R 简明教程

R - Normal Distribution

在来自独立来源的随机数据集合中，通常观察到数据的分布是正态的。这意味着，通过绘制一个图形，其中水平轴为变量值，垂直轴为值计数，我们可以得到一个钟形曲线。曲线的中心表示数据集的均值。在图形中，50% 的值位于均值的左侧，而其他 50% 位于图形右侧。在统计中，这称为正态分布。

In a random collection of data from independent sources, it is generally observed that the distribution of data is normal. Which means, on plotting a graph with the value of the variable in the horizontal axis and the count of the values in the vertical axis we get a bell shape curve. The center of the curve represents the mean of the data set. In the graph, fifty percent of values lie to the left of the mean and the other fifty percent lie to the right of the graph. This is referred as normal distribution in statistics.

R 具有四个内置函数用于生成正态分布。它们在下方进行了描述。

R has four in built functions to generate normal distribution. They are described below.

dnorm(x, mean, sd)
pnorm(x, mean, sd)
qnorm(p, mean, sd)
rnorm(n, mean, sd)

以下是上面函数中使用的参数的描述 -

Following is the description of the parameters used in above functions −

  1. x is a vector of numbers.

  2. p is a vector of probabilities.

  3. n is number of observations(sample size).

  4. mean is the mean value of the sample data. It’s default value is zero.

  5. sd is the standard deviation. It’s default value is 1.

dnorm()

此函数针对给定的均值和标准差提供每个点的概率分布高度。

This function gives height of the probability distribution at each point for a given mean and standard deviation.

# Create a sequence of numbers between -10 and 10 incrementing by 0.1.
x <- seq(-10, 10, by = .1)

# Choose the mean as 2.5 and standard deviation as 0.5.
y <- dnorm(x, mean = 2.5, sd = 0.5)

# Give the chart file a name.
png(file = "dnorm.png")

plot(x,y)

# Save the file.
dev.off()

当我们执行上述代码时，会产生以下结果 -

When we execute the above code, it produces the following result −

dnorm

pnorm()

此函数给出了正态分布随机数小于给定数字值的概率。它也称为 “累积分布函数”。

This function gives the probability of a normally distributed random number to be less that the value of a given number. It is also called "Cumulative Distribution Function".

# Create a sequence of numbers between -10 and 10 incrementing by 0.2.
x <- seq(-10,10,by = .2)

# Choose the mean as 2.5 and standard deviation as 2.
y <- pnorm(x, mean = 2.5, sd = 2)

# Give the chart file a name.
png(file = "pnorm.png")

# Plot the graph.
plot(x,y)

# Save the file.
dev.off()

当我们执行上述代码时，会产生以下结果 -

When we execute the above code, it produces the following result −

pnorm

qnorm()

此函数获取概率值并给出一个其累积值与概率值匹配的数字。

This function takes the probability value and gives a number whose cumulative value matches the probability value.

# Create a sequence of probability values incrementing by 0.02.
x <- seq(0, 1, by = 0.02)

# Choose the mean as 2 and standard deviation as 3.
y <- qnorm(x, mean = 2, sd = 1)

# Give the chart file a name.
png(file = "qnorm.png")

# Plot the graph.
plot(x,y)

# Save the file.
dev.off()

当我们执行上述代码时，会产生以下结果 -

When we execute the above code, it produces the following result −

qnorm

rnorm()

此函数用于生成分布呈正态分布的随机数。它以样本量作为输入并生成数量与之相等的随机数。我们绘制一个直方图来显示生成数字的分布。

This function is used to generate random numbers whose distribution is normal. It takes the sample size as input and generates that many random numbers. We draw a histogram to show the distribution of the generated numbers.

# Create a sample of 50 numbers which are normally distributed.
y <- rnorm(50)

# Give the chart file a name.
png(file = "rnorm.png")

# Plot the histogram for this sample.
hist(y, main = "Normal DIstribution")

# Save the file.
dev.off()

当我们执行上述代码时，会产生以下结果 -

When we execute the above code, it produces the following result −

rnorm