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The sequential probability ratio test (SPRT) is a specific sequential hypothesis test, developed by Abraham Wald [1] and later proven to be optimal by Wald and Jacob Wolfowitz. [2] Neyman and Pearson's 1933 result inspired Wald to reformulate it as a sequential analysis problem. The Neyman-Pearson lemma, by contrast, offers a rule of thumb for ...
If the distance measure is a metric (and thus symmetric), the problem becomes APX-complete, [53] and the algorithm of Christofides and Serdyukov approximates it within 1.5. [54] [55] [10] If the distances are restricted to 1 and 2 (but still are a metric), then the approximation ratio becomes 8/7. [56]
For example, the ratio 4:5 can be written as 1:1.25 (dividing both sides by 4) Alternatively, it can be written as 0.8:1 (dividing both sides by 5). Where the context makes the meaning clear, a ratio in this form is sometimes written without the 1 and the ratio symbol (:), though, mathematically, this makes it a factor or multiplier .
Secretary problem. Graphs of probabilities of getting the best candidate (red circles) from n applications, and k / n (blue crosses) where k is the sample size. The secretary problem demonstrates a scenario involving optimal stopping theory [1][2] that is studied extensively in the fields of applied probability, statistics, and decision theory.
Sample size determination or estimation is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined ...
Newsvendor model. The newsvendor (or newsboy or single-period[1] or salvageable) model is a mathematical model in operations management and applied economics used to determine optimal inventory levels. It is (typically) characterized by fixed prices and uncertain demand for a perishable product. If the inventory level is , each unit of demand ...
Likelihood-ratio test. In statistics, the likelihood-ratio test is a hypothesis test that involves comparing the goodness of fit of two competing statistical models, typically one found by maximization over the entire parameter space and another found after imposing some constraint, based on the ratio of their likelihoods.
Pseudoreplication due to correlation of samples: without accounting for correlation the 90% confidence interval for the sample mean is much too small. To get around this problem for example the blocking method can be applied where correlated samples are first grouped, then the (for each block) the corresponding sample means are computed. From ...