June 2020
Beginner to intermediate
522 pages
9h 6m
Chinese
Content preview from R 语言经典实例（原书第 2 版）
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216
｜
第
8
章
表 8-5：连续分布
分布 分布函数：
P
(
X
≤
x
)
正态分布
pnorm(
x
, mean, sd)
学生
t
分布
pt(
x
, df)
指数分布
pexp(
x
, rate)
伽马分布
pgamma(
x
, shape, rate)
卡方分布
pchisq(
x
, df)
我们可以使用 pnorm 计算一个人身高不超过 66 英寸（1 英寸
＝
0.0254 米）的概率，假
设人的身高是一个正态分布，均值为 70 英寸，标准差为 3 英寸。从数学上讲，我们需
要在
X
～
N
(70,3) 的条件下计算
P
(
X
≤
66)：
pnorm(66, mean = 70, sd = 3)
#> [1] 0.0912
同样，可以使用 pexp 来计算均值为 40 的指数变量小于 20 的概率：
pexp(20, rate = 1 / 40)
#> [1] 0.393
与离散概率相似，连续概率的函数使用 lower.tail=FALSE 来指定生存函数
P
(
X
>
x
)。
下面对 pexp 的调用给出了指数变量大于 50 的概率：
pexp(50, rate = 1 / 40, lower.tail = FALSE)
#> [1] 0.287
与离散概率一样，连续变量的区间概率
P
(
x
1
<
X
<
x
2
) 被计算为两个累积概率之差
P
(
X
<
x
2
)
-
P
(
X
<
x
1
)。对于上述指数变量，这里
P
(20<
X
<50) 表示它可能落在 20 到 50 之间：
pexp(50, rate = 1 / 40) - pexp(20, rate = 1 / 40)
#> [1] ...
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