Assign an age to a person based on known population average but no Date of birth - sql

Question

I would like to use Postgres SQL to assign an age category to a list of househoulds, where we don't know the date of birth of any of the family members.
Dataset looks like:
household_id
household_size
x1
5
x2
1
x3
8
...
...
I then have a set of percentages for each age group with that dataset looking like:
age_group
percentage
0-18
30
19-30
40
31-100
30
I want the query to calculate overall what will make the whole dataset as close to the percentages as possible and if possible similar at the household level(not as important). the dataset will end up looking like:
household_id
household_size
0-18
19-30
31-100
x1
5
2
2
1
x2
1
0
1
0
x3
8
3
3
2
...
...
...
....
...
I have looked at the ntile function but any pointers as to how I could handle this with postgres would be really helpful.

Answer 1

I didn't want to post an answer with just a link so I figured I'll give it a shot and see if I can simplify depesz weighted_random to plain sql. The result is this slower, less readable, worse version of it, but in shorter, plain sql:
CREATE FUNCTION weighted_random( IN p_choices ANYARRAY, IN p_weights float8[] )
RETURNS ANYELEMENT language sql as $$
select choice
from
( select case when (sum(weight) over (rows UNBOUNDED PRECEDING)) >= hit
then choice end as choice
from ( select unnest(p_choices) as choice,
unnest(p_weights) as weight ) inputs,
( select sum(weight)*random() as hit
from unnest(p_weights) a(weight) ) as random_hit
) chances
where choice is not null
limit 1
$$;
It's not inlineable because of aggregate and window function calls. It's faster if you assume weights will only be probabilities that sum up to 1.
The principle is that you provide any array of choices and an equal length array of weights (those can be percentages but don't have to, nor do they have to sum up to any specific number):
update test_area t
set ("0-18",
"19-30",
"31-100")
= (with cte AS (
select weighted_random('{0-18,19-30,31-100}'::TEXT[], '{30,40,30}')
as age_group
from generate_series(1,household_size,1))
select count(*) filter (where age_group='0-18') as "0-18",
count(*) filter (where age_group='19-30') as "19-30",
count(*) filter (where age_group='31-100') as "31-100"
from cte)
returning *;
Online demo showing that both his version and mine are statistically reliable.

Answer 2

A minimum start could be:
SELECT
household_id,
MIN(household_size) as size,
ROUND(SUM(CASE WHEN agegroup_from=0 THEN g ELSE 0 END),1) as g1,
ROUND(SUM(CASE WHEN agegroup_from=19 THEN g ELSE 0 END),1) as g2,
ROUND(SUM(CASE WHEN agegroup_from=31 THEN g ELSE 0 END),1) as g3
FROM (
SELECT
h.household_id,
h.household_size,
p.agegroup_from,
p.percentage/100.0 * h.household_size as g
FROM households h
CROSS JOIN PercPerAge p) x
GROUP BY household_id
ORDER BY household_id;
output:
household_id
size
g1
g2
g3
x1
5
1.5
2.0
1.5
x2
1
0.3
0.4
0.3
x3
8
2.4
3.2
2.4
see: DBFIDDLE
Notes:
Of course you should round the columns g to whole numbers, taking into account the complete split (g1+g2+g3 = total)
Because g1,g2 and g3 are based on percentages, their values can change (as long as the total split is OK.... (see, for more info: Return all possible combinations of values on columns in SQL )