A Topical Dictionary of Statistics by Gary L. Tietjen PDF

By Gary L. Tietjen

ISBN-10: 1461291682

ISBN-13: 9781461291688

ISBN-10: 1461319676

ISBN-13: 9781461319672

Statistics is the authorized physique of equipment for summarizing or describing facts and drawing conclusions from the precis measures. everybody who has facts to summarize hence wishes a few wisdom of records. step one in gaining that wisdom is to grasp the pro jargon. This dictionary is geared to supply greater than the standard string of remoted and self sufficient definitions: it offers additionally the context, purposes, and similar terminology. The meant viewers falls into 5 teams with quite assorted wishes: (1) expert statisticians who have to keep in mind a definition, (2) scientists in disciplines except records who want to know the suitable tools of summarizing info, (3) scholars of facts who have to develop their knowl­ fringe of their subject material and make consistent connection with it, (4) managers who might be studying statistical studies written through their staff, and (5) newshounds who have to interpret govt or medical stories and transmit the knowledge to the public.

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We say that the sequence converges to a point p if there is an N such that for all n>N, Xn is closer than E to p, where E is some small positive number. A sequence offunctionsfl(x),fz{x), ... converges pointwise to a functionj(x) if for every given Xo the sequence of pointsfl(xo),fz{xo), ... converges. That means that for any given x and E, there is an N such that for all n > N, lUx) - f(x) I < E. The value of N depends on the value of x and E chosen. If 1 value of N will work for the given E and for all x, the sequence converges uniformly to f(x).

In that case both the critical region and the test are described as uniformly most powerful. When a uniformly most powerful test does not exist, it may be possible to find a region close-in some sense-to the null hypothesis and a test T whose power is greater than that of any other test of the same size. The test T is then said to be locally most powerful. A family of densities fix;6) , where 6 lies in some interval, has a monotone likelihood ratio if there exists a function t(x I, . . , xn) such that the likelihood ratio L(6 1 )IL(6 2 ), for every 6, < 62 , is a monotone function of t.

Xn) , + C for all Xi and c; also, , a is + ais location c, ... , Xn scale + invariant c) = if 8(cxu ... , cXn) = c(8 X, ... , xn) for all Xi and positive c. e. ,J(x;8) can be written as hex - 8) for some hex). Specifically, 8 will equal zero. For 8 > 0, 8 is a scale parameter if the Estimation and Hypothesis Testing 33 distribution of xla is independent of a. That requires thatf(x;a) be expressible as (l/a)h(xla) for some density h(x) in which awill equal I. A shape parameter is a parameter in a pdf that is neither a location nor a scale parameter; it will affect the shape of the members of the family of distributions.

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A Topical Dictionary of Statistics by Gary L. Tietjen

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