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The lack of memory property of the exponential distribution plays an important part in the branch of applied probability. This property assumes the information regarding the probability distribution. In the present paper we give a characteristic property of the exponential distribution based on the means of the conditional distributions. Considering a random variable T with finite mean and such that P(T > O) > 0, and denoting by y a positive number such that P(T > y) > 0, we show that T has an exponential distribution if and only if the mean of the conditional distribution, given T > y, exceeds the mean of the unconditional distribution by the quantity y for all y. Also given in the paper is a similar characterization for the geometric distribution. Since the information concerning the expected values is easily accessible, we expect these properties to be useful in dealing with the practical problems. [ABSTRACT FROM AUTHOR]

The article discusses moments of the distribution of sample size, N in a sequential probability ratio test (SPRT). The present paper provides variance, the third and the fourth moments of N. The details are worked out in five common applications of the SPRIT. The relation of the variance of N to the truncation of a SPRT is discussed is also discussed in the paper. Scholar A. Wald indicated in passing how one can obtain the moments of N, but the only published literature where the author encountered a general expression for the variance of N. However, their expression is incorrect. Using scholar J. Wolfowitz's results, which they do, or differentiating Wald's, fundamental identity twice one gets provided. In many practical applications of the SPRT, μ and moments in an equation derived are differentiable functions of a real-valued parameter. The limiting expressions for the moments can then be determined by standard methods of mathematical analysis. However, for the third and fourth moments the actual technique may involve an excessive amount of arithmetic.

In an earlier paper [5] the authors compared the power of the BLUS test with the probability of a correct decision of the Durbin-Watson bounds test. A method to compute the distribution of the Von Neumann ratio under the null hypothesis and under the alternative hypothesis was given. In the present paper the latter method is used to tabulate the BLUS-test statistic and to compute the exact significance points of the Durbin-Watson test for several examples. Powers of both tests are computed and compared. It appears that, for the cases considered, the power of the exact Durbin-Watson test exceeds that of the BLUS procedure, while the latter is greater than the probability of a correct decision in the Durbin-Watson bounds test. [ABSTRACT FROM AUTHOR]

This paper concerns a new Normal approximation to the beta distribution and its relatives, in particular, the binomial, Pascal, negative binomial, F, t, Poisson, gamma, and chi square distributions. The approximate Normal deviates are expressible in terms of algebraic functions and logarithms, but for desk calculation it is preferable in most cases to use an equivalent expression in terms of a function specially tabulated here. Graphs of the error arc provided. They show that the approximation is good even in the extreme tails except for beta distributions which are J or U shaped or nearly so, and they permit correction to obtain still more accuracy. For use beyond the range of the graphs, some standard recursive relations and some classical continued fractions are listed, with some properties of the latter which seem to be partly new. Various Normal approximations are compared, with further graphs. The new approximation appears far more accurate than the others. Everything an ordinary user of the approximation might want to know is included in this paper. The theory behind the approximation and most proofs are postponed to a second paper immediately following this one. [ABSTRACT FROM AUTHOR]

In this paper a method is developed for estimating the parameters in the multivariate normal distribution in which the missing observations are not restricted to follow certain patterns as in most previous papers. The large sample properties of the estimators are discussed. Equivalence with maximum likelihood estimators has been established for a subclass of problems. The results of some simulation studies are provided to support the theoretical development. [ABSTRACT FROM AUTHOR]

The 1967 Committee on Publications, chaired by David L. Wallace, found that many American Statistical Association members desired more review and survey papers. These have been hard to come by and so as the author's last act before leaving office, decided to provide a short survey paper on some related ideas in a field where nearly all of the statisticians sometimes work — that of contingency tables. These ideas are largely available in literature and yet they have not often been put together, though statisticians I. J. Good's monograph and Leo Goodman's many papers form good sources. But the author's paper is not intended as a review of the literature, only as a survey of one set of ideas about estimation in the analysis of contingency tables. The author fears that the first act of most social scientists upon seeing a contingency table is to compute chi-square for it. Sometimes this process is enlightening, sometimes wasteful, but sometimes it does not go quite far enough. The author collected 500 samples of writing published about 1961.

Given N points independently drawn from the uniform distribution on (0, 1), let p[sub n], be the size of the smallest interval that contains n out of the N points; let n[sub p], be the largest number of points to be found in any subinterval of (0, 1) of length p. This paper uses a result of Karlin, McGregor, Barton and Mallows to determine the distribution of n[sub p] for p = 1/k, k an integer. The paper gives simple determinations for the expectations and variances of p[sub n], for all fixed n > (N + 1)/2, and of n[sub 1/2]. The distribution and expectation of n[sub p] are estimated and tabulated for the cases p = 0.1(0.1)0.9, N =2(1)10. [ABSTRACT FROM AUTHOR]

Various methods based on Student t variates have been suggested and used for obtaining simultaneous confidence intervals for several means, or for several contrasts among means. Determination of an overall confidence level for such intervals involves evaluating the probability mass of a multivariate t distribution over a hypercube centered at the origin, with sides paralleling the coordinate planes, or obtaining bounds for this probability mass. Since such distributions involve many nuisance parameters, an impossible number of tables would be necessary in order to make exact confidence intervals. In the virtual absence of tables, approximations and bounds become important. In this paper, an attempt has been made to investigate the adequacy of certain suggested approximations [2], [5], [8] by computing the exact distributions for some particular cases. These exact distributions have been compared with approximations. This paper is concerned with two-sided confidence intervals, rather than one-sided intervals. [ABSTRACT FROM AUTHOR]

This paper deals with the asymptotic relative efficiency (A.R.E.) and the asymptotic power of certain tests. These tests are distribution-free goodness-of-fit tests based on the empirical distribution function. They are the one and two sided Kolmogorov-Smirnov tests and a new one based on the absolute values of the order statistics. The method of obtaining the A.R.E. is due to Quade [5] and is outlined in Section 1. In this paper we are concerned with the case of scalar alternatives. The asymptotic power for the Kolmogorov-Smirnov tests is obtained in Section 2. Section 3 deals with a new test which allows a more facile use of a one-sided statistic while utilizing the same information normally included in a two-sided statistic. In Section 4, three examples are considered to illustrate the superiority of this new test. [ABSTRACT FROM AUTHOR]

The principal part of this paper is devoted to the study of the distribution and density functions of the ratio of two normal random variables. It gives several representations of the distribution function in terms of the vivariate normal distribution and Nicholson's V function, both of which have been extensively studied, and for which tables and computational procedures are readily available. One of these representations leads to an easy derivation of the density function in terms of the Cauchy density and the normal density and integral. A number of graphs of the possible shapes of the density are given, together with an indication of when the density is unimodal or bimodal. The last part of the paper discusses the distribution of the ratio (u[sub 1] + ... + u[sub n])/(v[sub I] + ... + v[sub m]) where the u's and v's are independent, uniform variables. The exact distribution for all n and m is given, and some approximations discussed. [ABSTRACT FROM AUTHOR]

The use of simulation, as a technique for attacking difficult problems, has increased greatly with the availability of the digital computer. This is illustrated by the large number of references in Shubik's (1960) bibliography[sup 2] and in the large number of studies published since then. Simulation is essentially an extension of a technique known as empirical sampling, or distribution sampling, which has been used in the field of statistics for many years. The limitations of the technique, which are well known to statisticians, are apparently not as well known, or at least not as well recognized, by those using simulation today. The first part of this paper contains an historical survey of distribution sampling as used by statisticians. The material was originally prepared in 1953 and is reproduced here in slightly revised form to bring this history to the attention of present day simulators in order that the lessons that can be learned from this part can more readily be incorporated in the development of methodology today. The second part of this paper discusses the relevance of empirical sampling to the present day state of the art of simulation. The technique of generating random members, developed for empirical sampling can be applied directly to simulation. However in other aspects simulation is more difficult than empirical sampling and here the theory of distribution sampling does not have much to offer. The difficulties are due to lack of independence among time series, non-stationarity of the time series, and the large number of parameters. [ABSTRACT FROM AUTHOR]

In 1965 Stanley Warner [8] illustrated a technique whereby one could estimate from a sample the proportion of persons in a population possessing some characteristic X, without pointedly asking the question, "Do you possess characteristic X?". The present article uses a variation of these ideas suggested by Warner in a later paper [7] to estimate the distribution function of a continuous-type random variable. The technique is illustrated by estimating an income distribution from the responses of a sample of 500 individuals. The potential use of devices of this type in maintaining confidentiality of existing data files is apparent. [ABSTRACT FROM AUTHOR]

The decision-theoretic approach to point estimation involves the choice of an estimate to minimize the expected loss associated with the estimate. The purpose of this paper is to indicate the influence of risk aversion on point estimates for classes of payoff functions including the piecewise linear and quadratic payoff functions. Increased risk aversion results in a point estimate closer to zero for a quadratic pay. off function and a lower estimate with a piecewise linear payoff function, for example. [ABSTRACT FROM AUTHOR]

This paper proposes several methods of estimating parameters in stable distributions. All the methods involve sample characteristic functions. One of the methods which is based upon the method of moments is treated in some detail. Asymptotic normal distributions for the proposed moment estimators are provided. Moreover, all methods provide consistent estimators. The estimation problem is treated for both univariate and multivariate stable distributions. [ABSTRACT FROM AUTHOR]

The article presents information on a nomogram for the "Student"-fisher t test. A nomogram is given for estimating the probability (P) for a given value of the "Student"-Fisher t test. W.S. Gosset, an employee of the Guiness brewing company in Dublin, published papers in 1908 in which he correctly solved three problems: the probable error of a mean, the distribution of the mean divided by its estimated standard deviation and the distribution of the estimated correlation coefficient between independent variates. Later "Student" and economist R.A. Fisher calculated tables of the relevant t distribution and Fisher gives a table of t and probabilities, corresponding to various degrees of freedom. Fisher and F. Yates, scholar provide in addition a column for P. It seemed that presentation of the P, degrees of freedom, t relationship in the form of a nomogram would be advantageous. It makes possible a fairly exact estimate of probabilities less than 0.0001 and makes it possible to get an estimate of P for any value of t from 1 to 65, instead merely of selected values.

In this paper methods for obtaining approximations and bounds for the moments of order statistics from a continuous parent distribution are discussed. These bounds and approximations depend on the distribution function only through certain moments of order statistics in small samples. It is shown that for the Cauchy distribution bounds and approximations of all finite moments can be obtained. Some numerical calculations for normal and Cauchy distributions are also given. [ABSTRACT FROM AUTHOR]

This paper uses a family of bivariate extreme-value distributions to estimate the probability of a large exceedance of a random variable given that a certain other random variable not independent of the first has exceeded a certain value. A simple method of reasonably good efficiency is given for estimating a bivariate extreme-value distribution from independent bivariate samples. The method is used to analyze the performance of a spacecraft command receiver which has an indication of data quality so that commands likely to be in error can be rejected. [ABSTRACT FROM AUTHOR]

Maximum likelihood and other BAN estimators have been shown to possess certain optimal asymptotic properties in estimating the parameters of probability distributions satisfying specific regularity conditions. The subject of non-regular estimation is concerned with problems in which these conditions do not hold. In many such problems, classical-lower bounds on the variance of unbiased estimators, such as the Cramer-Rao bound, lead to the trivial result V(t) * (These characters cannot be converted in ASCII text) 0, where t is any unbiased estimator. A number of alternative bounds for application in the non-regular case have been derived. In this paper previous results of this type are reviewed and an additional bound is given. The specific applications of interest involve estimation of a location parameter. Applications of the bounds to the exponential, uniform and Pearson Type III distributions are investigated. [ABSTRACT FROM AUTHOR]

In the early years of the eighteenth century A. De Moivre, N. Bernoulli, and P. R. Montmort found three solutions for the following problem of games of chance: Two players, A and B, play a series of games. In each game, independently of the others, either A wins a counter from B with probability p or B wins a counter from A with probability q (p + q = 1). The series ends if either A wins a total number of a counters from B or B wins a total number of b counters from A. What is the probability that A wins the series in at most n games? Denote this probability by P[sub n](a,b). In this paper simple and elementary proofs are given for the various formulas for P[sub n](a,b). Furthermore, it is shown how these formulas can be applied in the theories of order statistics, random walks, storage, queues, Brownian motion, and dams. [ABSTRACT FROM AUTHOR]

Let X[sub (1)] is less than or equal to X[sub (2] is less than or equal to ... is less than or equal to X[sub (n)] be an ordered sample of a random variable X which has continuous probability distribution function F (x), and let F[sub n] (x) be the corresponding empirical distribution function. The following three statistics, introduced by A. Renyi, are considered: [Multiple line equation(s) cannot be represented in ASCII text] The paper presents table of exact probabilities for these statistics for finite sample sizes. The limiting distributions of these statistics for sample size n arrow right Infinity are discussed, and sample sizes are indicated for which these limiting distributions can be used instead of the exact distributions. Numerical examples for the use of the tables are presented, as well as applications to testing hypotheses on life distributions and to one-sided estimation of probability distribution functions from censored data. [ABSTRACT FROM AUTHOR]

Tests for randomness are described, when the data consists of points on the circumference of a unit circle, and the alternative to the uniform distribution (randomness) is either a unimodal or a bimodal distribution: the yon Mises distribution or an adaptation. Tables of significance points are given for the test statistics, and the power is used to give a table of sample sizes needed to detect a given degree of clustering, measured by the parameters of the distributions. This paper is a close parallel, for two dimensions, to Stephens [15], which gave corresponding tests and tables for three dimensions. [ABSTRACT FROM AUTHOR]

This paper deals with certain aspects of variance-component estimation for the unbalanced two-way completely-random classification where the numbers of observations in the subclasses are treated as random variables not necessarily independent of some of the random effects of the model. General results are given on the expectations of two commonly-used estimators of the vector of variance components. Numerical approximations are presented for these expectations for one sub-family of the family of all possible joint distributions of the subclass numbers and the random effects. [ABSTRACT FROM AUTHOR]

The aim of this paper is two-fold: (1) To give a unified treatment of the theory of order statistics when the parent distribution is not necessarily continuous. (2) To assess the effects of grouping on the distribution of order statistics and to indicate the convenience, under suitable conditions, of using order statistics for the estimation of parameters from grouped data with or without censoring. [ABSTRACT FROM AUTHOR]

This paper describes and derives the asymptotic behavior of the new Normal approximation introduced in Part I and of a family of Normal approximations based on roots, including the square root approximations of Fisher, and Freeman and Tukey, and the cube root approximations of Wilson and Hilferty, Camp, and Paulson. Various asymptotic comparisons are made, all of which rank the new approximation first, the cube root approximations second, and the other root approximations (and the ordinary Normal approximation) third. For instance, in the binomial case, if the tail probability is fixed as n arrow right infinity, the errors resulting from the foregoing approximations are generally of order n[sup -3/2], n[sup -1], and n[sup -1/2] respectively, while for a tail probability approaching 0, the relative error in approximating it approaches 0 if the corresponding standard Normal deviate is of smaller order than n[sup 1/2] n[sup 1/4], or n[sup 1/6] respectively, but not generally otherwise. These comparisons are deduced from far more detailed results which are also given. [ABSTRACT FROM AUTHOR]

In this paper, maximum likelihood and Bayesian methods are presented for estimating transition probabilities when data in the form of aggregated proportions are available. The probability function for the observed proportions is assumed to have a multinomial distribution under the Lexis scheme. The multivariate beta distribution is used as the prior probability density function in formulating the Bayesian estimator. The results of some Monte Carlo experiments provide some evidence on the sampling properties of several alternative estimators. [ABSTRACT FROM AUTHOR]

This paper gives analytic expressions for the distribution function of t", a doubly noncentral t-distribution, with nu degrees of freedom and noncentrality parameters delta and lambda, in series of Incomplete Beta and Hypergeometric (Gauss and Confluent) functions. Numerical values of Pr(t" ≤ t|v, δ, λ) for v = 2 (1) 20, λ = 0 (2) 8, |δ| = 0 (1) 5, t=0 and 1 are given in Table I. [ABSTRACT FROM AUTHOR]

This paper deals with certain aspects of variance component estimation for the unbalanced one-way random classification where the number (N[sub I]) of observations in the ith class is treated as a random variable not necessarily independent of the class effect (A[sub iota]). It is assumed that in general P(N[sub I] = 0) > 0. The conditional expectations (given the number of observations in each class) of all estimators of the between variance component (sigma[sup 2, sub alpha]) belonging to a certain class of estimators are derived. A general expression is found for the expected value of that estimator of sigma[sup 2, sub alpha] yielded by analysis of variance of class means. The limit of this expression (as the number of classes arrow right Infinity) is given; and it is shown that, if the bivariate distribution function of A[sub I], N[sub I] belongs to a certain class of distribution functions, then this limit is less than sigma[sup 2, sub a]. Numerical approximations to the expected values of two estimators of sigma[sup 2, sub a] are presented for one subclass of such distribution functions. [ABSTRACT FROM AUTHOR]

While distribution-free procedures are often appropriate when testing statistical hypotheses, they may become complicated or involve loss of power when the data are grouped. For rank tests the ties caused by grouping are generally broken either by using a randomization procedure or averaging the tied ranks. In this paper the power loss due to equi-spaced grouping (in terms of Pitman asymptotic relative efficiency) is investigated for some commonly used tests, for each method of tie-breaking. The tests considered are Wilcoxon's and Mood's tests for the two-sample problem, Mann's test for randomness, and Pitman's independence test. It is shown how the power loss depends on the width of the grouping intervals and the distribution of the data, and some numerical studies are given. The results seem to indicate that the power loss is small even for a sizable group interval, and that it may be preferable to break ties by randomization than by averaging ranks. [ABSTRACT FROM AUTHOR]

The robustness properties of four estimators of location are studied with respect to eight distribution types. For each type, the probability density function is symmetric about the median and the range of variate is infinite. For the entire class of distributions, the estimator with the highest guaranteed efficiency is the mean of the middle fifty percent of the sample. This study supplements the paper by Crow and Siddiqui (1967). [ABSTRACT FROM AUTHOR]

This paper gives analytic expressions for the moments and recurrence relations for the first four raw moments of a doubly noncentral t-distribution with v degrees of freedom and noncentrality parameters δ and λ. Table I provides numerical values of these moments for v = 2 (I) 20, λ = 2 (2) 8 (4) 20 and any suitable σ. Two approximations to the t"-distribution, involving the moments, are considered. [ABSTRACT FROM AUTHOR]

The experiments to be discussed in this article was designed to investigate empirically the distribution of the sample version of the measure of association (G), &b.gamma;. Professors, William H. Kruskal and Leo A. Goodman have published an article giving interpretive motivation for the coefficient, and have developed the large sample theory for G. In the present research, sampling experiments were performed to test the adequacy of the large sample theory for 5X5 population cross classifications and samples of size ten, twenty-five and fifty. The numerical experiment described in this paper was based on a number of 25 cells multinomial populations, each considered as represented by the probabilities in a 5X5 population cross classification. Gamma is defined by Goodman and Kruskal in terms of probabilities. The 100 population cross classifications were chosen to be representative of practical situations in psychology. The method use to obtain them was to begin with 5X5 cross classification having complete association along the main diagonal and with a variety of marginal distributions.

A number of examples which involve restricted alternatives are given; each of these, except one, deals with normal distributions. The examples demonstrate the following: (a) one way to construct a simple test when the alternative hypothesis is restricted, (b) a method by which the additional restrictions can be justified, and (c) a procedure that can be used to defend the original model. An interesting relationship between Bartholomew's chi[sup 2] and a test statistic, which is used in this paper, is pointed out. Finally, a certain distribution-free problem and a solution of it are proposed. [ABSTRACT FROM AUTHOR]

In a logical probability approach to inference, distributions on a parameter space are interpretable as representing states of knowledge, and any prevailing state of knowledge may be taken to have been arrived at from a previous state of ignorance (indifference) followed by an accumulation of prior data. In this paper an indifference procedure is introduced that requires postulating what size and what kind of samples will and will not (in a special sense) permit statistical inference and prediction--e.g., one observation from a two-parameter normal model is not (in our special sense) sufficient to permit inference about the variance but two observations are. In essence, the procedure stipulates that prior indifference distributions be improper but become proper after an appropriate minimal sample. With some limitation on the family of priors considered, this procedure permits unique specification of indifference for the more commonly encountered statistical models. Furthermore, these specifications are affected neither by change of the scale of measurement of the observations, nor by the sampling rule. [ABSTRACT FROM AUTHOR]

This paper presents a simple method for increasing the limiting Pitman efficiency of rank tests relative to the best tests for samples normal distributions without using complicated scoring systems. Our proposal is to select two numbers p and r (0 < p, r < 1) and then score, with integer weights, the data in the top p[sup th] and bottom r[sup th] fractions of the combined sample. The percentile modified tests for scale are quite effective. When p = r = 1/8 (i.e., we score only the extreme quarter of the combined sample) the A.R.E. of the test to the F test is .85. [ABSTRACT FROM AUTHOR]

In this paper we obtain a multivariate generalization of the inverted beta distribution. Properties of this distribution and its connection with the multivariate Student-t distribution are discussed. Two asymptotic formulae for approximating the related probability integral are developed and illustrated with numerical examples. Application of this distribution to a problem in Bayesian inference is given. [ABSTRACT FROM AUTHOR]

In this paper we review the derivation of the predictive density function for the normal multiple regression model, state and prove a general theorem on optimal point prediction, and show how the predictive density can be employed in the analysis of an illustrative investment problem. Then we derive the predictive density function for the multivariate normal regression model and indicate how it can be used in the analysis of several problems. [ABSTRACT FROM AUTHOR]

In this paper the robustness of some of the existing tests for the exponential distribution when some outliers are present is reviewed. It is noted that the tests proposed by Epstein and Sobel [4] can be used without any major modification in the presence of outliers and a more suitable flexible test criterion is proposed for the exponential lower limit which is superior to Carlson's statistic [2] in all situations. The distribution of this statistic is derived and tables are constructed to facilitate the use of this statistic. Also some tests for outliers in the exponential case are proposed. [ABSTRACT FROM AUTHOR]

In this paper the first two moments of the ratio (treatment sum of squares)/(treatment sum of squares + error sum of squares)over all possible random assignment of treatments to the experimental plots, for a class of 2 associate PBIBD has been obtained. These two moments are compared with the corresponding moments of a continuous beta distribution to settle the question of approximating the randomization test by the usual F-test. It has been shown that a reasonable approximation to the randomization test based on the statistic F is equivalent to modifying the normal theory test by multiplying the numbers of d.f. of the F-distribution by a factor depending on the heterogeneity of the blocks. [ABSTRACT FROM AUTHOR]

The posterior distribution for parameters of a data distribution is usually the major objective of a Bayesian statistical analysis. Relatively little attention has been given to the fact that either a prior or a posterior distribution implies a marginal distribution, which may be called a "predictive distribution," for outcomes of any sample not yet observed. Predictive distributions have been mainly applied to design problems, such as determination of optimal sample size. In this paper tentative suggestions are made for applications to statistical inference, especially problems of appropriateness, selection, interpretation, and validation of formal models. [ABSTRACT FROM AUTHOR]

Regression upon principal components of the percentage points of the income and education distributions for 1950 census tracts in the city of Chicago led to the estimation of "beta coefficient profiles" for television receiver and refrigerator ownership, for central heating system usage, and for a measure of dwelling unit overcrowding. The betas are standardized coefficients of regression of a dependent variable upon the proportions of families in the classes of the marginal income and education distributions. They measure the relative contribution of families in these classes to the over-all per cent saturation of the dependent variable in the tract. The coefficients were estimated by techniques developed in the first portion of the paper; estimation by classical regression methods would have been impossible because of multicollinearity. The empirical results are in substantial agreement with findings from regressions of the dependent variables upon the mean values of income and education, and their squares. The statistical devices appear to be useful in exploratory empirical research. [ABSTRACT FROM AUTHOR]

This paper presents theorems which can be used to obtain sufficient and minimal sufficient statistics for the two-way classification mixed model design. Using the general linear hypothesis model Y = X tau + Z beta + e the authors prove that the dimension of a minimal sufficient statistic is a function of the ranks of certain submatrices of Z'X. Minimal sufficient statistics are presented in tabular form for some two-way classification designs and some of the distributional properties are given. [ABSTRACT FROM AUTHOR]

Past work on prediction formulas for time series, e.g., that of Wiener and Yaglom, has used powerful and general spectral techniques that result in integral formulas difficult to evaluate in practical eases. In this paper the more direct, less powerful approach developed by Muth produces useful and specific results for a broad class of cases that includes virtually every case of a higher order Markov process observed with error. The results provide plausible theoretical support for the expectations model widely and successfully applied by economists, although the distributions of the estimators of the prediction parameters (when the latter are unknown) are still unknown. The two-hundred-year series of sunspot data provides an illustrative application of the theoretical results, which bears comparison with the previous analyses of these data by Yule and others. [ABSTRACT FROM AUTHOR]

The need for data compression, a consequence of the demands made on the telemetry system of a space vehicle, prompts consideration of the use of sample quantiles in estimating population parameters and obtaining tests of goodness of fit for large samples. In this paper optimal unbiased estimators of the mean and standard deviation are given using up to twenty quantiles when the parent population is normal. Moreover, the estimators are relatively insensitive to deviations from normality. A distribution-free goodness-of-fit test is presented based on the sum of the squares of four quantiles after an orthogonal transformation to independent normal deviates. If a frequency function is of the form f(x; p) = pf[sub 1](x) + (1 - p) f[sub 2](x), 0 < p < 1, where f, and f[sub 2] are normal frequency functions, the distribution is likely to be bimodal. Another goodness-of-fit test is obtained using four quantiles, which is likely to have considerable power with a null hypothesis of normality and the alternative hypothesis of bimodality. The "data compression ratios" obtained with the use of a quantile system can be on the order of 100 to 1. [ABSTRACT FROM AUTHOR]

This paper considers some problems in the probabilistic analysis of physical evidence in criminal investigations. Two basic assumptions are made: (1) That the number of persons or objects possessing a particular set of properties can be considered as a random variable, and (2) that it is possible to estimate the probability function of this random variable. Two models (one with and one without the assumption that the suspect is a random selection from the set of possible suspects) which arc applicable to the evaluation of partial transfer evidence--an important category of physical evidence that is found in most criminal investigations--are developed. A detailed analysis of the models and an example are presented for the case when the estimated probability distribution is binomial with an expected value less than 1. As the expected value becomes smaller, the assumption of randomness in the selection of the suspect becomes immaterial to the evaluation of the evidential significance. [ABSTRACT FROM AUTHOR]

The intent of this paper is to provide a definition of a sociometric clique in the language of graph theory. This problem is viewed from two perspectives: maintaining fidelity to the intuitive notion of a clique; and providing adequate computational mechanics for large bodies of data. Luce's (1950) concept of an n-clique is used, but further qualifications are added. Two statistics or measures with associated probability distributions are defined for testing the adequacy of a subgraph which qualifies according to the definition. [ABSTRACT FROM AUTHOR]

This paper presents an explicit procedure for finding improving cycles or paths in the distribution model. The procedure developed may be incorporated in the row-column sum method. When this is done, both the row and column numbers and the predecessor index numbers may be determined simultaneously, a fact which contributes to the rapidity of the method. The chief difference between our method and other labeling procedures derives from the fact that the ordinary procedures are implemented in a 'dual' framework and are concerned with identifying a flow augmenting path that maintains dual feasibility. [ABSTRACT FROM AUTHOR]

The article discusses some of the major implications of the developing area of objective psycho-diagnostics that were selected for special consideration and for the bearing they have for some of the research papers appearing in 1955. The antecedent probability, or base rate, of a given characteristic in the general run of clinical cases being seen is of crucial importance in determining the efficiency of a cutting point on any score distribution. Since these values will fluctuate from installation to installation and undoubtedly from time to time in any given clinical agency, the test producer cannot provide this additional information for the individual clinician in the use of a diagnostic device.

Reliability data often include information that the failure event has not yet occurred for some items, while observations of complete lifetimes are available for other items. Bayesian analysis requires a conjugate posterior density function after any combination of complete and incomplete observations. This paper considers density functions having failure rate function consisting of a known function multiplied by an unknown scale factor. It is shown that a gamma family of priors is conjugate for both complete and incomplete experiments. A very flexible and convenient model results from the assumption of a piecewise constant failure rate function. [ABSTRACT FROM AUTHOR]

This article focuses on the recurrence relation for distribution functions from bivariate distributions. In the univariate case, a number of recurrence relations between the densities and the moments of the order statistics are available ([1], [2], [3], [4], [5]). In this paper, a similar result is derived for bivariate distributions. Let F(x, y) be a bivariate distribution function with continuous margins F1(x) and F2(y).