#This function calculates the (K-1)-fold integral of the function 
#f_thetaj(x) = (K/(thetaj)^K)*(thetaj-x)_{+}^{K-1}.

J.Func <- function(theta,thetaj,K){
   Out <- NULL	
    if(theta <= thetaj){
	 Out <- (factorial(K-1)/factorial(2*K-1))*(-1)^{K-1} * sum(choose(2*K-1,0:(K-1))*(-1)^{0:(K-1)}*thetaj^{2*K-1-(0:(K-1))}*theta^{0:(K-1)})+ (-1)^{K}*(factorial(K-1)/factorial(2*K-1))*(thetaj-theta)^{2*K-1}
	 }
	 else
	 Out <- (factorial(K-1)/factorial(2*K-1))*(-1)^{K-1} * sum(choose(2*K-1,0:(K-1))*(-1)^{0:(K-1)}*theta^{2*K-1-(0:(K-1))}*thetaj^{0:(K-1)})+(-1)^{K}*(factorial(K-1)/factorial(2*K-1))*(theta - thetaj)^{2*K-1}

	 Out <- (K/thetaj^{K})*Out 
	 Out	
		
	
	
	
}