数学中国w, madio,net The Most Expensive is Not the Best 163 for responsiveness leve el, R- Responsiveness x a for responsiveness inequality, RI= 100(1-Responsivenesslnequality ); for faimess in financing, FF- FaimessofFinancing Contribution x 100 The overall composite was, therefore, a number from 0 to 100 Dipartite Degree analysis As we know, a good metric should distinguish. But the WHOs method cant for example, its method gives 36 countries the same value in its metric of responsiveness, We evaluate the degree of distinction via DD=√m+…+n where N- iis the number of countries that can t be distinguished in crite rioni. The smaller DD, the better the degree of distinction. Monte Carlo Simulation To test the dipartite degree(degree of distinction)of every method, we use Monte Carlo simulation to make a small change to every data value since the value must contain some error. The process is as below. First, we use the beta distribution to determine the change in each value Because the beta distribution is restricted to the interval [0, 1], a linear func tion of a beta-distributed random variable can be used to scale the sampling interval appropriatel The beta distribution can be described by the probability density func (a+ Beta(a,B)()=r(r(s) 1(1-x)1,0<x<1; 0 el It has expected value E X]=a/(a+ B) Suppose that Tij, withl s i< 191 and 1 <3< 10, is the unknown true mean of the random variable X: representing the jth metric in country i. x=(xy-1)+2Beta(22)(X) which takes values in ry-1, Iy+l] and has expected value E[(xy-1)+2Beta(2,2)(x) 1+22/(2+2)=z Ne use Monte Carlo simulation to create 1, U numbers randomly in the interval([ze-1, ry+1] and calculate a 95% confidence interval for rs数学中国 www.madio.net