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The article discusses forecasting in a time series which follows a seasonal pattern. Recursive forecast models are used, as well as the general linear regression model, to forecast for a seasonal time series. An econometric model, which is used in analyzing the relationships among economic variables, helps to develop a forecast model.

The article comments on the paper "Comparative Values of Information Structures," by Theodore J. Mock, that appears in the December 1, 1969 issue of the "Journal of Accounting Research." The author states that the statistical tests conducted by him assume that profit differences are independent random variables obtained in random sample. He explains that the participants of the study do not apparently comprise a random sample of a larger universe of businessmen or students. He states that these particular observations are not a random sample of how the particular subjects might perform out of a large number of repetitions of the experiment given random starting conditions.

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The cumulation of a sum of N observations from a distribution of Y where N and y are linearly related random variables may serve as a model for the description of sales, insurance payments, changes in stock prices and other economic processes. The expectation and variance of such a sum and other results are presented with an empirical example. This model may prove useful for description of various flow magnitudes per interval of time that are, in turn, random cumulations of random outcomes. [ABSTRACT FROM AUTHOR]

The article presents commentary and analysis of the over-application of the Markowitz-Tobin portfolio analysis theory of asset choice under uncertainty to various investment problems outside its original scope. The empirical and theoretical difficulties of computing such applications are described in detail, highlighting the two elements of asset evaluation based on conditional or multiplicative random variables.

Efficiency analysis is concerned with isolating the efficient subset of investments (portfolios) for all investors belonging to a specified group. In order to construct a meaningful efficiency criterion, i.e., one which holds for more than one investor, care must be exercised to ensure that the investors' efficient set is independent of their wealth. In recent articles, Hadar and Russell [1] and Hanoch and Levy [2] analyze the mathematical properties of two new general efficiency criteria for the following two cases: (a) those in which no restrictions are placed on the shape of investors' utility functions, and (b) those in which investors are assumed to be risk-averse. However, in both articles the efficiency criteria are defined in terms of a variable x which denotes the money returns from a given venture, thereby ignoring the possible influence of investors' wealth on preferences. Because the money returns represent increments (or decrements) to individuals' wealth, the additional utility from the random variable x cannot be measured by U(x) but must be measured by U(w+x), where U denotes the utility function and w the investor's wealth. Consequently, these new efficiency criteria, based on U(x) instead of U(w+x), may lead to incorrect inferences. The purpose of this note is to determine the validity of these criteria under varying assumptions regarding the nature of investors' wealth. [ABSTRACT FROM AUTHOR]

The article focuses on methods of frequency function estimations using limited data. It states that the use of sparse data in frequency function estimations can be used in determining the expected value that added data would provide, and if its value exceeds the cost of gathering the data. It comments on the use of constrained maximization of entropy in frequency function estimation, which can result in the same frequencies in large parent populations of random variables as the most probable combination of observations which the constraints can satisfy.

The random walk theory consists of two distinct hypotheses, one economic, the other statistical. The economic argument assumes security markets are, for all practical purposes, efficient markets such that no investor can earn a systematically superior return. The statistical argument, on the other hand, asserts that, for any particular security, price changes are independent random variables. If the statistical hypothesis is to be completely consistent with the economic hypothesis, it is not sufficient simply for successive price changes to be independent, but rather price changes must be mutually stochastically independent and not just pairwise independent. If efficient markets exist, then mutual independence follows. Tests of the economic hypothesis are usually constructed so as to prove or disprove that, following some mechanical rule, a certain investment strategy can, or cannot, earn a greater return than a simple buy-and-hold strategy [1]. The buy-and-hold strategy under efficient markets is an optimal strategy since it minimizes transaction costs. [ABSTRACT FROM AUTHOR]

The literature on portfolio selection is also concerned with a comparison of projects (portfolios). Assumptions are made about the utility structure or distribution of cash flows to reduce the problem to one involving the mean and variance of future cash flows only, e.g., Markowitz and Mossin. In addition, the comparison of portfolios is done on a one-period basis, that is, the period between the present and the end of the next period. Under these conditions, the expected rate of return can be calculated on the basis of the expected values of the cash flows because present prices are known, not random. In a multiperiod problem, it is clear that knowing the mean and variance of future cash flows is not sufficient to compute the expected rate of return for each period. This follows because of the additional ignorance about the prices at the outset of each future period. Therefore, the return in a multiperiod problem must be defined as the ratio of two random variables, in this note we begin an investigation in another context into the concept of a rate of return as the ratio of random variables. [ABSTRACT FROM AUTHOR]

Dans cet article, nous obtenons, par un théorème concernant k+1 variables aléatiores à distributions gamma, une distribution de Districhlet inversée à K variables. Un certain nombre de résultats pour cette distribution sont démontrés et il est établi que l'on peut obtenir une distribution logistique é plusieurs variables à k dimension à partir d'une distribution de Districhlet inversée à k variables. [ABSTRACT FROM AUTHOR]

Soit une suite stationnaire {X [ABSTRACT FROM AUTHOR]

Dans cet article, nous obtenons la distribution de Z = Σ [ABSTRACT FROM AUTHOR]

The article presents a mathematical analysis of the power function distribution using a positive and bounded random variable with absolutely continuous distribution function F(x). The result of a random sample of size n from F(x) using an order statistics is extended with an independent statistics X(r)/X(s) and X(t). This independent statistics is also used as further proof of the condition for F(x) as the density function of the power function distribution.

Des résultats, correspondant à la sistribution symmétrique d'une fonction linéaire vactorielle de variables vectorielles étant donnée une autre founction linéaire vectorielle e vatiables vectorielles, sont obtenus par la réduction du problème à un problème de deux fonction linéaires ayant une distribution indentique. Pour la mormalité de chque variable vectorielle, des conditions plus restrictives sure les coefficients des conctions linéaires, que celles du théorème de Darmois et Skitovich, sont nécessaire. Nous faisons remarquer que le résultat de Heyde ←1970→ concernant la distribution symmétrique d'une fonction linéire étant donné une autre fonction linéaire, et qui requiert les mêmes conditions sure les coefficients que celles due théorème de Darmois et Skitovich, n'est pas valide. Dans certains cs, if existe quelques variables aléatories non normales parmi les composantes des conctions linéaires. [ABSTRACT FROM AUTHOR]

Two derivations are given for an absolutely continuous bivariate extension of the exponential distribution. This distribution turns out to be the absolutely continuous part of the bivariate exponential distribution of Marshall and Olkin and a variant of the bivariate exponential extension of Freund. One derivation utilizes the loss of memory property (LMP) which Marshall and Olkin used to derive their bivariate exponential distribution. Distributional properties, reliability considerations and estimation for this distribution are discussed. Further, the LMP is characterized for absolutely continuous bivariate random variables (X, Y) through the independence of rain (X, Y) and X - Y. [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]

A general method is developed for obtaining confidence limits on the mean of X+ Y where X and Yare two independent random variables whose individual distributions and percentiles are in standard statistical tables. The procedure uses this information to obtain approximations for the percentiles of the sum or approximate confidence limits on the mean of the sum. The method is applied to two problems: approximating the percentiles of the noncentral t distribution, and determining confidence limits for variance components in a one-way classification. Numerical examples compare it to other approximations. [ABSTRACT FROM AUTHOR]

The concept of population weighted-symmetry (a generalization of population symmetry) is discussed and a characterization of weighted- symmetry provided. For the special case of population symmetry, this characterization yields a strong converse to the well-known result: if the distribution of a continuous random variable X is symmetric about 0, then Z= |x- θ| and the indicator function for the event {X ≥ θ} are stochastically independent. lmplications and possible applications of the general weighted-symmetry results are considered. [ABSTRACT FROM AUTHOR]

Let a 1's and M- a 0's be randomly arranged in a rows Saperstein [11] defines the random variable km* to be the maximum number of 1's within any m consecutive positions in the arrangement, and finds Pr (k*m < k) for k> a/2. This article derives the distribution of k*m, for all a,k for M/m = L, L an integer. Simplified farms are given for M/m =L,k> a/2. [ABSTRACT FROM AUTHOR]

Rasch [4] considered a logistic model for item analysis where the probability of a subject solving an item in a test is given by the probability δζ/(1 + δζ), where 5 characterizes the ability of the person and ζ characterizes the easiness of the item. The same model was used by Sanathanan [6] in a visual scanning set up where a "scanner" takes the role of an "item" and an "event" that of a "subject." In the visual scanning model it is further assumed that the event parameter is a random variable. Some properties of the logistic model in relation to both the item analysis and scanning problems are studied here. [ABSTRACT FROM AUTHOR]

A cluster analysis can be interpreted as a function which maps the input dissimilarity matrix into an output dissimilarity matrix whose elements indicate the dissimilarity between pairs of objects. Some cluster analyses leave invariant the dissimilarities between certain pairs of objects. The set of elements left invariant by the single-linkage clustering method corresponds to the edges in the minimum spanning trees The properties of the graphs whose edges correspond to the dissimilarities left invariant by the Jardine-Sibson Bk clustering method are examined and algorithms are given for the determination of Bk clusters. [ABSTRACT FROM AUTHOR]

Some of the known properties of a particular family of distributions derived as a model for fatigue failure by Birnbaum and Saunders [3] are shown to bald far a class of families. These results stem from the fact that each variate in the class suitably scaled has the same distribution as its reciprocal. This clarifies the utility of certain distributions proposed for fatigue life, e.g., lognormal. This property also influences the estimation of the scale parameter and makes possible the solution of two important practical problems, a special solution of which had been presented in Saunders [11]. [ABSTRACT FROM AUTHOR]

Various methods have been used to find truncated SPRT's. The approach used here is to find the exact distribution of the sum of random variables and to treat the SPRT problem as a Markov chain with absorbing barriers, Exact and approximate formulas are given for the average sample number and for the error probabilities. Monte Carlo simulation shows this approach to be an improvement over that suggested by Anderson [1] when testing for the mean of a normal distribution. The present approach is general and applies to other distributions as well. [ABSTRACT FROM AUTHOR]

Let X[sub 2 i], X[sub i 2], ... ,X[sub in], i =1, 2, be a pair of independent random samples from normal populations with means theta[sub i], and common known variance tau[sup 2]. Suppose we select the population which provides the larger sample mean. In this article our main aim is to investigate different estimators for the mean of the selected population. Two different estimators are suggested by Sarkadi [9] and Putter and Rubinstein [8]. Two alternative estimators are suggested here and the bias and the mean square error of all the different types of estimators are tabled and compared. [ABSTRACT FROM AUTHOR]

This article deals with the problem of estimating the set of seemingly unrelated regressions (SUR) when the regression coefficients are random. In the article, an estimator has been proposed which is consistent and has the same asymptotic normal distribution as the Aitken generalized least squares estimator which assumes the covariance matrix to be known. Further, it has been shown that the proposed estimator is asymptotically more efficient than Zellner's SUR estimator provided that the true model is one with random coefficients. [ABSTRACT FROM AUTHOR]

In this article the problem of testing for homogeneity of k (k > 3) independent negative binomial distributed random variables with parameters r[sub i], p (for i = 1, ..., k) is studied. The alternative hypotheses which are considered are a p-mixture of negative binomial distributions and a positive trend of the p's. Several cases may be distinguished: (1)p known, (2) p unknown and r[sub 1] =...= r[sub k],(3)p unknown and r[sub 1], ..., r[sub kappa] possibly unequal. The proposed tests are based on explicit optimality criteria. [ABSTRACT FROM AUTHOR]

This article applies the counting rule strategy to the problem of estimating the proportion of population elements with a specified characteristic based on a sample of enumeration units. The distribution of population elements among the enumeration units is a function of the counting rule which specifies the conditions for linking population elements to enumeration units. The counting rule strategy involves the selection of the counting rule which minimizes the variance of the estimate for fixed cost. The strategy is illustrated by a problem which involves estimating the proportion of incorrect statistical statements in the text of a report based on a sample of lines of text. [ABSTRACT FROM AUTHOR]

The article differentiates between two systematic self-administered methods of inducing high response rates in a survey. There are two self administered methods that have been propounded after an armed force survey. The first being the field self-administered method. Normally, this method calls for drawing probability samples from military installations, and from individuals within units, so that finally the names of specific respondents are selected. Respondents are then asked to fill out the questionnaires. Such questionnaires are unsigned, and every effort is made to insure uniformity of administration and the respondents' anonymity. The second and more credible method is the by-mail self-administered method. This can effect a vast saving in personal and travel costs over the field self-administered method. Its other advantages are, less disruption of field operations for the mustering of officers and men to fill out questionnaires, the ability to draw truly random, unclustered samples from personnel rosters stratified by a number of variables and greater flexibility in planned oversampling of certain relatively small populations for sampling and reporting efficiency.

A method of generating random variables with the gamma or beta distribution having non-integral shape parameters from uniform random variables is given. [ABSTRACT FROM AUTHOR]

A cluster analysis procedure is described in which 288 journals in the disciplines of physics, chemistry and molecular biology are grouped into clusters. Most of the clusters are easily identified as subdisciplinary subject areas. The data source was the cross citing amongst the journals derived from the Journal Citation Index UCI), a file derived in turn from the Science Citation Index (SCI)®. The JCI consists of journal by journal tabulation of citings to and from each journal processed in the SCI. Two-step citation maps linking the clusters ore presented for each discipline. Within the disciplines the clusters of journals form fully transitive hierarchies with very few relational conflicts. [ABSTRACT FROM AUTHOR]

This paper is concerned with the role played by the standardized regression coefficients in linear regression analysis. The linear regression model is reparameterized to explicitly contain standardized regression coefficients. Several estimators of these coefficients are considered. It is shown that the usual beta coefficient is a good estimator of the coefficients in the linear regression model with random predictor variables. However, in the linear regression model with nonstochastic predictors, alternative estimators are better than the usual beta coefficient. A sociological application is included in order to display the empirical behavior of the various estimators. [ABSTRACT FROM AUTHOR]

Within the framework of chance-constrained programming, this paper formulates two related stochastic models for players competing in a random-payoff two-person zero-sum game. Under certain assumptions, it shows that a one-to-one correspondence (called stochastic pseudoduality) exists between the two formulations at their optimal values, and, furthermore, exact deterministic equivalents can be obtained for these formulations. The optimal solution for a deterministic equivalent can be found by considering an appropriate class of subproblems. [ABSTRACT FROM AUTHOR]

This paper concerns developing methods for approximating a chance-constrained set when any information concerning the random variables must be derived from actual samples. Such a situation has not been presented in the literature. When existing chance-constrained programming techniques are used, it is not possible to relate the accuracy of sample-based assumptions to actual constraint satisfaction. The methods presented here employ the concept of a distribution-free tolerance region to construct various sets whose elements have the common property of satisfying the chance constraint with a preassigned level of confidence. The sample size required to meet the desired confidence is readily available in tabular or graphical form. [ABSTRACT FROM AUTHOR]

MILLER and WAGNER have shown that a deterministic equivalent of a joint chance-constrained programming model with independent random right-and-side elements is a concave programming problem. This paper obtains similar equivalents for chance-constrained programming models with coefficient matrices whose elements are normally distributed and with dependent random right-hand-side elements. [ABSTRACT FROM AUTHOR]

Markov duels are a general class of stochastic duels in which each weapon has Markov-dependent fire, that is, the outcomes of shots by each weapon form a Markov process. This paper develops duel models for the situation in which the outcomes form a finite stationary Markov chain and both weapons have an unlimited supply of ammunition, fire at constant intervals of time, and duel until one is killed. Based on these assumptions, the probability of a given side winning the duel is obtained for two sets of starting conditions: (1) both weapons begin with unloaded weapons and have tactical equity, and (2) one weapon has the advantage of surprise and can fire y rounds at the other before the two-sided duel begins, where y is a random variable with a geometric distribution. The mean and variance of the number of rounds to kill a passive target are also derived and two example duels are solved. Finally, methods are indicated for obtaining the solution to a Markov duel between weapons having exponential firing times and either fixed, limited ammunition supplies or infinite supplies. [ABSTRACT FROM AUTHOR]

This paper shows that analytical techniques can be applied in the analysis of a wide class of combat problems by specializing the inputs of a general functional model. The generating functions of the losses, and the corresponding expected values and variances, are derived and expressed as integrals with respect to a supplementary time variable. [ABSTRACT FROM AUTHOR]

Identification and estimation problems concerning simultaneous equation models which have random parameters are considered, and some results are derived. For instance, a reducibility condition is derived under which the conditions for identification of such a system are identical to those that would be relevant if the parameters were not random. This condition is then weakened to one which relates to the identification and estimation problems of a particular equation in the model. Examples are given. Further generalizations are also considered but only conditional results are given. Further work is suggested. [ABSTRACT FROM AUTHOR]

The article discusses the irreversibility effect of investment decisions under uncertainty. According to the author "irreversible decision" means a decision, which significantly reduces for a long time the variety of choices that would be possible in the future. In fact using an information structure, the author proves that, by replacing initial random problem, even a risk-neutral decision maker facing a binary alternative is led to adopt an irreversible decision more often than he should. He states that it is not surprising that, in general, replacing random variables by their expectations will not lead to appropriate decisions. The point is that this replacement will, systematically and unduly, favor irreversible decisions, for example, destroying forests and building a highway. In the representative case that is numerically explored, the size of this "irreversibility effect" appears fairly important. The author also considers a problem of sequential decision under irreversibility and uncertainty, where uncertainty is measured by an information structure.

The goal of this study was to investigate the effects of experience and training upon performance in a LGD. Since the effects of these two variables were estimated across three criterion measures of the Ss' rated performance, a multivariate analysis (Clyde, Cramer, and Sherin, 1966) was performed so that all the differences due to experimental treatments could be evaluated simultaneously. Without the multivariate analysis, the nine F ratios (three for each criterion measure) produced by the univariate tests would be difficult to interpret since the probability of at least one Type 1 error would be equal to at least 1-(1-alpha level) (Hays, 1963, page 488). That is, the probability of rejecting the null hypothesis that there is no experimental effect when the null hypothesis is true would be at least .37 if a 5% level of significance were used. [ABSTRACT FROM AUTHOR]

The assumed situation is as follows: two cumulative distribution functions F and G are in constant (unknown) ratio θ, for values of the random variables below t* (assumed known); F and G may behave entirely independently above t*. Observations on a sample from F are then used to obtain unbiased maximum likelihood estimates of θ and of other unknown parameters G, denoted by λ. The estimators have application in problems of stochastic dominance in the context of portfolio analysis and in other situations of intertwining cumulative probability distributions. [ABSTRACT FROM AUTHOR]

This paper provides a computational technique for the evaluation of the distribution of the net present value (NPV) of an investment, in which the cash inflows occur at random time points, as in the case of venture capital. The initial cash outlay is deterministic and the magnitudes of the cash inflows are nonnegative, random variables with known distributions. The lengths of the intervals between successive cash inflows are independently distributed and independent of the magnitude of the inflows. The Laplace transforms and the first two moments of the distribution are computed for both independent and perfectly correlated inflows. It is shown that the use of constant time intervals when the timing of the inflows is random underestimates the variance of the distribution of the NPV. [ABSTRACT FROM AUTHOR]

This paper considers the problem of describing optimal issuing policies when the field life, X (s), is a nonnegative random variable. A new optimality criterion involving stochastic ordering is introduced and sufficient conditions given for the optimality of FIFO and LIFO. Two specific models of perishable inventory are then considered; Model I allows for the perishing of items in the stockpile and Model II does not. It is demonstrated that both LIFO and FIFO are optimal for Model I when the items age at the same rate in the stockpile as in the field. Under the assumption that X (s) is uniformly distributed the optimality of FIFO is established for Model II. [ABSTRACT FROM AUTHOR]

The article discusses priority pricing as it relates to queueing phenomena. The author attempts to study the price structure that should be set to charge facility services that are subject to queueing phenomena. Also discussed are methods with which to discover the optimal industrial capacity of a facility. According to the author, the manager of a facility should decentralize the allocation of priorities in order to avoid overstating waiting costs. The author also discusses issues surrounding resource allocation.

This paper considers a stationary discrete dynamic programming model that is a generalization of the finite state and finite action Markov programming problem. We specify conditions under which an optimal stationary linear decision rule exists and show how this optimal policy can be calculated using linear programming, policy iteration, or value iteration. In addition we allow the parameters of the problem to be random variables and indicate when the expected values or these random variables are certainty equivalents. [ABSTRACT FROM AUTHOR]