同样错一格，低估更贵时该预测哪个数？

"""Exact empirical pinball minimizer intervals with ties."""
from fractions import Fraction as F
import json
from pathlib import Path


def loss(values,q,tau):
    if not values or not 0<tau<1:
        raise ValueError('nonempty sample and 0<tau<1 required')
    return sum(tau*max(y-q,0)+(1-tau)*max(q-y,0) for y in values)/len(values)


def minimizers(values,tau):
    if not values or not 0<tau<1:
        raise ValueError('nonempty sample and 0<tau<1 required')
    ys=sorted(values); rank=len(ys)*tau
    if rank.denominator==1:
        k=int(rank)
        return ys[k-1],ys[k]
    k=(rank.numerator+rank.denominator-1)//rank.denominator
    return ys[k-1],ys[k-1]


def cdf_bracket(values,q):
    n=len(values)
    return F(sum(y<q for y in values),n),F(sum(y<=q for y in values),n)


def main():
    data=[F(1),F(2),F(4),F(8)]
    tied=[F(0),F(0),F(0),F(10)]
    rows=[]
    for label,values in [('distinct',data),('ties',tied)]:
        for tau in [F(1,4),F(1,2),F(3,4),F(9,10)]:
            lo,hi=minimizers(values,tau)
            optimum=loss(values,lo,tau)
            assert loss(values,hi,tau)==loss(values,(lo+hi)/2,tau)==optimum
            for q in [F(k,4) for k in range(-4,49)]:
                got=loss(values,q,tau)
                below,at=cdf_bracket(values,q)
                assert got>=optimum
                assert (got==optimum)==(lo<=q<=hi)==(below<=tau<=at)
                if tau==F(1,2):
                    mae=sum(abs(y-q) for y in values)/len(values)
                    assert got==mae/2
            rows.append(dict(dataset=label,tau=str(tau),interval=[str(lo),str(hi)],minimum=str(optimum)))
    assert minimizers(data,F(1,2))==(F(2),F(4))
    assert minimizers(tied,F(3,4))==(F(0),F(10))
    # Underprediction cost 3 and overprediction cost 1 give tau=3/4.
    q=F(5); tau=F(3,4)
    costs=sum(3*max(y-q,0)+max(q-y,0) for y in data)/len(data)
    assert costs==4*loss(data,q,tau)
    rejected=0
    for values,tau in [([],F(1,2)),(data,F(0)),(data,F(1)),(data,F(-1))]:
        try: minimizers(values,tau)
        except ValueError: rejected+=1
    assert rejected==4
    report=dict(datasets=dict(distinct=list(map(str,data)),ties=list(map(str,tied))),results=rows,
        grid_checks=2*4*53,cost_ratio=[3,1],invalid_rejections=rejected,checks_passed=True)
    Path('report.json').write_text(json.dumps(report,indent=2)+'\n',encoding='utf-8')
    for row in rows:
        print(f"{row['dataset']} tau={row['tau']}: minimizers=[{','.join(row['interval'])}], loss={row['minimum']}")
    print('tau=1/2 pinball=MAE/2; CDF bracket and 424 grid checks=PASS')
    print('report.json written')


if __name__=='__main__': main()