Q-Q Plots¶

In [1]:

%useLatestDescriptors
%use dataframe
%use lets-plot

In [2]:

LetsPlot.getInfo()

Out[2]:

Lets-Plot Kotlin API v.4.9.0. Frontend: Notebook with dynamically loaded JS. Lets-Plot JS v.4.5.1.

In [3]:

var mpg = DataFrame.readCSV("https://raw.githubusercontent.com/JetBrains/lets-plot-kotlin/master/docs/examples/data/mpg.csv")
mpg.head(3)

Out[3]:

DataFrame: rowsCount = 3, columnsCount = 12

untitled	manufacturer	model	displ	year	cyl	trans	drv	cty	hwy	fl	class
1	audi	a4	1.800000	1999	4	auto(l5)	f	18	29	p	compact
2	audi	a4	1.800000	1999	4	manual(m5)	f	21	29	p	compact
3	audi	a4	2.000000	2008	4	manual(m6)	f	20	31	p	compact

In [4]:

val hwy = "hwy"
val cty = "cty"
val drv = "drv"

Two types of Q-Q plots¶

`geomQQ()` and `geomQQLine()` functions.¶

In [5]:

letsPlot(mpg.toMap()) {sample = hwy} + 
    geomQQ(size = 5, alpha = .3) + 
    geomQQLine(size = 1) + 
    ggtitle("Distribution of highway miles per gallon",
            "Comparison of sample quantiles with normal distribution quantiles")

Out[5]:

`geomQQ()` and `geomQQ2Line()` functions.¶

In [6]:

letsPlot(mpg.toMap()) {x = cty; y = hwy} + 
    geomQQ2(size = 5, alpha = .3) + 
    geomQQ2Line(size = 1) + 
    ggtitle("City miles vs. highway miles (per gallon)",
            "Comparison of quantiles of two sample distributions")

Out[6]:

Quick Q-Q plot: the `qqPlot()` function¶

In [7]:

qqPlot(mpg.toMap(), sample = hwy) + 
    ggtitle("Distribution of highway miles per gallon",
            "Comparison of sample quantiles with normal distribution quantiles")

Out[7]:

In [8]:

qqPlot(mpg.toMap(), x = cty, y = hwy) + 
    ggtitle("City miles vs. highway miles (per gallon)",
            "Comparison of quantiles of two sample distributions")

Out[8]:

Comparison with other 'theoretical' distributions¶

The distribution parameter of the qq_plot() function.

In [9]:

val p1 = qqPlot(mpg.toMap(), hwy, distribution = "norm", quantiles = .1 to .9) + 
    ggtitle("Normal distribution")
val p2 = qqPlot(mpg.toMap(), hwy, distribution = "uniform", quantiles = .1 to .9) + 
    ggtitle("Uniform distribution")
val p3 = qqPlot(mpg.toMap(), hwy, distribution = "t", quantiles = .1 to .9) + 
    ggtitle("Student's t-distribution distribution")
val p4 = qqPlot(mpg.toMap(), hwy, distribution = "exp", quantiles = .1 to .9) + 
    ggtitle("Exponential distribution")

    
gggrid(listOf(p1, p2, p3, p4), 2, 400, 250)

Out[9]:

Q-Q stats with other geometries¶

In [10]:

letsPlot(mpg.toMap()) {x = cty; y = hwy; color = drv} + 
    geomLine(stat = Stat.qq2()) +  
    geomPoint(stat = Stat.qq2(), shape = 15) +
    geomLine(stat = Stat.qq2Line(), color = "#636363", linetype = 5) +
    facetGrid(x = drv, scales = "free") +
    xlab("cty quantiles") + ylab("hwy quantiles")

Out[10]: