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Quantile-quantile plots help you determine whether two samples come from the same distribution family. Quantile-quantile plots are scatter plots of quantiles computed from each sample together with a reference line along the diagonal of the plot. If the data forms the line, it is reasonable to assume that the two samples come from the same distribution family. If the data falls near the reference line, you also can assume that the two samples have the same mean and the same variance.
To create a quantile-quantile plot, use the
plot::QQplot function. For example,
create the data samples
contain random floating-point numbers from the interval [0.0, 1.0).
to create the
data1 sample. Use the
to create the
data2 sample. Both functions produce
uniformly distributed numbers. The quantile-quantile plot of these
two data samples confirms that the samples come from the same distribution
family. The plot is close to the line with a slope of 1:
data1 := [frandom() $ i = 1..100]: data2 := [stats::uniformRandom(0, 1)() $ k = 1..100]: p := plot::QQplot(data1, data2): plot(p)
The following quantile-quantile plot clearly shows that these two data samples come from different distribution families:
data1 := [stats::uniformRandom(0, 1)() $ k = 1..100]: data2 := [stats::exponentialRandom(0, 1)() $ k = 1..100]: p := plot::QQplot(data1, data2): plot(p)