r - dnorm(x, mean=200, sd=20) 的积分不是 1

Question

我试图计算期望值为 200 和标准差为 20 的正态分布密度的积分。从 -Inf 到 Inf 这应该是 1。

我得到以下信息:

> integrate(dnorm, mean=200, sd=20,-Inf, Inf)$value
[1] 1.429508e-08

对于低于 169 的预期值，我得到正确的值 1。如何获得更大的期望值的正确值？

Answer 1

或者

integrate(dnorm, mean=200, sd=20, lower= -Inf, upper= Inf, abs.tol = 0)$value
[1] 1

见 here .

要查看发生了什么，请注意以下分割的数量:

js <- integrate(dnorm, mean=200, sd=20, lower = -Inf, upper = Inf)
as <- integrate(dnorm, mean=200, sd=20, lower = -1e4, upper = 1e4)
cj <- integrate(dnorm, mean=200, sd=20, lower = -Inf, upper = Inf, abs.tol = 0)

str(js)
List of 5
 $ value       : num 1.43e-08
 $ abs.error   : num 2.77e-08
 $ subdivisions: int 2
 $ message     : chr "OK"
 $ call        : language integrate(f = dnorm, lower = -Inf, upper = Inf, mean = 200, sd = 20)
 - attr(*, "class")= chr "integrate"

str(as)
List of 5
 $ value       : num 1
 $ abs.error   : num 2e-07
 $ subdivisions: int 9
 $ message     : chr "OK"
 $ call        : language integrate(f = dnorm, lower = -10000, upper = 10000, mean = 200,      sd = 20)
 - attr(*, "class")= chr "integrate"

str(cj)
List of 5
 $ value       : num 1
 $ abs.error   : num 9.37e-05
 $ subdivisions: int 12
 $ message     : chr "OK"
 $ call        : language integrate(f = dnorm, lower = -Inf, upper = Inf, mean = 200, sd = 20,      abs.tol = 0)
 - attr(*, "class")= chr "integrate"