Make "quantile" classification with an expression

Question

I have a vector layer with an attribut called "value". To make the explanation easier, we can say that "value" goes between 0 and 100.

I can't find a way the calculate a new attribute called "effect" in expression panel for something like that:

CASE
WHEN "value" is under the 20% lowest possible value THEN 'Very low'
WHEN "value" is between 20-40% lowest possible value THEN 'Low'
WHEN "value" is between 40-60% lowest possible value THEN 'Medium'
WHEN "value" is between 60-80% lowest possible value THEN 'High'
ELSE 'Very high'
END

So as you can see, I have a problem to find a way to do "value" is between x-y% lowest possible value.

Answer 1

Given that Percentile = (Number of Values Below “x” / Total Number of Values), how about:

with_variable(
'percentile',
array_find(array_agg("val",order_by:="val"),"val") / array_length(array_agg("val")),
    
    CASE
    WHEN @percentile < 0.2 THEN 'Very low'
    WHEN @percentile < 0.4 THEN 'Low'
    WHEN @percentile < 0.6 THEN 'Medium'
    WHEN @percentile < 0.8 THEN 'High'
    WHEN @percentile <= 1 THEN 'Very High'
    ELSE 'Undefined'
    END
)

Answer 2

I would do it that other way...which I think is not the same statistically..these are not percentiles

CASE
WHEN "value" < minimum("value")+ 0.2*(maximum("value")-minimum("value")) THEN 'Very low'
WHEN "value" > minimum("value")+ 0.2*(maximum("value")-minimum("value")) AND "value" < minimum("value")+ 0.4*(maximum("value")-minimum("value"))THEN 'Low'
WHEN "value" > minimum("value")+ 0.4*(maximum("value")-minimum("value")) AND "value" < minimum("value")+ 0.6*(maximum("value")-minimum("value"))THEN 'Medium'
WHEN "value" > minimum("value")+ 0.6*(maximum("value")-minimum("value")) AND "value" < minimum("value")+ 0.8*(maximum("value")-minimum("value"))THEN 'High'
ELSE 'Very high'
END