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Survey methodology textbooks generally consider simple random sampling without replacement as the benchmark to compute the relative efficiency of other sampling approaches. [3] An unbiased random selection of individuals is important so that if many samples were drawn, the average sample would accurately represent the population.
Reservoir sampling is a family of randomized algorithms for choosing a simple random sample, without replacement, of k items from a population of unknown size n in a single pass over the items. The size of the population n is not known to the algorithm and is typically too large for all n items to fit into main memory. The population is ...
Sampling schemes may be without replacement ('WOR' – no element can be selected more than once in the same sample) or with replacement ('WR' – an element may appear multiple times in the one sample). For example, if we catch fish, measure them, and immediately return them to the water before continuing with the sample, this is a WR design ...
In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of successes (random draws for which the object drawn has a specified feature) in draws, without replacement, from a finite population of size that contains exactly objects with that feature, wherein each draw is either a success or a failure.
A 1-way tournament (k = 1) selection is equivalent to random selection. There are two variants of the selection: with and without replacement. The variant without replacement guarantees that when selecting N individuals from a population of N elements, each individual participates in exactly k tournaments.
A random sample can be thought of as a set of objects that are chosen randomly. More formally, it is "a sequence of independent, identically distributed (IID) random data points." In other words, the terms random sample and IID are synonymous. In statistics, "random sample" is the typical terminology, but in probability, it is more common to ...
binomial distribution: the distribution of the number of successful draws (trials), i.e. extraction of white balls, given n draws with replacement in an urn with black and white balls. [3] Hoppe urn: a Pólya urn with an additional ball called the mutator. When the mutator is drawn it is replaced along with an additional ball of an entirely new ...
An inefficient brute-force method for sampling without replacement could select from the numbers between 1 and n at every step, retrying the selection whenever the random number picked is a repeat of a number already selected until selecting a number that has not yet been selected. The expected number of retries per step in such cases will ...