A Topical Dictionary of Statistics by Gary L. Tietjen

By Gary L. Tietjen

Statistics is the accredited physique of tools for summarizing or describing info and drawing conclusions from the precis measures. every person who has information to summarize hence wishes a few wisdom of information. 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 presents additionally the context, purposes, and comparable terminology. The meant viewers falls into 5 teams with fairly diverse wishes: (1) expert statisticians who have to keep in mind a definition, (2) scientists in disciplines except statistics who want to know the suitable equipment of summarizing information, (3) scholars of records who have to increase their knowl­ fringe of their subject material and make consistent connection with it, (4) managers who should be interpreting statistical stories written by way of their staff, and (5) newshounds who have to interpret executive or clinical experiences and transmit the data to the public.

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05 for. a discrete distribution. We reject the null hypothesis if the observed number of successes in n trials is less than tl or greater than t2 • The sign test is a binomial test with p = 112. We can use it to test whether the p-th quantile is equal to a specified value. It is then called the quantile test. d. A possible form of non independence is correlation between consecutive observations, called serial correlation or autocorrelation, meaning that observations a distance of k units apart are correlated.

For the same reason, (T2 is a scale parameter. In the gamma distribution the parameter r is a shape parameter. :; a+'A) for all 'A> and all a. An estimator is most concentrated if it is more concentrated than any other estimator. Most concentrated estimators do not generally exist. The estimator T' is Pitnuin closer than T if p(lT' - al < IT - al) ;:,: 1/2 for all S. An estimator is Pitman closest if it is Pitman closer than any other estimator of S. We now classify several types of estimators according to the method used in finding them.

F(x» , and n+l n+l p is the cdf. In small samples the optimal weights are derived from the expected values and covariances of the order statistics. An R-estimator (for ranks) is a solution of 'i, sgn(Xj - A) r [R(IX j - AI)/ (n+ 1)] = 0, where r(u) = 1(112 + ul2), R(u) is the rank of u, and sgn is the signum function. The most efficient score function is leu) = (-f (x)! f(x)(P-\u». We now proceed to interval estimation, which consists of obtaining a pair of estimators to serve as the endpoints of a random interval in which the parameter will lie with some stated probability.

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