Showing papers on "Cumulative distribution function published in 1986"
TL;DR: In this article, the strength distribution of silicon carbide and alumina fibres has been evaluated by a multimodal Weibull distribution function, based on the concept that the fracture of the fibre is determined by competition among the strength distributions of several kinds of the defect subpopulation.
Abstract: The strengh distributions of silicon carbide and alumina fibres have been evaluated by a multimodal Weibull distribution function. This treatment is based on the concept that the fracture of the fibre is determined by competition among the strength distributions of several kinds of the defect sub-population. Since those fibres were observed to have two types of fracture mode, the evaluation of a bi-modal Weibull distribution was performed in comparison with the single Weibull distribution usually employed. The accuracy of the fit for these two distributions was judged from maximum logarithm likelihoods and cumulative distribution curves. The result showed that the logarithm likelihood calculated using the bi-modal Weibull distribution function gave a larger value, as compared with those using the single Weibull distribution function. The curve predicted from the former function was also in good agreement with the data points. In addition, the strength distribution and the average value at a different gauge length were extrapolated from the Weibull parameters estimated at the original gauge length. In this case, also, the bi-modal Weibull distribution gave a more accurate prediction of the data points.
123 citations
TL;DR: It is shown that it is important to consider the variability of the base time for all processes after the response has been decided on but before it has actually been carried out, and that this variability influences the determination of the detection-time correlation.
Abstract: If a subject is required to respond to either of two different target signals, reaction times (RTs) are especially fast when both target signals are presented. Separate-activation models can account for this finding. This model class assumes that each target signal is detected in a different channel and that the detection time of each channel is a random variable. If two different target signals are presented, RT is simply the lesser of the two detection times. Cumulative distribution functions of RTs are commonly used to test channel independence or, if channel independence is rejected, to evaluate the detection-time correlation. The present paper shows that it is important to consider the variability of the base time for all processes after the response has been decided on but before it has actually been carried out. It is shown that this variability influences the determination of the detection-time correlation. In addition, it is shown that Miller’s (1982) test of separate-activation models versus coactivation models can also be applied to models with variable base times.
63 citations
TL;DR: In this article, the authors characterized the domains of attraction of the univariate extreme value distributions using inverse cumulative hazard functions and showed that the results are much simpler than those using cumulative distribution functions.
Abstract: The domains of attraction of the univariate extreme value distributions are characterized using inverse cumulative hazard functions. The results are much simpler than those using cumulative distribution functions. We also characterize the differentiable domains of attraction. A particularly simple characterization is given for the twice differentiable domain of attraction.
37 citations
TL;DR: In this article, the authors present a method for estimating persistence statistics from cumulative probability distributions, which is more reliable and much simpler to apply than Graham's method and gives results in good agreement with a range of measured data sets for both exceedance and non exceedance.
33 citations
TL;DR: Generalized Q -function expressions are developed for the transient state occupancy cumulative distribution function (cdf), probability density function (pdf), and expected value for an M/M/1 queue.
Abstract: Generalized Q -function expressions are developed for the transient state occupancy cumulative distribution function (cdf), probability density function (pdf), and expected value for an M/M/1 queue. The pdf equation is an extension of a previous result. When Parl's method is used to calculate the generalized Q -function, the equations are computationally efficient and accurate. For a Q -function relative error of 2\cdot10^{-12} , the relative error of the result is typically 10-10or better. Relative error will increase, however, for cdf and pdf values on the order of the Q function relative error. Execution time per point on a VAX 11/750 is on the order of tens of milliseconds for the range of parameters considered.
24 citations
TL;DR: In this paper, linear transformations of nonskewed variates with explicit inverse cumulative density function are used to derive general approximations for the inverse DF of the approximated variable.
Abstract: Linear transformations of a nonskewed random variable are employed to derive simple general approximations for a random variable having known cumulants. Introducing the unit normal variate, these become linear normal approximations.Some nonskewed variates with explicit inverse cumulative density function are then used to derive general approximations for the inverse DF of the approximated variable.The approximations are applied to the binomial, Poisson, Fisher's z and F, gamma (chi-square in particular) and the t distributions and their accuracy examined.Simple general approximations for the loss function of a random variable either continuous or discrete are developed. A simple approximation for the loss function of the Poisson distribution is then derived and demonstrated by an example from inventory analysis.Two further examples from interval estimation and from hypothesis testing highlight the usefulness of the new approximations.
22 citations
TL;DR: In this article, a method of estimating the probability density function and cumulative distribution function when only the ordinary or central moments of the distribution are known is examined, and the results are then compared to those obtained by a nearly exact numerical scheme.
14 citations
TL;DR: In this paper, the authors investigated the probability of introducing modal noise in a singlemode lightguide system with a short length of straight depressed-cladding fiber between high-loss splices.
Abstract: The probability of introducing modal noise in a single-mode lightguide system with a short length of straight depressed-cladding fiber between high-loss splices is investigated. The cumulative probability of modal noise is useful for evaluating the risk involved in violating the fiber minimum splicing length (the fiber length for zero probability of modal noise). The probability of encountering modal noise is less than 0.6 percent for fiber lengths as short as 3 m with splice losses of 0.5 dB. For this example, the minimum laser wavelength is 1285 nm and the maximum cutoff wavelength is 1330 nm measured on a 5-m length of fiber with 50-cm diameter loops. The results are also valid for depressed-cladding fiber measured by CCITT recommendations.
12 citations
TL;DR: In this article, the cumulative distribution function of positive definite quadratic forms in normal random variables has been derived for the analysis of variance of unbalanced data and some additional results concerning the distribution function and some extensions are also provided which make it possible to compute exact significance levels for certain test statistics.
Abstract: Some existing representations for the cumulative distribution function of positive definite quadratic forms in normal random variables lead to inefficient computational algorithms. These inefficiencies are overcome with the derivation of some alternative recurrence relations. Some additional results concerning the distribution function and some extensions are also provided which make it possible to compute exact significance levels for certain test statistics proposed for the analysis of variance of unbalanced data.
10 citations
TL;DR: Recently, P. D. Finch and R. Groblicki as mentioned in this paper gave the complete solution to the problem of determining all n-dimensional cumulative probability distribution functions with specified one-dimensional margins, which was solved by one of us in 1959.
Abstract: Recently, P. D. Finch and R. Groblicki determined all bivariate probability densities with specified margins. We point out that their result follows immediately from the complete solution to the problem of determining all n-dimensional cumulative probability distribution functions with specified one-dimensional margins, which was solved by one of us in 1959.
TL;DR: One-sided confidence regions for continuous cumulative distribution function are constructed using empirical cumulative distribution functions and the generalized Kolmogorov-Smirnov distance as mentioned in this paper, where the band width of such regions becomes narrower in the right or left tail of the distribution.
Abstract: One-sided confidence regions for continuous cumulative distribution function are constructed using empirical cumulative distribution functions and the generalized Kolmogorov-Smirnov distance. The band width of such regions becomes narrower in the right or left tail of the distribution. Significance levels necessary for implementation are given. Some other K-S type distances useful in constructing a confidence region with nonconstant width are also included.
TL;DR: In this article, a set of Fortran-77 subroutines are described which compute a nonparametric density estimator expressed as a Fourier series and a subroutine is given for the estimation of a cumulative distribution.
Abstract: A set of Fortran-77 subroutines is described which compute a nonparametric density estimator expressed as a Fourier series. In addition, a subroutine is given for the estimation of a cumulative distribution. Performance measures are given based on samples from a Weibull distribution. Due to small size and modest space demands, these subroutines are easily implemented on most small computers.
TL;DR: In this paper, two-variable cubic spline representations of the appropriate cumulative distribution functions are developed and their use is demonstrated in Monte Carlo simulation of energy-dispersive x-ray fluorescence analysers.
Abstract: In Monte Carlo simulation of energy-dispersive x-ray fluorescence analysers, one must account for both x-ray scattering effects and photoelectric absorption. To access the required random values of differential coherent and incoherent scattering angles, two-variable cubic spline representations of the appropriate cumulative distribution functions are developed and their use is demonstrated. In this approach the scattering angle is taken to be the dependent variable while the two independent variables are the x-ray energy and the normalized cross-sections.
Cubic spline coefficients for the elements from sodium to nickel have been obtained for x-ray energies from 1 to 150 keV for all scattering angles for both coherent and incoherent scattering. Compared with the commonly used method of numerically integrating tabular values of coherent and incoherent cross-sections to produce a table of values for subsequent interpolation, use of cubic spline representations gives a 90% reduction in storage space and a 25–80% reduction in the amount of computer time required for equal accuracy.
TL;DR: The normalized cumulative probability of detection curves are presented as a new evaluation tool of search radar systems that does not need interpolation for constant false-alarm number, provides the distance of the performance from the optimum, and is easily programmable.
Abstract: The normalized cumulative probability of detection curves are presented as a new evaluation tool of search radar systems. This tool 1) does not need interpolation for constant false-alarm number, 2) provides the distance of the performance from the optimum, and 3) is easily programmable.
15 Feb 1986
TL;DR: The SIMRAND methodology models the alternative subsets of systems or tasks under consideration and combines, in a Monte Carlo simulation model, the network structure, the equations, the cumulative distribution functions, and the utility functions.
Abstract: A research and development (R&D) project often involves a number of decisions that must be made concerning which subset of systems or tasks are to be undertaken to achieve the goal of the R&D project. To help in this decision making, SIMRAND (SIMulation of Research ANd Development Projects) is a methodology for the selection of the optimal subset of systems or tasks to be undertaken on an R&D project. Using alternative networks, the SIMRAND methodology models the alternative subsets of systems or tasks under consideration. Each path through an alternative network represents one way of satisfying the project goals. Equations are developed that relate the system or task variables to the measure of reference. Uncertainty is incorporated by treating the variables of the equations probabilistically as random variables, with cumulative distribution functions assessed by technical experts. Analytical techniques of probability theory are used to reduce the complexity of the alternative networks. Cardinal utility functions over the measure of preference are assessed for the decision makers. A run of the SIMRAND Computer I Program combines, in a Monte Carlo simulation model, the network structure, the equations, the cumulative distribution functions, and the utility functions.
01 Jan 1986
TL;DR: In this paper, a new and simple definition of the Rain Flow Cycle count method for the analysis of a random load process is presented, combined with the Palmgren-Miner damage rule, and a stochastic model for the fatigue life and fatigue limit variability.
Abstract: -We present a new and simple definition of the Rain Flow Cycle count method for the analysis of a random load process. It is combined with the Palmgren-Miner damage rule, and a stochastic model for the fatigue life and fatigue limit variability. Algorithms are presented which make it possible to calculate the RFC-amplitude distribution, based on a Markov Chain approximation of local maxima and minima. The method derived would apply to structures subjected to random fatigue loads such as acoustic noise, random vibration or sea waves, etc. NOMENCLATURE P(A) = probability of the event A E(X) = mathematical expectation of the random variable X P(A 1 B) = conditional probability of A given B E(X I Y = y ) = conditional expectation of A' given Y = y Var(Y) = variance of the random variable X F,( .) = distribution function of the random variable or vector X a E A = a is an element of the set A # {.} =the number of elements in the set I.]. F,,,( .Iy) = conditional distribution function of the random variable