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In mathematics, the ratio test is a test (or "criterion") for the convergence of a series. where each term is a real or complex number and an is nonzero when n is large. The test was first published by Jean le Rond d'Alembert and is sometimes known as d'Alembert's ratio test or as the Cauchy ratio test. [1]
exists there are three possibilities: if L > 1 the series converges (this includes the case L = ∞) if L < 1 the series diverges. and if L = 1 the test is inconclusive. An alternative formulation of this test is as follows. Let { an } be a series of real numbers. Then if b > 1 and K (a natural number) exist such that.
In evidence-based medicine, likelihood ratios are used for assessing the value of performing a diagnostic test. They use the sensitivity and specificity of the test to determine whether a test result usefully changes the probability that a condition (such as a disease state) exists. The first description of the use of likelihood ratios for ...
The likelihood-ratio test, also known as Wilks test, [2] is the oldest of the three classical approaches to hypothesis testing, together with the Lagrange multiplier test and the Wald test. [3] In fact, the latter two can be conceptualized as approximations to the likelihood-ratio test, and are asymptotically equivalent.
The subsampling scheme is commonly expressed as a three-part ratio J:a:b (e.g. 4:2:2) or four parts, if alpha channel is present (e.g. 4:2:2:4), that describe the number of luminance and chrominance samples in a conceptual region that is J pixels wide and 2 pixels high. The parts are (in their respective order):
Uniformly most powerful test. In statistical hypothesis testing, a uniformly most powerful (UMP) test is a hypothesis test which has the greatest power among all possible tests of a given size α. For example, according to the Neyman–Pearson lemma, the likelihood-ratio test is UMP for testing simple (point) hypotheses.
Reliability theory shows that the variance of obtained scores is simply the sum of the variance of true scores plus the variance of errors of measurement. [7] This equation suggests that test scores vary as the result of two factors: 1. Variability in true scores. 2.
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 ...
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