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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.
A simple algorithm to generate a permutation of n items uniformly at random without retries, known as the Fisher–Yates shuffle, is to start with any permutation (for example, the identity permutation), and then go through the positions 0 through n − 2 (we use a convention where the first element has index 0, and the last element has index n − 1), and for each position i swap the element ...
The example includes link to a matrix diagram that illustrates how Fisher-Yates is unbiased while the naïve method (select naïve swap i -> random) is biased. Select Fisher-Yates and change the line to have pre-decrement --m rather than post-decrement m--giving i = Math.floor(Math.random() * --m);, and you get Sattolo's algorithm where no item ...
This gives "2343" as the "random" number. Repeating this procedure gives "4896" as the next result, and so on. Von Neumann used 10 digit numbers, but the process was the same. A problem with the "middle square" method is that all sequences eventually repeat themselves, some very quickly, such as "0000".
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 .
An analogy for the working of the latter version is to sort a deck of cards by throwing the deck into the air, picking the cards up at random, and repeating the process until the deck is sorted. In a worst-case scenario with this version, the random source is of low quality and happens to make the sorted permutation unlikely to occur.
Quickselect was presented without analysis by Tony Hoare in 1965, [41] and first analyzed in a 1971 technical report by Donald Knuth. [11] The first known linear time deterministic selection algorithm is the median of medians method, published in 1973 by Manuel Blum, Robert W. Floyd, Vaughan Pratt, Ron Rivest, and Robert Tarjan. [5]
This is especially noticeable in scripts that use the mod operation to reduce range; modifying the random number mod 2 will lead to alternating 0 and 1 without truncation. Contrarily, some libraries use an implicit power-of-two modulus but never output or otherwise use the most significant bit, in order to limit the output to positive two's ...