R dnorm() pnorm() qnorm() functions - Normal distribution function family
R Language ExamplesR provides four core functions for the normal distribution: dnorm() density function, pnorm() cumulative probability, qnorm() quantile function, rnorm() random number generation.
They each answer different questions: What is the probability density of a certain value? What is the cumulative probability? What is the quantile corresponding to a certain probability?
The syntax of each function is as follows:
dnorm(x, mean = 0, sd = 1) # 密度函数 pnorm(q, mean = 0, sd = 1) # 累积分布函数 P(X <= q) qnorm(p, mean = 0, sd = 1) # 分位数函数
Parameter description:
x/qThe value to be calculated.
pProbability value (0 to 1).
meanMean, default 0.
sdStandard deviation, default 1.
Example
# Assume test scores N(70, 10)
# dnorm: probability density at score 70
print(paste("dnorm(70):", round(dnorm(70, mean = 70, sd = 10), 4)))
# pnorm: probability of score below 85
print(paste("P(score <= 85):", round(pnorm(85, mean = 70, sd = 10), 4)))
# pnorm: probability of score above 85
print(paste("P(score > 85):", round(1 - pnorm(85, mean = 70, sd = 10), 4)))
# qnorm: cutoff for top 10%
print(paste(Top 10% cutoff score:, round(qnorm(0.9, mean = 70, sd = 10), 2)))
# dnorm: probability density at score 70
print(paste("dnorm(70):", round(dnorm(70, mean = 70, sd = 10), 4)))
# pnorm: probability of score below 85
print(paste("P(score <= 85):", round(pnorm(85, mean = 70, sd = 10), 4)))
# pnorm: probability of score above 85
print(paste("P(score > 85):", round(1 - pnorm(85, mean = 70, sd = 10), 4)))
# qnorm: cutoff for top 10%
print(paste(Top 10% cutoff score:, round(qnorm(0.9, mean = 70, sd = 10), 2)))
Executing the above code outputs the following:
[1] "dnorm(70): 0.0399" [1] "P(score <= 85): 0.9332" [1] "P(score > 85): 0.0668" [1] "前 10% 分数线: 82.82"Other extensions