Book on probability proportional to size sampling Can anyone please  suggest a book to study probability proportional to size sampling with and without replacement and all its details ?

$\bullet$ Sampling Theory and Methods, S. Sampath, CRC Press, $2001.$
For most of the purpose pertaining to sampling survey, my study was based on Sampling Techniques by William Cochran but for the topic in question, I switched to the above book - it's not that Cochran didn't cover it. However, for me, it was bit of scattered and the treatment was not standard.
The author put forth a lucid exposition on unequal probability sampling, treating both thr $\sf PPSWR$ and $\sf PPSWOR$ cases explaining all the important relevant concepts: cumulative total method, Lahiri's method, Desraj ordered estimator, Midzuno scheme, PPS systematic scheme. The derivations are concise without concealing or leaving any steps. One added advantage is that the author at the end provided solved theoretical problems which surely would be helpful for a beginner to comprehend the working and interplay of the concepts.
