Estimation of parameters in a truncated trivariate normal distribution

This paper gives maximum-likelihood estimators for certain parameters in a truncated trivariate normal distribution when the values of the other parameters are known. The estimators are functions of a random sample. Approximate variances and covariances of the estimators, when the sample size is large, are also given. The type of truncation considered is merely restriction of the range of one of the variates, whose true mean and variance are assumed to be known. Two cases of such restriction are treated: (a) ( x < + ); (b) (- <x '), where and ' are arbitrary cutoff points which are assumed to be known. A precise statement of the estimation problem is given in Section 1. Section 2 contains preliminary calculations. The estimators appear in Section 3. The asymptotic variances and covariances of the estimators are given in Section 4. The estimators and their asymptotic variances and covariances can be easily specialized to be suitable for the case of a certain truncated bivariate normal distribution (Sections 3 and 4).     

Теория нормативных предлозений

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O regułach rachunku zdań

Streszczenie Zmienn istotn wyraenia rachunku zda nazywam zmienn, której warto przy pewnym ukadzie wartoci innych zmiennych wpywa na warto caego wyraenia.     

О правилах исчисления предложе ий

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Prototetyka St. Lesniewskiego

Streszczenie Prototetyka St. Len'ewskiego jest uogólnieniem dwuwartociowego rachunku zda. Wystpuj w niej obok terminów tego rachunku funktory (zarówno stae jak i zmienne) tych wszystkich kategorii semantycznych, jakie mog by zdefiniowane, gdy punktem wyjcia jest kategor a zda.W pracy zreferowane s trzy systemy prototetyki. Terminem pierwotnym dwu z nich jest implikacja, terminem pierwotnym systemu trzeciego jest równowano. Systemy o terminie pierwotnym implikacji róni s. reguami wnioskowania. W jednym z nich obowizuje regua weryfikacji, w drugim regua ekstensjonalnoci. Pierwsza z tych regu jest uogólnieniem nastpujcej reguy rachunku zda, wzbogaconego o terminy 0 i 1:Wyraenie jest tez systemu, gdy tezami systemu s oba wyraenia powstae z przez podstawienie za pewn jego zmienn symboli 0 i 1.W myl reguy ekstensjonalnoci tezami systemu s prawa ekstensjonalnoci, sformuowane dla funktorów dowolnych kategorii semantycznych wac-wych prototetyce.W pracy podaj dowody równowanoci trzech systemów prototetyki i dowód ich zupenoci.Znaczna cz wyników Leniewskiego, zreferowanych w pracy, nie bya dotd opublikowana. Opracowujc te wyniki opieraem si na notatkach z wykadów Leniewskiego, spisanych przez jego uczniów. Oryginalne notatki Leniewskiego ulegy zniszczeniu w czasie powstania warszawskiego.     

A factor analysis of mechanical ability tests

The intercorrelations of thirty-seven variables, including the Minnesota battery of mechanical ability tests, the seven MacQuarrie tests of mechanical ability, O'Connor's Wiggly blocks, and the Stenquist picture-matching test, were analyzed by Thurstone's centroid method. Five factors, Perceptual, Verbal, Youth, Manual Agility, and Spatial, were taken out. Factors prominent in so-called mechanical ability tests are the Spatial and Perceptual ones with Mac-Quarrie's dotting test significantly high in the Manual Agility factor. Each of the factors can be measured with group pencil-and-paper tests.Acknowledgment is gratefully made to the State Engineering Experiment Station at the Georgia School of Technology for sponsoring and financially supporting the studies; to the Graduate Research Committee of the University of Illinois for providing funds for the purchase of tests and the tabulation of data; and to Dr. E. L. Welker of the University of Illinois Mathematics Department for assistance with statistical problems.     

Synthesis of variance

The distribution of a linear combination of two statistics distributed as is Chi-square is studied. The degree of approximation involved in assuming a Chi-square distribution is illustrated for several representative cases. It is concluded that the approximation is sufficiently accurate to use in many practical applications. Illustrations are given of its use in extending the Chi-square, the Student t and the Fisher z tests to a wider range of problems.     

A simplified method for approximating multiple regression coefficients

A method of exhaustion has been described for calculating regression coefficients. This method dispenses with the solution of simultaneous equations but utilizes a process of successive extraction in obtaining's, where each successive is maximized. This procedure permits the worker to discard as he goes along those weights which are deemed unsatisfactory for purposes of prediction. The coefficients and theR in a problem involving a criterion and six independent variables were calculated in sixty minutes. TheR's obtained by this method are smaller than those yielded by the Doolittle technique, but in problems which have been considered this discrepancy has not exceeded .05.     

A technique for facilitating the rotation of factor axes,based on an equivalence between persons and tests

A technique is outlined which may facilitate the rotation of factor axes to a meaningful position. It is based on certain relationships between the results of test and person factor analysis, and consists essentially of supplementing the test factor space with tests which are thetest-equivalents of persons or groups of persons. These persons may be, for instance, well-known types in the domain being investigated, or even freaks. The ways in which these persons may be selected and used to determine the final rotated position of the factor axes is discussed.     

Over de Zedelijke Beoordeeling van Oorlog

Fragment uit het hoofdstukOorlog en Vrede van het boek Neen en Ja, in Mei verschijnend bij H. J. Paris, Amsterdam.     

An analytical solution for approximating simple structure in factor analysis

It is proposed that a satisfactory criterion for an approximation to simple structure is the minimization of the sums of cross-products (across factors) ofsquares of factor loadings. This criterion is completely analytical and yields a unique solution; it requires no plotting, nor any decisions as to the clustering of variables into subgroups. The equations involved appear to be capable only of iterative solution; for more than three or four factors the computations become extremely laborious but may be feasible for high-speed electronic equipment. Either orthogonal or oblique solutions may be achieved. For illustrations, the Johnson-Reynolds study of flow and selection factors and the Thurstone box problem are reanalyzed. The presence of factorially complex tests produces a type of hyperplanar fit which the investigator may desire to adjust by graphical rotations; the smaller the number of such tests, the closer the criterion comes to approximating simple structure.     

The act of surrender in the treatment of the alcoholic

The success of A. A. in the alleviation of alcoholism has provided psychiatrists with a rich source of clinical material for a study of the religious process. The paper which follows is a discussion of one aspect of that process, namely, the act of surrender. It was prepared for a psychiatric audience; it may have some pertinence for the pastoral group since it represents at least an effort at understanding the religious life. Fully aware of its deficiencies, I offer the paper in the hope that it may seem to contain a measure of truth and be of some value to pastors in their relationships with their parishioners.This article is reprinted from Quarterly Journal of Studies on Alcohol, June, 1949 where it appeared under the title The Act of Surrender in the Therapeutic Process, by permission of author and publisher.s     

Der Faktor der Umstrukturierung und 2 Tests zu seiner Messung

Zusammenfassung Mit der hohen Korrelation zwischen einem visuellen und einem verbalen Test wurde die Existenz eines Faktors in der Wahrnehmung bzw. im Denken nachgewiesen, den man Verfügbarkeit von motorischen Schematen oder kurz B-Faktor nennen könnte.     

A re-analysis of a test of the theory of two factors

The study of William Brown and William Stephenson, A Test of the Theory of Two Factors, is re-analyzed by means of the Thurstone multiple factor methods. No tests or correlations are left out of the original table of correlations as is done in the original analysis in an attempt to validate the two-factor theory. Space, verbal, and perceptual speed factors similar to those found by Thurstone, Wright, and Garrett are identified. A common factor of Maturation is postulated to account for the remaining communality of the tests. A fifth factor is considered to have no significance due to the small amount of variance which it contributes to the total.Master's Thesis, University of Chicago, Department of Psychology, 1939.     

A factor analysis of intra-task performance on two psychomotor tests

There are indications that even during the short time of administration of a single psychomotor test, the ability or abilities sampled may shift materially in importance. It then becomes important to know the stages in which these fluctuations occur, the stage at which the test is most complex, and the stage at which the test most nearly measures one ability at a time. This paper describes an application of factorial methods to this problem. Factor analysis of inter-trial correlations on two models of the Rudder Control Test revealed three factors, Steadiness-Control, Precision of Movement, and Strength. The same factor pattern was confirmed in a separate factor analysis on another sample in which the order of administration of the tests was reversed. Implications are pointed out for future psychomotor test development.Perceptual and Motor Skills Research Laboratory, Lackland Air Force Base, San Antonio, Texas. The opinions or conclusions contained in this report are those of the author. They are not to be construed as reflecting the views or indorsement of the Department of the Air Force.     

In de Schaduwen van Gisteren

Ohne ZusammenfassungNoot van de Red.:Prof. Huizinga, wien wij het hier volgende artikel van Prof. Mannoury ter inzage zonden, deelt ons mede, dat hij van de aangeboden gelegenheid, op dit hem in meer dan één opzicht sympathieke artikel te repliceeren, geen gebruik zal maken.     

The measurement of conformity

Allport'sJ-curve hypothesis of conforming behavior and its attendant treatment of appropriate data are criticized on the following points: (1) narrowness of application; (2) flexibility of interpretation of results; (3) arbitrary selection of a criterion of conformity; (4) lack of a means by which the extent of conformity in one situation can be compared with that in another; (5) inequality of telic units. As an alternative treatment of such data, the method of higher moments is suggested and rationalized. Data from Allport and Solomon are reworked by this method and results compared.     

An I.B.M. technique for the computation of ΣX 2 and ΣXY

Given I.B.M. cards punched with scores (or any numbers)—but not their squares—a method is presented of tabulating them (on the No. 405 alphameric I.B.M. tabulator) so as to obtain the sum of squares. The technique is also adaptable to summation of cross-products. The principle is an extension of the Mendenhall-Warren-Hollerith technique of vertical progressive digiting, without the necessity of manual addition or summary-punching, and is designed for machines not equipped with the card cycle total transfer device or progressive total device. Use is made of counter rolling. Efficient use of machine capacity is made only when intercorrelations between no more than two variables are requiredin addition to sums of squares. A resumé of some techniques now commonly employed is included.The author is indebted to Dr. Paul Dwyer, Associate Professor of Mathematics, University of Michigan, for valuable criticism of the original draft; and to Mr. Alan Meacham, in charge of the University's Tabulating Station, for testing the method.     

Het Belang van de Taalkundige Psychologie

Uit de Rede uitgesproken bij de aanvaarding van het ambt van buitengewoon hoogleeraar in de zedekunde en de wijsbegeerte van den Godsdienst aan de Universiteit van Amsterdam, op 28 September 1939.In druk verschenen bij H. J. Paris, Amsterdam.