为什么我的ccdf图以0.4而不是1开始？

Question

我使用社区发布的代码在R中绘制ccdf。在许多情况下，它工作正常，但是对于以下数据，其绘制的ccdf图从0.4开始而不是从1开始；有人可以帮忙吗？

x = c(50.76535,54.89802,74.12376,72.67228,50.76535,50.76535,50.76535,50.76535,50.76535,50.76535,72.67228,59.54455,72.67228,72.67228,72.67228,50.76535,50.76535,72.20198,50.76535,89.10891,50.76535,72.67228,50.76535,72.20198,50.76535,50.76535,50.76535)

plot(sort(x) , 1-ecdf(x)(sort(x) ), xlab = "x = log mean rain", ylab = "P(X > x)", pch = 1
     , ylim = c(0,1),t='b', log = 'x')

Answer 1

ecdf 从0开始。它是右连续的，并且在每个数据点处跳转。也就是说，它在min(x)之前等于0，并且它的第一个跳转点是min(x)：

x <- c(50.76535,54.89802,74.12376,72.67228,50.76535,50.76535,50.76535,50.76535,
       50.76535,50.76535,72.67228,59.54455,72.67228,72.67228,72.67228,50.76535,
       50.76535,72.20198,50.76535,89.10891,50.76535,72.67228,50.76535,72.20198,
       50.76535,50.76535,50.76535)
Fn <- ecdf(x)

Fn(min(x) - 1)
# 0
Fn(min(x))
# 0.5555556

ecdf 及其补充功能是 step函数。当您执行 ecdf（x）时，您将获得一个步进函数。要定义互补的 ecdf ，您必须使用stepfun：

jumps_at <- sort(unique(x))
CFn <- stepfun(jumps_at, c(1, 1-Fn(jumps_at)))

plot(CFn, xlab = "x = mean rain", ylab = "P(X > x)", 
     verticals = FALSE, pch = 19, ylim = c(0,1))