Sampling without replacement: History and applications (Q1862654)

The problem of sampling without replacement is being traced back until the Jewish Torah and the Talmud. In 1657 Christian Huygens was the first to formulate this problem mathematically. Other special cases were considered by Jacob Bernoulli (1713) and by Abraham de Moivre (1756). Mathematical formulas were given by Pierre Simon Laplace when he initiated scientific sample studies of the population, and by Michail Vasilievich Ostrogradsky (1848) when he examined the foodstuffs supplied to the armed forces. The contributions of A. R. Luchterhandt (1842) in a still unpublished memoir had still one of the formulas and he noted that Siméon Denis Poisson could have well derived the same formula. In 1877 Eugène C. Catalan formulated an extremely general theorem, about the same time Joseph Louis François Bertrand was also concerned with this problem. Applications are being mentioned to games such as blackjack, to select pieces of meal to be kosher, to draft lotteries in the army forces, to statistical inspections of mass manufactured commodities, to opinion surveys. Illustrations are given showing that the fairness of drawing without replacement was being questioned. At the end of the 19th century Wilhelm Lexis begun his studies of the stability of statistical series, hereby he attempted to distinguish whether a statistical series was or was not composed of outcomes of independent Bernoulli trials. Alexandr Alexandrvich Chuprov developed and finally largely refuted the Lexian criterion. 24 references.