摘要:

An iterative procedure for making a life table is described, whereby a first draft, which can be very rough, is successively made to approach a final table, not dependent on the starting point, which meets a certain criterion of fidelity to the observations. At each successive table through which the process iterates an estimate is made of what the age-specific death rates in the actual population would be if that table were applicable, taking account of the rate of increase of the population as it is likely to affect the distribution within the five-year or other age groups. These age-specific rates are then compared with those observed, and an adjustment made for the next iteration. At most three iterations are sufficient to reproduce the observations to six places of decimals.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480866

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

A winning strategy is developed for the nine to oneside beton a Banker natural nine. Letnbe the number of cards that remain for play. Lettbe the number of nines that remain for play. Ifp(n, t) is the probability of a natural nine whennandtare given, thenp(n, t) is greater than 0.1 frequently enough to make the counting ofnandtthe basis for a practical winning strategy. The Kelly criterion (play to maximize the expected value of the log of capital) is used to determine bet sizes for favorable situations. Similar strategies are developed for the side bets on Banker natural eight, Player natural nine, and Player natural eight. The relationships between the four side bets are analyzed. It is shown that themain(roughly 1:1) bets on Banker and Player occasionally favor the player. There are theoretical favorable strategies but none exists which is currently practical.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480867

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

A technique frequently used in athletic competitions, the bestkof 2k— 1 comparison, is analyzed with a view toward its use in deciding between two alternative courses of action. The test is defined and, under a certain model, formulas for its expected duration and the variance of its duration are obtained both in the case where ties can occur and where ties cannot occur. A procedure for arriving at an optimum choice forkis presented for the case where ties cannot occur. The application of the test to situations in which ties can occur is discussed and a multi-level procedure is presented that could sometimes be useful in such situations.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480868

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

The behavior of the probability limits of differentk-class estimators under specification error is examined. Despite the fact that the probability limits are different when errors are not zero, it is shown that there exists no case in which either of the two leading estimators is uniformly more robust than the other if the criterion is any positive semi-definite quadratic form in the inconsistencies.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480869

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

The problem studied is that of utilizing measured concomitant information in sequential trials for the comparison of two treatments. The analysis is based on the treatment 1 minus treatment 2 response differencey=y1—y2and the corresponding concomitant observation differencex=x1—x2, wherexandyare assumed to be distributed bivariate normally. A simple asymptotically valid test procedure and its performance in Monte Carlo experiments are described. It is shown that appreciable covariance economy may be expected when ρ, the correlation coefficient between the (x, y) values, is high since average sample numbers are reduced by the factor (1 — ρ2) from those obtained in the absence of covariance.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480870

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

A simple mathematical relationship amongk-class estimators is demonstrated when a regression equation in a simultaneous system involves the regression of an endogenous variable (y0) on exogenous variables (x1, …,xλ) and on a single endogenous “independent” variable (y1). The relation is that given any set of observations on the relevant variables, we can calculate a constantk* and set of constantsb1*,ci*,hb1, andhci(i= 1, …, λ) such that any estimated coefficientsb1andciare related to the value ofkcorresponding to the estimating procedure by rectangular hyperbolas

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480871

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

A review of some of the steps the Bureau of Labor Statistics has taken to integrate the computer with its schedule screening processes is presented. The underlying principles which were used are explained and examples of their modifications in practice are analyzed. The author gives some suggestions for the future as derived from these attempts at automated quality control.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480872

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

Given a population ofNunits, it is required to draw a sample ofndistinct units in such a way that the probability πi, (i= 1, …,N) for theith unit to be in the sample is proportional to its ‘size’xi.One way to achieve this is as follows: TheNunits in the population are listed in a random order and theirxiare cumulated and a systematic selection ofnelements from a “random start” is then made on the cumulation. The mathematical theory associated with this procedure has been presented in [1], where with the help of asymptotic theory, compact expressions for the variance of the estimate of the population total are derived. These expressions contain probabilitiesPii′ (i≠i′i, i′ = 1, …,N) that unitsiandi′ both are in the sample. Forn= 2,N= 3 andn= 2,N= 4, exact formulae are derived in [1], but for othernandNonly approximate formulae are obtained. It is the purpose of this paper to derive an exact formula forPii′ for any values ofnandN.The argument makes use of the solution given in [1] for the casen= 2 andN= 4. The new formula forn= 2 is derived in Section 1 and illustrated in Section 2 by a numerical example forN= 10. An exact formula for generalnis derived in Section 3 and examplified in Section 4.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480873

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

A general rule is proved for estimating the variance in multistage designs when the primary sampling units (psu's) are selected without replacement with unequal probabilities. The rule is used for variance estimation in the sampling scheme in which theN psu's in the stratum are split at random intongroups and onepsuis selected with probability proportionate to size within each group. The status of a simpler variance estimator is examined.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480874

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

It is shown that when a deterministic signal is observed in quasi-linear noise (herein defined), the usual estimate of the signal amplitude spectrum for a finite time interval converges uniformly and exponentially fast in probability to this spectrum as the length of the time interval becomes infinite. When the limiting amplitude spectrum exists, the estimate tends to this function exponentially fast but no longer uniformly, in general.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480875

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor