如何在R中创建分布函数？ [英] How to create a distribution function in R?

问题描述

给出以下函数：

  f（x）=（1/2 * pi）（1 /（1+ x ^ 2/4））
  

我如何确定其分布并在R中编写此分布函数？

解决方案

所以这是您的函数（希望您知道如何编写R函数；如果没有，请检查

Given the following function:

f(x) = (1/2*pi)(1/(1+x^2/4))

How do I identify it's distribution and write this distribution function in R?

解决方案

So this is your function right now (hopefully you know how to write an R function; if not, check writing your own function):

f <- function (x) (pi / 2) * (1 / (1 + 0.25 * x ^ 2))

f is defined on (-Inf, Inf) so integration on this range gives an indefinite integral. Fortunately, it approaches to Inf at the speed of x ^ (-2), so the integral is well defined, and can be computed:

C <- integrate(f, -Inf, Inf)
# 9.869604 with absolute error < 1e-09

C <- C$value  ## extract integral value
# [1] 9.869604

Then you want to normalize f, as we know that a probability density should integrate to 1:

f <- function (x) (pi / 2) * (1 / (1 + 0.25 * x ^ 2)) / C

You can draw its density by:

curve(f, from = -10, to = 10)

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