The equivalence between the length-biased and the random sampling on a non-negative, discrete random variable is established. The length-biased versions of the binomial and Poisson distributions are discussed.
Ratnaparkhi, Makarand V. and Naik-Nimbalkar, Uttara V.
"The Length-Biased Versus Random Sampling for the Binomial and Poisson Events,"
Journal of Modern Applied Statistical Methods: Vol. 12
, Article 10.
Available at: http://digitalcommons.wayne.edu/jmasm/vol12/iss1/10