R/variance_pre_mood_nm.R

In fabriziomaturo/AnnuityRIR: Annuity Random Interest Rates

variance_pre_mood_nm=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))


ex=1-un1
ey=u-1
vx=u2-2*un2+u2n1-u^2+2*un1*u-un1^2
vy=u2-u^2
covxy=u2-u^2-un2+un1*u

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

return(var_nm)

}