Weibull累积分布函数从"fitdistr"命令开始

Question

我使用了fitdistr来自R MASS包的函数来调整Weibull 2参数概率密度函数(pdf).

这是我的代码:

require(MASS)

h = c(31.194, 31.424, 31.253, 25.349, 24.535, 25.562, 29.486, 25.680, 26.079, 30.556,      30.552, 30.412, 29.344, 26.072, 28.777, 30.204, 29.677, 29.853, 29.718, 27.860, 28.919, 30.226, 25.937, 30.594, 30.614, 29.106, 15.208, 30.993, 32.075, 31.097, 32.073, 29.600, 29.031, 31.033, 30.412, 30.839, 31.121, 24.802, 29.181, 30.136, 25.464, 28.302, 26.018, 26.263, 25.603, 30.857, 25.693, 31.504, 30.378, 31.403, 28.684, 30.655,  5.933, 31.099, 29.417, 29.444, 19.785, 29.416, 5.682, 28.707, 28.450, 28.961, 26.694, 26.625, 30.568, 28.910, 25.170, 25.816, 25.820)

weib = fitdistr(na.omit(h),densfun=dweibull,start=list(scale=1,shape=5))

hist(h, prob=TRUE, main = "", xlab = "x", ylab = "y", xlim = c(0,40), breaks = seq(0,40,5))
curve(dweibull(x, scale=weib$estimate[1], shape=weib$estimate[2]),from=0, to=40, add=TRUE)

现在,我想创建Weibull累积分布函数(cdf)并将其绘制为图形:

,其中x> 0,b =比例,a =形状

我试图使用比例和形状参数来h使用上面的公式,但它不是这样的.

Answer 1

这是对累积密度函数的一种刺激.您只需要记住包括对采样点间距的调整(注意:它适用于均匀间距小于或等于1的采样点):

cdweibull <- function(x, shape, scale, log = FALSE){
  dd <- dweibull(x, shape= shape, scale = scale, log = log)
  dd <- cumsum(dd) * c(0, diff(x))
  return(dd)
}

尽管有关比例差异的上述讨论,您可以将其绘制在图表上,如下所示dweibull:

require(MASS)

h = c(31.194, 31.424, 31.253, 25.349, 24.535, 25.562, 29.486, 25.680,
      26.079, 30.556, 30.552, 30.412, 29.344, 26.072, 28.777, 30.204, 
      29.677, 29.853, 29.718, 27.860, 28.919, 30.226, 25.937, 30.594, 
      30.614, 29.106, 15.208, 30.993, 32.075, 31.097, 32.073, 29.600, 
      29.031, 31.033, 30.412, 30.839, 31.121, 24.802, 29.181, 30.136, 
      25.464, 28.302, 26.018, 26.263, 25.603, 30.857, 25.693, 31.504, 
      30.378, 31.403, 28.684, 30.655,  5.933, 31.099, 29.417, 29.444, 
      19.785, 29.416, 5.682, 28.707, 28.450,  28.961, 26.694, 26.625, 
      30.568, 28.910, 25.170, 25.816, 25.820)

weib = fitdistr(na.omit(h),densfun=dweibull,start=list(scale=1,shape=5))

hist(h, prob=TRUE, main = "", xlab = "x", 
     ylab = "y", xlim = c(0,40), breaks = seq(0,40,5), ylim = c(0,1))

curve(cdweibull(x, scale=weib$estimate[1], shape=weib$estimate[2]),
  from=0, to=40, add=TRUE)