R/triangular_moments_dis_U.R

In fabriziomaturo/AnnuityRIR: Annuity Random Interest Rates

triangular_moments_dis_U=function(data,order){



  r=order

  # trovo la moda

  Mode <- function(x, na.rm = FALSE) {
    if (na.rm) {
      x = x[!is.na(x)]
    }
    ux <- unique(x)
    return(ux[which.max(tabulate(match(x, ux)))])
  }



  # fit della vc triangolare

  fCvM <-
    fitdistrplus::fitdist(
      data,
      "triang",
      method = "mge",
      start = list(
        min = min(data),
        mode = Mode(data),
        max = max(data)
      ),
      gof = "CvM"
    )


  # parametri della triangolare di U
  param=c(fCvM$estimate[1], fCvM$estimate[3], fCvM$estimate[2])

  a=1+param[1]/100
  b=1+param[3]/100
  c=1+param[2]/100

    a=as.numeric(a)
    b=as.numeric(b)
    c=as.numeric(c)


#split the triangular distribution into 2 pieces

    f1=function(u){u^(-r)*2*(u-a)/((b-a)*(c-a))}
    f2=function(u){u^(-r)*2*(b-u)/((b-a)*(b-c))}


#compute 2 approssimate integrals for each part

# from lower point to the mode c

    i1=integrate(f1,a,c)

    # from the mode c to the highest value

    i2=integrate(f2,c,b)

    # the moment is the sum of the integrals

    mom=i1$value+i2$value

    return(mom)
  }