 
  plot(3:n, theta_emp_var[3:n],type='l',ylab='Variance',xlab='n')
  lines(3:n,Theo_var[3:n], col='blue')
  lines(3:n,CRLB[3:n], col='red')
  legend("topright",
         legend = c('Emp','Theo','CRLB'),lty=c(1,1,2),
         col = c('black','blue','red')) 
  
  plot(3:n, emp_MSE[3:n],type='l',ylab='MSE',xlab='n')
  lines(3:n,Theo_MSE[3:n], col='blue')
  legend("topright",
         legend = c('Emp','Theo'),lty=1,
         col = c('black','blue')) 
  
  par(mfrow=c(1,1))
  return(list(theta_est,theta_emp_bias,theta_emp_var,Theo_bias, Theo_var, CRLB , emp_MSE,Theo_MSE))
  
}