R/variance_pre_mood_pm.R

In AnnuityRIR: Annuity Random Interest Rates

variance_pre_mood_pm=function(data,years=10){

  n=years
  U=1+data
  u=mean(U)

  u2=moment(U,
            central = FALSE,
            absolute = FALSE,
            order = 2)

  un=moment(U,
            central = FALSE,
            absolute = FALSE,
            order = n)

  u2n=moment(U,
             central = FALSE,
             absolute = FALSE,
             order = 2*n)

  un1=moment(U,
             central = FALSE,
             absolute = FALSE,
             order = (n-1))

  un2=moment(U,
             central = FALSE,
             absolute = FALSE,
             order = (n-2))

  u2n1=moment(U,
              central = FALSE,
              absolute = FALSE,
              order = 2*n-1)

  u2n2=moment(U,
              central = FALSE,
              absolute = FALSE,
              order = 2*n-2)

  ex=un-1
  ey=un-un1
  vx=u2n-un^2
  vy=u2n-2*u2n1+u2n2-(un-un1)^2
  covxy=u2n-un^2-u2n1+un*un1

  var_nm=((ex/ey)^2)*((vx/(ex)^2)+(vy/(ey)^2)-(2*covxy/(ex*ey)))

  return(var_nm)

}