Unequal probability sampling, Advanced Statistics

Unequal probability sampling is the sampling design in which the different sampling units in the population have different probabilities of being included in sample. The differing inclusion probabilities might result from some inherent feature of sampling process, or they might be deliberately imposed in order to attain better estimates by including 'more important' units with the higher probability. The unequal inclusion probabilities required to be accounted for in order to come up with the reasonable estimates of the population quantities. An instance of such a design is line-intercept sampling of the vegetation cover, in which the size of the patch of vegetation is measured whenever the randomly selected line intersects it. The larger the patch, the higher will be probabilities of inclusion in sample. This kind of sampling might be carried out by assigning to each unit the interval whose length is equal to the required probability and selecting random numbers from uniform distribution: a unit is involved if the random number is in its interval.

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