用于查找MLE的R代码

Question

我想找到以下分布和desnity函数参数的最大似然估计（MLE）：

        F(x) = 1- exp{-(ax)^b-(cx)^d}
        f(x) = (a^b x^{b-1}-c^d x^{d-1})

对于x> 0，a，c> 0，b> 1，且d <1。

我编写了以下用于查找数据集MLE的R代码：

     x = c(0.1, 0.2, 1, 1, 1, 1, 1, 2, 3, 6, 7, 11, 12, 18, 18, 18, 18, 18, 21, 32,
     36, 40, 45, 46,47, 50, 55, 60, 63, 63, 67, 67, 67,67, 72, 75, 79, 82, 82, 83, 
     84, 84, 84, 85, 85, 85, 85, 85, 86, 86) 

     daddweibull = function(t, a, b, c, d){
               - (a^b*(t^(b-1))-c^d*(t^(d-1)))*exp(-(a*t)^b-(c*t)^d)
     }


    AW.LIK.ADD.WEI=function(theta, x){
          x = sort(x)
          a=theta[1]
          b=theta[2]
          c=theta[3]
          d=theta[4]
          n=length(x)
          logL = sum(log(daddweibull(x, a, b, c, d)))
          return(logL)
          }

          applyDefault <- function(AW.LIK.ADD.WEI, x=x) {
                    function(theta) AW.LIK.ADD.WEI(theta, x)
          }

          constrOptim(c(1e-6, 1.2, 1e-6, 1e-6), applyDefault(AW.LIK.ADD.WEI,                  
          x=x), NULL, ui=rbind(c(1, 0, 0, 0), c(0, 1, 0, 0),
          c(0, 0, 1, 0), c(0, 0, 0, -1)), ci=c(0, 1, 0, -1),
          control = list(fnscale = -1, abstol=1e-10))

          $par
          [1] 2.322322e-09 1.311376e+00 2.755276e-03 3.451048e-05

          $value
          [1] -203.9492

          $counts
          [1] 0

         $convergence
         [1] 0

         $message
         NULL

         $outer.iterations
         [1] 1

        $barrier.value
        [1] -0.0001547508


        Warning messages:
        1: In log(daddweibull(x, a, b, c, d)) : NaNs produced
        2: In log(daddweibull(x, a, b, c, d)) : NaNs produced
        3: In log(daddweibull(x, a, b, c, d)) : NaNs produced
        4: In log(daddweibull(x, a, b, c, d)) : NaNs produced
        5: In log(daddweibull(x, a, b, c, d)) : NaNs produced
        6: In log(daddweibull(x, a, b, c, d)) : NaNs produced
        7: In log(daddweibull(x, a, b, c, d)) : NaNs produced

正如我在一些论文中所看到的，参数估计的结果应该如下：

     a ~ 0; b =30:069; c =0.0912, d=0:4996

我该如何解决这个问题？