Add CI/SE, fix quantile for StratifiedSample

[iuliadmtru]

We made a lot of changes to the design lately but svyquantile was not tested. @sayantikaSSG can you write some tests for svyquantile? And maybe @smishr can take a look at the source code and update it.

[smishr]

Will look into this in next few days

[smishr]

The current quantile function doesnt quite work for both SimpleRandomSample or StratifiedSample.

In R:

`library(survey)
data(api)
srs = svydesign(id=~1, fpc = ~fpc, data=apisrs)
svyquantile(~enroll,srs,c(0.1,0.2,0.5,0.75,0.95))

$enroll
quantile ci.2.5 ci.97.5 se
0.1 247 213 276 15.97398
0.2 318 290 344 13.69199
0.5 453 413 531 29.91952
0.75 682 621 734 28.65175
0.95 1589 1293 1888 150.86539
attr(,"hasci")
[1] TRUE
attr(,"class")
[1] "newsvyquantile"

dstrat = svydesign(id=~1, strata=~stype,fpc = ~fpc, data=apisrs)
svyquantile(~enroll,dstrat,0.5)

$enroll
quantile ci.2.5 ci.97.5 se
0.1 267 196 328 33.46722
0.2 354 318 419 25.60749
0.5 639 570 734 41.58048
0.75 1135 1016 1410 99.89458
0.95 1888 1678 NaN NaN
attr(,"hasci")
[1] TRUE
attr(,"class")
[1] "newsvyquantile"`

But in Julia (after modifying the printing layout to be like R):
`
julia> apisrs = load_data("apisrs");

julia> srs = SimpleRandomSample(apisrs;popsize=:fpc);

julia> quantile(:enroll, srs, [0.1,0.2,0.5,0.75,0.95])
5×2 DataFrame
Row │ qth_quantile quantile
│ Float64 Float64
─────┼────────────────────────
1 │ 0.1 245.5
2 │ 0.2 317.6
3 │ 0.5 453.0
4 │ 0.75 668.5
5 │ 0.95 1473.1

julia> strat = load_data("apistrat");

julia> dstrat = StratifiedSample(strat, :stype; popsize=:fpc);

julia> quantile(:enroll, dstrat, [0.1,0.2,0.5,0.75,0.95])
5×2 DataFrame
Row │ qth_quantile quantile
│ Float64 Float32
─────┼────────────────────────
1 │ 0.1 307.882
2 │ 0.2 385.01
3 │ 0.5 712.02
4 │ 0.75 1305.98
5 │ 0.95 2130.95
`

Which means currently, only the median (0.5th qauntile) is coming correctly for SimpleRandomSample, no other quantiles, and nothing is correct for StratifiedSample. I checked that both R quantile and Julia Statistics.quantile use the same Type=7 default. Am investigating. I think there is some conflict in the method quantile that is being used, as Statistics and StatsBase have different definitions from what i could see.

https://docs.julialang.org/en/v1/stdlib/Statistics/#Statistics.quantile
https://juliastats.org/StatsBase.jl/stable/scalarstats/#Statistics.quantile

[smishr]

Further, R returns the CIs (default alpha = 0.05) and SE by default. This option should be investigated.

[smishr]

For now, quantile with StratifiedSample returns some form of quantiles, which I couldn't identify from the Hyndman and Fan defintions and their weighted versions applied in R.

[smishr]

Also, CI/SE havent been implemented yet

[smishr]

See #130 as well

[smishr]

We have stopped creating domain-specific functions like mean, total, or quantile for now, using arbitrary user defined functions now