Poisson sampling - The adjusted and unadjusted estimator revisited

where yi = the value of interest for unit i n x X i e i , / π = is the probability of selecting unit i based on a covariate x n i , is the achieved sample size with expected sample size E n ne [ ] , = and X is the sum of all xi in the population. Grosenbaugh (1964) introduced 3-P sampling into the forestry literature as an alternative to Poisson sampling. He used a slightly biased estimator defined by