R quantile function fails at finding deciles of very small values, is there any algorithm that works better than others?
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2can you show an example pleaseuser20650– user206502020-05-29 11:13:21 +00:00Commented May 29, 2020 at 11:13
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2 Answers
The R quantile function doesn't fail at finding deciles of very small values; it's just that the concept of deciles becomes ambiguous if you don't have many samples in your set. There are actually 9 different ways to calculate quantiles using the quantile function in R, which you can change by setting the type parameter.
Here is an example of attempting to extract the deciles of the vector c(1, 2, 3), with each of the 9 methods available. Do any of these meet your expectations? Personally, I like method 7 here, but I guess it really depends on how you define a decile, and for what purposes.
sapply(1:9, function(x) quantile(c(1:3), probs = seq(0, 1, 0.1), type = x))
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
#> 0% 1 1 1 1.0 1.0 1.0 1.0 1.000000 1.000
#> 10% 1 1 1 1.0 1.0 1.0 1.2 1.000000 1.000
#> 20% 1 1 1 1.0 1.1 1.0 1.4 1.000000 1.025
#> 30% 1 1 1 1.0 1.4 1.2 1.6 1.333333 1.350
#> 40% 2 2 1 1.2 1.7 1.6 1.8 1.666667 1.675
#> 50% 2 2 2 1.5 2.0 2.0 2.0 2.000000 2.000
#> 60% 2 2 2 1.8 2.3 2.4 2.2 2.333333 2.325
#> 70% 3 3 2 2.1 2.6 2.8 2.4 2.666667 2.650
#> 80% 3 3 2 2.4 2.9 3.0 2.6 3.000000 2.975
#> 90% 3 3 3 2.7 3.0 3.0 2.8 3.000000 3.000
#> 100% 3 3 3 3.0 3.0 3.0 3.0 3.000000 3.000
Comments
The formal quantile function is not implemented in software R. Otherwise, this software has a mistake. The quantile function is left continuous, for probability p in the interval [0,1]. See Seccion 12 in Parzen, E. (2004) Quantile probability and statistical data modeling. Statistical Science, 19(4), 652-662.
In this sense, if the sample is {1,2,3,4,5,6,7,8,9,10}, the sample quantile are:
1 as 0.1-quantile,
2 as 0.2-quantile,
3 as 0.3-quantile, and so on.
However, the quantile() function in R, type=1, gives:
4 as 0.3-quantile and
8 as 0.7-quantile.
See this example below.
> sapply(1:9,function(x) quantile(c(1:10),probs=seq(0,1,0.1),type=x))
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
0% 1 1.0 1 1 1.0 1.0 1.0 1.000000 1.000
10% 1 1.5 1 1 1.5 1.1 1.9 1.366667 1.400
20% 2 2.5 2 2 2.5 2.2 2.8 2.400000 2.425
30% 4 4.0 3 3 3.5 3.3 3.7 3.433333 3.450
40% 4 4.5 4 4 4.5 4.4 4.6 4.466667 4.475
50% 5 5.5 5 5 5.5 5.5 5.5 5.500000 5.500
60% 7 7.0 6 6 6.5 6.6 6.4 6.533333 6.525
70% 8 8.0 7 7 7.5 7.7 7.3 7.566667 7.550
80% 8 8.5 8 8 8.5 8.8 8.2 8.600000 8.575
90% 9 9.5 9 9 9.5 9.9 9.1 9.633333 9.600
100% 10 10.0 10 10 10.0 10.0 10.0 10.000000 10.000
