stat.Quantile returns wrong value when dataset is even size

[Iriko0606]

What are you trying to do?

I'm trying to get median value when I request even size of dataset to stat.Quantile

What did you do?

func main() {
	xs := []float64{2, 3, 5, 9}
	median := stat.Quantile(0.5, stat.Empirical, xs, nil)

	fmt.Println(median)
}

https://go.dev/play/p/8b6vDMunna8

What did you expect to happen?

I expect return value 4

What actually happened?

its returns 3

What version of Go and Gonum are you using?

1.19

Does this issue reproduce with the current master?

Yes

[romanwerpachowski]

The current behaviour is consistent with the documentation. I think you will get the behaviour you want if you call Quantile with stat.LinInterp instead of stat.Empirical.

[Iriko0606]

Thanks for your reply.
I've already tried it but I could not get expect value 4.
Its also returns value 3

https://go.dev/play/p/lM8ZNR0rTsi

func main() {

	xs := []float64{2, 3, 5, 9}
	median := stat.Quantile(0.5, stat.LinInterp, xs, nil)

	fmt.Println(median)
}

[romanwerpachowski]

I see. I agree the documentation may be understood as promising a different behaviour, but I am not sure if the problem is with the code, or the documentation. @sbinet, what is your opinion?

[kortschak]

I really need to not do things before my first coffee. Using the correct value in the R, this is not a bug.

> quantile(c(2, 3, 5, 9), probs=0.5, type=4)
50% 
  3 

@Iriko0606 You are looking for the R-7 behaviour. I thought we had implemented that. This should be added.

[Iriko0606]

Thanks for your investigation and reply.

Is the method should be implemented as Quantile method of another case Empirical or LinInterp,
or be implemented as a Median method as a new method?

[kortschak]

Yes, there should be another CumulantKind. The name than numpy uses is Internal, so that's probably a reasonable starting point. I took a look at implementing this the other day, but it's complicated by the impact of weighting.