  In this research paper, we address the Distinct Elements estimation problem
in the context of streaming algorithms. The problem involves estimating the
number of distinct elements in a given data stream $\mathcal{A} = (a_1,
a_2,\ldots, a_m)$, where $a_i \in \{1, 2, \ldots, n\}$. Over the past four
decades, the Distinct Elements problem has received considerable attention,
theoretically and empirically, leading to the development of space-optimal
algorithms. A recent sampling-based algorithm proposed by Chakraborty et
al.[11] has garnered significant interest and has even attracted the attention
of renowned computer scientist Donald E. Knuth, who wrote an article on the
same topic [6] and called the algorithm CVM. In this paper, we thoroughly
examine the algorithms (referred to as CVM1, CVM2 in [11] and DonD, DonD' in
[6]. We first unify all these algorithms and call them cutoff-based algorithms.
Then we provide an approximation and biasedness analysis of these algorithms.
