如何在R语言中绘制Q-Q图？含手动实现多数据集Q-Q图任务

Got it, let's walk through how to complete this task properly, step by step. You've got a good start with fitting the normal distribution to your data, but we need to expand it to generate the required samples and build custom Q-Q plots without relying on qqnorm() or qqplot().

First, let's clean up the code for calculating the mean and standard deviation of your original data—we can use R's built-in functions for clarity and accuracy:

# Original observed data
y <- c(194, 209, 205, 180, 196, 178, 214, 199, 224, 230)

# Fit normal distribution parameters (sample mean and standard deviation)
mu <- mean(y)
sigma <- sd(y)

# Print the fitted parameters for reference
cat("Fitted Normal Distribution:\nMean =", round(mu, 2), "\nStandard Deviation =", round(sigma, 2), "\n")

We'll generate 3 independent samples, each with 100 values from the fitted normal distribution. Adding a seed ensures your results are reproducible:

# Set random seed for consistent results
set.seed(123)

# Generate 3 datasets (100 observations each)
num_datasets <- 3
sample_size <- 100
samples <- replicate(num_datasets, rnorm(n = sample_size, mean = mu, sd = sigma))

# Check the structure: 100 rows (observations) × 3 columns (datasets)
str(samples)

Q-Q plots work by comparing sorted sample values to theoretical quantiles from the reference distribution (our fitted normal). Here's a custom function to create these plots, plus a loop to plot all 3 datasets:

# Define a function to create a custom Q-Q plot
custom_qqplot <- function(sample_data, dist_mean, dist_sd, plot_title) {
  # 1. Sort the sample observations
  sorted_sample <- sort(sample_data)
  
  # 2. Calculate empirical quantile positions (using (i - 0.5)/n for continuity correction)
  n <- length(sorted_sample)
  quantile_positions <- (1:n - 0.5) / n
  
  # 3. Get theoretical quantiles from the fitted normal distribution
  theoretical_quantiles <- qnorm(quantile_positions, mean = dist_mean, sd = dist_sd)
  
  # 4. Create the scatter plot
  plot(theoretical_quantiles, sorted_sample,
       xlab = "Theoretical Normal Quantiles",
       ylab = "Sorted Sample Values",
       main = plot_title,
       pch = 16, col = "#2c3e50")
  
  # 5. Add a reference line (ideal fit line: y = mu + sigma*x)
  abline(a = dist_mean, b = dist_sd, col = "#e74c3c", lwd = 2)
}

# Plot all 3 datasets in a 3-row grid
par(mfrow = c(3, 1), mar = c(4, 4, 2, 1)) # Adjust plot margins for readability
for (i in 1:num_datasets) {
  custom_qqplot(samples[, i], mu, sigma, title = paste("Q-Q Plot: Dataset", i))
}
par(mfrow = c(1, 1)) # Reset plotting layout to default

Quick explanation of the Q-Q logic: #

• We sort the sample to get empirical order statistics
• The quantile_positions formula adjusts for the fact that we can't have a quantile at exactly 0 or 1 for finite samples
• qnorm() gives us the values we'd expect from a perfect normal distribution at those positions
• The red reference line shows where points would lie if the sample perfectly matched the fitted normal

If you want to double-check the fits, you can plot histograms with the fitted normal density curve for each dataset:

# Plot histograms with fitted density curves
par(mfrow = c(3, 1), mar = c(4, 4, 2, 1))
for (i in 1:num_datasets) {
  hist(samples[, i], breaks = 15, freq = FALSE,
       main = paste("Histogram: Dataset", i),
       xlab = "Observed Value", col = "#bdc3c7")
  curve(dnorm(x, mu, sigma), add = TRUE, col = "#2980b9", lwd = 2)
}
par(mfrow = c(1, 1))

This completes all your requirements: we've fitted the normal distribution to your original data, generated 3 samples of 100 observations each, and created custom Q-Q plots without using R's built-in qqnorm() or qqplot() functions.

内容的提问来源于stack exchange，提问作者Kate