Aggarwal (2006) studied this problem and showed that by altering the sampling probability (f (n, k) in Algorithm 1) in the reservoir sampling algorithm, it is possible to achieve different agerelated biases in the sample.
he showed that by setting the sampling probability to the constant function f (n, k) = k/β, it is possible to approximately achieve exponential bias in the sample with scale parameter β (Aggarwal, 2006).