Implement Percentile Calculator support linear interpolation

[ShukriChiu]

For example, the data is (3.8,4.5,4.6,4.7,4.9) while I'm using tech.tablesaw.aggregate.AggregateFunctions.percentile function, the 90th percentile is 4.9, however, if the percentile function supports linear interpolation, the 90th percentile should be 4.82, which is adopted by most other programming languages.

[mo20053444]

Hi @lwhite1 @ShukriChiu, it looks like the underlying method implemented by Apache does return an interpolated value. There is a total of 10 (LEGACY + R_1 ~9) formulae enumerated in Apache's class to calculate the index of the percentile. If we change the field estimationType from LEGACY (the default input) to R_7, the returned interpolated value will be 4.82. Apache's implementation An intro from Wikipedia

[lwhite1]

I would prefer adding a new method rather than changing the current one in a way that would change the result. That's a subtle and significant breaking change.

On Thu, Aug 25, 2022 at 1:18 PM mo20053444 @.***> wrote:

Hi @lwhite1 https://github.com/lwhite1 @ShukriChiu https://github.com/ShukriChiu, it looks like the underlying method implemented by Apache does return an interpolated value. There is a total of 10 (LEGACY + R_1 ~9) formulae enumerated in Apache's class to calculate the index of the percentile. If we change the field estimationType from LEGACY (the default input) to R_7, the returned interpolated value will be 4.82. Apache's implementation https://github.com/apache/commons-math/blob/master/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/stat/descriptive/rank/Percentile.java#:~:text=public%20enum-,EstimationType,-%7B An intro from Wikipedia https://en.wikipedia.org/wiki/Quantile#Estimating_quantiles_from_a_sample

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[mo20053444]

@lwhite1 Yes, I totally agree. Do we add another method with the Estimation Type of R_7 hard coded in it? Or give users an option (as a parameter) to pick what Estimation Type they would like to use (among R_1 through 9)? I think the latter will need to expose Apache’s implementation of Estimation Type Enumerator to the users (i.e., the users will have to type in EstimationType.R_1 as a parameter if they want to use it).

[lwhite1]

I think the ideal approach might be to wrap the estimation types in a tablesaw enum.

On Sat, Aug 27, 2022 at 10:15 AM mo20053444 @.***> wrote:

@lwhite1 https://github.com/lwhite1 Yes, I totally agree. Do we add another method with the Estimation Type of R_7 hard coded in it? Or give users an option (as a parameter) to pick what Estimation Type they would like to use (among R_1 through 9)? I think the latter will need to expose Apache’s implementation of Estimation Type Enumerator to the users (i.e., the users will have to type in EstimationType.R_1 as a parameter if they want to use it).

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[mo20053444]

Hi @lwhite1, I created a PR earlier this week for another percentile method allowing users to choose a specific estimation type from a newly created tablesaw enum to calculate percentile. However, after some further thinking, do you think it is a better idea to just add 9 new percentile methods among which an estimation type (R1 to 9) is provided in each method?

For example: /* Returns the given percentile of the values in the argument with R1 as estimation type/ public static Double percentileR1(NumericColumn<?> data, Double percentile) { return new Percentile().withEstimationType(EstimationType.R_1).evaluate(removeMissing(data), percentile); }

/* Returns the given percentile of the values in the argument with R2 as estimation type/ public static Double percentileR2(NumericColumn<?> data, Double percentile) { return new Percentile().withEstimationType(EstimationType.R_2).evaluate(removeMissing(data), percentile); } ...

In this way users don't need to input a potential tablesaw's Enum.R1 as an argument since neither the potential tablesaw's enum nor Apache's enum of EstimationType needs to be exposed to users.