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Showing papers on "Cumulative distribution function published in 1977"


Journal ArticleDOI
01 Sep 1977
TL;DR: It is shown that for any ordering on the probability of error as a function of the subset of measurements (subject to an obvious set monotonicity condition), there exists a multivariate normal two-hypothesis problem N(K) versus N(¿¿,K) that exhibits this ordering.
Abstract: An aspect of the measurement selection problem?the existence of anomalous orderings on the probability of error obtained by selected subsets of measurements?is discussed. It is shown that for any ordering on the probability of error as a function of the subset of measurements (subject to an obvious set monotonicity condition), there exists a multivariate normal two-hypothesis problem N(?,K) versus N(??,K) that exhibits this ordering. Thus no known nonexhaustive sequential k-measurement selection procedure is optimal, even for jointly normal measurements.

275 citations


Proceedings ArticleDOI
05 Dec 1977
TL;DR: Methods of modelling probabilistic components which are not adequately represented by the standard continuous distributions are surveyed and emphasis is on generality, determination of appropriate parameter values, and random variate generation.
Abstract: Methods of modelling probabilistic components which are not adequately represented by the standard continuous distributions (such as normal, gamma, and Weibull) are surveyed. The methods are categorized as systems of distributions, approximations to the cumulative distribution function, and four-parameter distributions. Emphasis is on generality, determination of appropriate parameter values, and random variate generation.

40 citations


Journal ArticleDOI
TL;DR: Using extended forms of the Fokker-Planck-Kolmogorov equation, the so-called vth-order equations, a general expression is derived for p(y) and some specific eases are investigated, which are applied to find the average number of zero and level-crossings per unit time of the output process.
Abstract: We consider the probability density function p(y) of the output y(t) of the first-order non linear system [ydot] + β ƒ(y) = βx, where x = x(t) is the random telegraph signal and ƒ(·) is a non-linear function Employing extended forms of the Fokker-Planck-Kolmogorov equation, the so-called vth-order equations, a general expression is derived for p(y) and some specific eases are investigated These results are applied to find the average number of zero and level-crossings per unit time of the output process

22 citations


Journal ArticleDOI
TL;DR: In this paper, the authors proposed a time-dependent event cross-impact model, in which an undisturbed world view, prior to new information being obtained, is projected for a set of events to occur with specified probability densities over an indefinite time horizon.

18 citations


Journal ArticleDOI
Irving Kanter1
TL;DR: In this paper, a new method was developed for determining the pdf of the ratio f(X)lg(X), where f and g are arbitrary functions and g is correlated Gaussians with arbitrary means and variances.
Abstract: Given the joint probability density function (pdf), pX(xl, ..., xN), of the random variables x1, xN, a new method is developed for determining the pdf of the ratio f(X)lg(X) where f and g are arbitrary functions. The method is then applied to calculate the pdf of x1 lx2 where x1 and x2 are correlated Gaussians with arbitrary means and variances.

16 citations


Journal ArticleDOI
TL;DR: A bivariate extension of the m-Interval Partition Statistic is introduced for the problem of robust detection of a shift of mean in bivariate data and is shown to be robust and amenable to digital implementation.
Abstract: In this paper, a bivariate extension of the m-Interval Partition Statistic is introduced for the problem of robust detection of a shift of mean in bivariate data. This extension is obtained in a manner similar to Hodges bivariate extension of the sign test. The resulting Bivariate m-Interval Partition Statistic is shown to be robust and amenable to digital implementation. To use the Bivariate m-Interval Partition Statistic, a finite number of quantiles of a specified number of cumulative distribution functions are required. A computationally simple algorithm based upon the Robbins—Monro procedure is presented for estimating these parameters in most realistic noise environments. Simulations of this procedure illustrate its practicality and add considerable insight as to the nature of these quantiles. The performance of the Bivariate m-Interval Partition Statistic as a classifier is discussed in term of its type I error and power and simulated curves for several different noise distributions are included. Two sets of scores are discussed and then incorporated in an application of the Bivariate m-Interval Partition Statistic to edge detection. This example illustrates both the performance and robustness of this classifier in severe noise environments.

13 citations



Journal ArticleDOI
TL;DR: In this article, interval estimation on the smallest of the θ's and related topics are studied, and applications are considered for location parameter, normal variance, binomial parameter, and Poisson parameter.
Abstract: There are given k (⩾ 2) univariate cumulative distribution functions (c.d.f.'s) G(x; θi) indexed by a real-valued parameter θi, i=1,…, k. Assume that G(x; θi) is stochastically increasing in θi. In this paper interval estimation on the ith smallest of the θ's and related topics are studied. Applications are considered for location parameter, normal variance, binomial parameter, and Poisson parameter.

8 citations


Journal ArticleDOI
TL;DR: In this paper, the discharge pulse rates at different magnitude levels are used as criteria for monitoring the partial-discharge aging of insulation systems, and suggested corrections for errors in cumulative probability counting leads to better use of available counters.
Abstract: The discharge pulse rates at different magnitude levels are often used as criteria for monitoring the partial-discharge aging of insulation systems Use of suggested corrections for errors in cumulative probability counting leads to better use of available counters

3 citations


Journal ArticleDOI
TL;DR: In this article, an alternative approach of characterizing the adjustment trajectory by a cumulative probability distribution function (CPDF) was proposed, which leads to substantial improvements over standard OLS estimation.
Abstract: This paper forwards an alternative approach of characterizing the adjustment trajectory by a cumulative probability distribution function. Estimates of Wilton's (1975) automobile import equation over the period 1984-1973 are obtained in the case where a binomial CDF is used. Confirming Wilton's results, the use of transition functions to characterize coefficient adjustment between two regimes leads to substantial improvements over standard OLS estimation. Also the CDF transition estimates compare very favourably with the polynomial results, at the same time yielding more reliable coefficient transition paths and an improved framework for more precise hypothesis testing of structural change. (This abstract was borrowed from another version of this item.)

1 citations