Log-Normal calculations using R

对数正太分布

R

packages

作者

Reddy Lee

发布于

2023年11月6日星期一

修改于

2023年12月23日星期六

代码

library(tidyverse)

对数正态分布数据是指对数据取对数后，数据呈正态分布的数据模型。和正态分布一样，对数正态分布也有两个基本的参数：\(\sigma\) 和\(\mu\)。用R计算对数正态分布有4个基本的函数。

1 随机生成对数正态分布数据： rlnorm(n,meanlg,sdlg)

代码

x <- rlnorm(120,6.1,1.0)

2 计算累积概率： plnorm(q,meanlg,sdlg)

代码

plnorm(717,6.1,1.0)

[1] 0.6826335

代码

plnorm(831,6.1,1.0)

[1] 0.7332361

代码

plnorm(c(717,744,831),6.1,1.0)

[1] 0.6826335 0.6956889 0.7332361

3 计算临界值： qlnorm(p,meanlg,sdlg)

代码

qlnorm(0.6956889,6.1,1.0)

[1] 744.0001

代码

qlnorm(c(0.6826335, 0.6956889, 0.7332361),6.1,1.0)

[1] 716.9999 744.0001 831.0000

4 pdf值: dlnorm(x,meanlg,sdlg)

代码

dlnorm(0.6956889,6.1,1)

[1] 4.881891e-10

代码

ggplot()+
  geom_function(fun=dlnorm,
                args=list(mena=6.1,
                          sd=1.0))+
  xlim(0,1500)+
  labs(y="Density")

5 练习

Example. Freshman undergraduate enrollments at U.S. colleges have an approximate log-normal distribution with parameters mean = 6.1 and sd = 1.0. ### What is the probability that a randomly-selected college enrolls between 500 and 1000 freshmen in a year?

代码

plnorm(1000,6.1,1)-plnorm(500,6.1,1)

[1] 0.2447621

5.1 What is the 99th percentile for U.S. college enrollment?

代码

qlnorm(0.99,6.1,1)

[1] 4565.795

5.2 Simulate selecting 100 colleges at random. Plot a histogram of freshman enrollments at those colleges.

代码

freshmen <- rlnorm(100,6.1,1)

qplot(freshmen,geom="histogram")

代码

qplot(freshmen,geom="density")

---
title: Log-Normal calculations using R
subtitle: 对数正太分布
author: Reddy Lee
date: "2023-11-06"
date-format: full
date-modified: last-modified

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----

```{r}
#| label: setup

library(tidyverse)
```


对数正态分布数据是指对数据取对数后，数据呈正态分布的数据模型。和正态分布一样，对数正态分布也有两个基本的参数：$\sigma$ 和$\mu$。用R计算对数正态分布有4个基本的函数。

## 随机生成对数正态分布数据： rlnorm(n,meanlg,sdlg)
```{r}
x <- rlnorm(120,6.1,1.0)
```

## 计算累积概率： plnorm(q,meanlg,sdlg)

```{r}
plnorm(717,6.1,1.0)
plnorm(831,6.1,1.0)
plnorm(c(717,744,831),6.1,1.0)
```
## 计算临界值： qlnorm(p,meanlg,sdlg)

```{r}
qlnorm(0.6956889,6.1,1.0)
qlnorm(c(0.6826335, 0.6956889, 0.7332361),6.1,1.0)
```
## pdf值: dlnorm(x,meanlg,sdlg)

```{r}
dlnorm(0.6956889,6.1,1)
```
```{r}
ggplot()+
  geom_function(fun=dlnorm,
                args=list(mena=6.1,
                          sd=1.0))+
  xlim(0,1500)+
  labs(y="Density")
```

## 练习
Example. Freshman undergraduate enrollments at U.S. colleges have an
approximate log-normal distribution with parameters mean = 6.1 and sd = 1.0.
### What is the probability that a randomly-selected college enrolls between 500 and 1000 freshmen in a year?
```{r}
plnorm(1000,6.1,1)-plnorm(500,6.1,1)
```

### What is the 99th percentile for U.S. college enrollment?

```{r}
qlnorm(0.99,6.1,1)
```
### Simulate selecting 100 colleges at random. Plot a histogram of freshman enrollments at those colleges.

```{r}
freshmen <- rlnorm(100,6.1,1)

qplot(freshmen,geom="histogram")
qplot(freshmen,geom="density")
```