R Under development (unstable) (2024-03-19 r86153 ucrt) -- "Unsuffered Consequences"
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> ## check poisson sampling
> library(survey)
Loading required package: grid
Loading required package: Matrix
Loading required package: survival

Attaching package: 'survey'

The following object is masked from 'package:graphics':

    dotchart

> data(api)
> set.seed(2021-7-15)
> apipop$prob<-apipop$api00/1000
> insample<-rbinom(nrow(apipop),1,apipop$prob)
> apipois<-apipop[insample,]
> des<-svydesign(id=~1, prob=~prob, pps=poisson_sampling(apipois$prob), data=apipois)
> 
> stopifnot(isTRUE(all.equal(
+  as.vector(SE(svytotal(~api00,design=des))),
+  as.vector(sqrt(sum( (apipois$api00*weights(des))^2*(1-apipois$prob))))
+  )))
>  
> 
> proc.time()
   user  system elapsed 
   1.76    0.34    2.04