R/derivative_kernel_function.R

In kerdiest: Nonparametric kernel estimation of the distribution function. Bandwidth selection and estimation of related functions.

derivative_kernel_function <-
function(type_kernel,u)
# INPUTS:
#   "type_kernel" kernel function: "e" Epanechnikov,	"n" Normal, 
#                                  "b" Biweight, "t" Triweight         
#   "u" array or single value where the kernel is evaluated

{
	if(type_kernel == "e")	
	{
	  result <- u
        logic0 <- (u <= -1 | u >= 1)
    		logic1 <- (u > -1 & u < 1)
		    result[logic0] <- 0
	  Uval <- result[logic1]
    result[logic1] <- -1.5 * Uval
    return(result)
	}

	else 
		if(type_kernel == "n")	
		{
		result <- (1/(sqrt(2 * pi))) * exp(-(u^2)/2) * (-u)
		return(result)
		}

	else 
		if(type_kernel == "b")	
		{
		  result <- u
         	logic0 <- (u <= -1 | u >= 1)
    		  logic1 <- (u > -1 & u < 1)
		      result[logic0] <- 0
		  Uval <- result[logic1]
      result[logic1] <- -(15/4) * Uval * (1 - (Uval^2))
      return(result)
	  }
		 
	else 
		if(type_kernel == "t")	
		{
		  result <- u
         	logic0 <- (u <= -1 | u >= 1)
    		  logic1 <- (u > -1 & u < 1)
		      result[logic0] <- 0
		  Uval <- result[logic1]
      result[logic1] <- -(105/16) * Uval * ((1 - (Uval^2)))^2
      return(result)
	  }

}