Draw QQ charts with different distribution

brief introduction

In this paper, we need to plot the data under different distribution assumptions QQ chart . Here, Xiaobian mainly uses qqplotr Package to draw , Reference blog ：An Introduction to qqplotr.

Simple version

Draw a normal distribution of QQ chart

For the classical normal distribution QQ chart , You may not be new , And you can find a lot on the Internet “ Carry ” Of Chinese tweets . But the explanation is not very clear .

Here I take an example from this blog , To introduce ：

1. Load package

library(qqplotr)
library(ggplot2)

2. Randomly generate data

set.seed(0)
smp <- data.frame(norm = rnorm(100))

3. Draw a normal distribution of QQ chart

gg <- ggplot(data = smp, mapping = aes(sample = norm)) +
    stat_qq_band() +
    stat_qq_line() +
    stat_qq_point() +
    labs(x = "Theoretical Quantiles", y = "Sample Quantiles")
gg

4. expand

Here is a simple expansion , If you want to use different confidence bands to construct confidence intervals , You can use parameters bandType Adjustment . The following code gives the results of three different methods to construct confidence intervals . And use viridis package , Modify its color matching .

library(viridis)
gg <- ggplot(data = smp, mapping = aes(sample = norm)) +
    geom_qq_band(bandType = "ks", mapping = aes(fill = "KS"), alpha = 0.9) +
    geom_qq_band(bandType = "ts", mapping = aes(fill = "TS"), alpha = 0.9) +
    geom_qq_band(bandType = "pointwise", mapping = aes(fill = "Normal"), alpha = 0.9) +
    geom_qq_band(bandType = "boot", mapping = aes(fill = "Bootstrap"), alpha = 0.9) +
    stat_qq_line() +
    stat_qq_point() +
    labs(x = "Theoretical Quantiles", y = "Sample Quantiles") +
    scale_fill_viridis(discrete = T,direction = -1)

gg

Advanced version

The reader draws a normal distribution of QQ chart , It's still relatively simple . But what about other distributions ？

Here is a Reliability data As an example , The data comes from the literature ：Badar, M. G., Priest, A. M. (1982). Statistical aspects of fiber and bundle strength in hybrid composites. In: Hayashi, T., Kawata, K., Umekawa, S., eds. Progress in Science and Engineering Composites. Tokyo: ICCM-IV, pp. 1129–1136.

data = data.frame('y' = c(1.339, 1.434, 1.549, 1.574 ,1.589, 1.613, 1.746 ,1.753, 1.764 ,1.807, 1.812, 1.84, 1.852, 1.852, 1.862, 1.864, 1.931, 1.952, 1.974, 2.019, 2.051, 2.055, 2.058 ,2.088, 2.125, 2.162, 2.171, 2.172 ,2.18 ,2.194 ,2.211 ,2.27, 2.272, 2.28, 2.299, 2.308, 2.335 ,2.349 ,2.356 ,2.386, 2.39, 2.41, 2.43, 2.431, 2.458, 2.471, 2.497, 2.514 ,2.558, 2.577, 2.593, 2.601, 2.604, 2.62 ,2.633, 2.67, 2.682, 2.699, 2.705, 2.735, 2.785, 2.785,3.02, 3.042, 3.116, 3.174))

Plot the exponential distribution QQ chart

Here we first plot the exponential distribution of QQ chart . After fitting the data according to the parameters of the exponential function , obtain rate =2.2867, And save it to list in .

How to fit , Readers search by themselves R Related functions in the package .

Other codes remain basically the same , Mainly is to stat_qq_line() and stat_qq_point() Under the distribution setting in , Under parameter setting .

# exponential distribution
dp <- list(rate = 2.2867)
di <- "exp"
p1 = ggplot(data = data, mapping = aes(sample = y)) +
  stat_qq_band(distribution = di, dparams = dp) +
  stat_qq_line(distribution = di, dparams = dp) +
  stat_qq_point(distribution = di, dparams = dp) +
  labs(x = "Theoretical Quantiles", y = "Sample Quantiles") +
  theme_bw() + 
  theme(panel.grid = element_blank())
p1

Plot the Weibull distribution QQ chart

Empathy , Apply this data to Weibull distribution . give the result as follows ：

# weibull distribution
di <- "weibull" # exponential distribution
dp <- list(shape=5.4766,scale=2.4113)
p2 = ggplot(data = data, mapping = aes(sample = y)) +
  stat_qq_band(distribution = di, dparams = dp) +
  stat_qq_line(distribution = di, dparams = dp) +
  stat_qq_point(distribution = di, dparams = dp) +
  labs(x = "Theoretical Quantiles", y = "Sample Quantiles") +
  theme_bw() + 
  theme(panel.grid = element_blank())
p2

You can see that this dataset is more suitable for Weibull The distribution is fitted , The fitting result of exponential distribution is worse . Readers can use other distributions to fit , And compare the corresponding QQ chart , Find the most suitable distribution .

Then put these QQ chart Merge together , Through visual comparison .

Use here cowplot package , Merge the two figures . Xiaobian has made several issues of introduction to the package , so ： . There are other ways to merge ：.

#  Merge two  QQ  chart 
library(cowplot)
plot_grid(p1, p2, ncol = 2, nrow = 1)