Operations Research · 1961 · 727 citations · 5 references
Natural SciencesMathematicsProbability TheoryStatisticsStochastic ModelingComputational StatisticsInferential StatisticsMethod Of MomentsProbability DistributionsRandom VariablesMoment EstimationMomentsVariances
The study concerns jointly normal random variables, noting that existing tables assume independence with equal means and variances, while the problem becomes cumbersome for more than two variables. The authors aim to calculate or approximate the maximum of these variables, providing formulas and tables for the general case with n = 2 and approximations for n > 2. They approximate moments by iterating a three‑parameter computation or by successive use of a three‑parameter table, which is supplied. Recent applications of the theory are described.
The variables ξ 1 , …, ξ n have a joint normal distribution. We are concerned with the calculation or approximation of max(ξ 1 , …, ξ n ). Current analyses and tables handle the case in which the ξ ı are independently distributed with common expected values and common variances. This paper presents formulas and tables for the most general case with n = 2. When n > 2, the problem becomes cumbersome. This paper presents formulas and tables that permit approximations to the moments in case n > 2. The moments are approximated by iteration of a three-parameter computation or, alternatively, through successive use of a three-parameter table, which is given. Recent applications of the theory are described.
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MOMENTS OF ORDER STATISTICS FROM A NORMAL POPULATION
R. C. Bose, Shanti S. Gupta · Biometrika · 1959 · 47 citations · Full text