Discrete Density Function Research Articles

THE MATHEMATICAL MODELS FOR THE MULTISTAGE INVENTORY CONTROL PROCESSES

In this paper two mathematical models of multistage inventory control processes with continuous and discrete density functions of demands are investigated. These processes are modelled by recursion equations of the dynamic programming. For inventory control problem with the continuous density function there was created a new continuous optimal control problem, which is equivalent to the given one. Applying the maximum principle solves this new problem. The optimal policy ordering policy is defined. Also, we have found the optimal policy for ordering of products in the multistage inventory control problem with the discrete density function of demands. In this case such number of moments of time was found that the demands are satisfied without extra products.

Nonparametric estimation of a two dimensional continuous–discrete density function by wavelets

We consider the estimation of a two dimensional continuous–discrete density function. A new methodology based on wavelets is proposed. We construct a linear wavelet estimator and a non-linear wavelet estimator based on a term-by-term thresholding. Their rates of convergence are established under the mean integrated squared error over Besov balls. In particular, we prove that our adaptive wavelet estimator attains a fast rate of convergence. A simulation study illustrates the usefulness of the proposed estimators.

NON-STATIONARY DYNAMICS DATA ANALYSIS WITH WAVELET-SVD FILTERING

Non-stationary time–frequency analysis is used for identification and classification of aeroelastic and aeroservoelastic dynamics. Time–frequency multiscale wavelet processing generates discrete energy density distributions. The distributions are processed using the singular-value decomposition (SVD). Discrete density functions derived from the SVD generate moments that detect the principal features in the data. The SVD standard basis vectors are applied and then compared with a transformed-SVD, or TSVD, which reduces the number of features into more compact energy density concentrations. Finally, from the feature extraction, wavelet-based modal parameter estimation is applied. The primary objective is the automation of time–frequency analysis with modal system identification. The contribution is a more general approach in which distinct analysis tools are merged into a unified procedure for linear and non-linear data analysis. This method is first applied to aeroelastic pitch-plunge wing section models. Instability is detected in the linear system, and non-linear dynamics are observed from the time-frequency map and parameter estimates of the non-linear system. Aeroelastic and aeroservoelastic flight data from the drone for aerodynamic and structural testing and F18 aircraft are also investigated and comparisons made between the SVD and TSVD results. Input–output data are used to show that this process is an efficient and reliable tool for automated on-line analysis. Published by Elsevier Science Ltd.

Single- and multiple-pulse noncoherent detection statistics associated with partially developed speckle

Single- and multiple-pulse detection statistics are presented for aperture-averaged direct detection optical receivers operating against partially developed speckle fields. A partially developed speckle field arises when the probability density function of the received intensity does not follow negative exponential statistics. The case of interest here is the target surface that exhibits diffuse as well as specular components in the scattered radiation. An approximate expression is derived for the integrated intensity at the aperture, which leads to single- and multiple-pulse discrete probability density functions for the case of a Poisson signal in Poisson noise with an additive coherent component. In the absence of noise, the single-pulse discrete density function is shown to reduce to a generalized negative binomial distribution. The radar concept of integration loss is discussed in the context of direct detection optical systems where it is shown that, given an appropriate set of system parameters, multiple-pulse processing can be more efficient than single-pulse processing over a finite range of the integration parameter n.

Feature sets for nonstationary signals derived from moments of the singular value decomposition of Cohen-Posch (positive time-frequency) distributions

This article presents a new method for determining the principal features of a nonstationary time series process based on the singular value decomposition (SVD) of the Cohen-Posch (1985) positive time-frequency distribution. This new method uses density functions derived from the SVD singular vectors to generate moments that are associated with the principal features of the nonstationary process. Since the SVD singular vectors are orthonormal, the vectors whose elements are composed of the squared elements of the SVD vectors are discrete density functions. Moments generated from these density functions are the principal features of the nonstationary time series process. The main reason for determining features of a time series process is to characterize it by a few simple descriptors.

Principal features for nonstationary signals from moments of the singular value decomposition of Cohen–Posch (positive time-frequency) distributions

This paper presents a new method for determining the principal features of a nonstationary time series process based on the singular value decomposition (SVD) of the Cohen–Posch positive time-frequency distribution. This new method uses density functions derived from the SVD singular vectors to generate moments that associate with the principal features of the nonstationary process. Since the SVD singular vectors are orthonormal, the vectors whose elements are composed of the squared-elements of the SVD vectors are discrete density functions. Moments generated from these density functions are the principal features of the nonstationary time series process. These descriptive features can be used in a variety of ways to gain information about the specific aspects of the time series process. This new technique has application to a broad area of fields and applications such as the medical field (nonintrusive diagnostics and condition classification), the defense industry (classification of acoustics transient signals), the field of machinery diagnostics, the field of marine mannal acoustics, and the manufacturing industry. An example is presented which illustrates how the new technique can be used to classify acoustic transient signals from underwater vehicles.

A unifying approach to evaluating block accesses in database organizations

A nonrecursive discrete density function to compute the probability of retrieving k records from exactly i blocks of a file is introduced here. This function is shown to be equivalent to Siler's recursive one. Furthermore, we prove that Yao's formula is the expected value of our (and Siler's) probability function.

A NUMERICAL METHOD FOR PROPAGATION OF UNCERTAINTY IN NONLINEAR SYSTEMS

A numerical method is presented which propagates uncertainty through dynamical systems. It is a fast method of solving the Fokker-Planck equation in the special case of zero diffusion, and requires only that sufficient moments of the initial joint density function be known to adequately characterize it. The method relies upon approximating a continuous density function with a discrete density function. For some systems an interesting linearity condition holds for the uncertainty.

On the Unimodality of High Convolutions of Discrete Distributions

It is shown that if $\{p_j\}$ is a discrete density function on the integers with support contained in $\{0, 1, \cdots, d\}$, and $p_0 > 0, p_1 > 0, p_{d - 1} > 0, p_d > 0$, then there is an $n_0$ such that the $n$-fold convolution $\{p_j\}^{\ast_n}$ is unimodal for all $n \geq n_0$. Examples show that this result is nearly best possible, but weaker results are proved under less restrictive assumptions.

On the Unimodality of High Convolutions

It has been conjectured, for any discrete density function $\{p_j\}$ on the integers, that there exists an $n_0$ such that the $n$-fold convolution $\{p_j\}^{\ast n}$ is unimodal for all $n \geq n_0$. A similar conjecture has been stated for continuous densities. We present several counterexamples to both of these conjectures. As a positive result, it is shown for a discrete density with a connected 3-point integer support that its $n$-fold convolution is fully unimodal for all sufficiently large $n$.

Protection System Modelling in a Probabilistic Assessment of Transient Stability

The application of probability methods in the evaluation of power system transient stability has been demonstrated in recent papers1-3. A probabilistic index for transient stability was developed which in addition to considering the random variations in the operating conditions, included the probabilistic aspects associated with the type, location and clearance of the system faults. It was realized during these studies that there was a need to develop stochastic models for the protection system behaviour which include the actual design aspects. The operational behaviour of the protection system is an important component in the high degree of security and service continuity associated with bulk power systems. This paper illustrates an approach used to model the protection system in the probabilistic assessment of transient stability. The probability density functions of the operating times associated with the components of the protection system such as relays, breakers, etc. are used in conjunction with the reliabilities of the main and back-up protection schemes to obtain the probability density functions of the fault clearing time for different fault locations. These density functions are used together with the critical fault clearing time for a given fault type and location to obtain a probabilities index for transient stability. A simple distance impedance protection system is used to illustrate the procedure. Continuous as well as discrete density functions for the operating times of the protection system components are used. This paper illustrates the basic probabilistic nature of the fault clearing phenomenon and its importance in transient stability assessment.

Multiple features analysis of intervocalic English plosives.

A controlled study involving a multi-feature acoustic analysis of intervocalic English plosives has been conducted for the purpose of evaluating acoustic stop features for automatic stop recognition. Both time-domain and frequency-domain features were measured via computer interaction. The resulting discrete density functions allowed for a comparative evaluation of individual (and in some instance conditional or combined) feature contributions to stop identification. This evaluation consisted of the maximum a posteriori probability of a correct identification of either the voicing mode (voiced or voiceless) or the place of articulation (labial, alveolar, or palato-velar) of a stop independent of the talker or of a limited phonetic context. These features included variations on ten acoustic features for voicing mode identification and seven for place-of-articulation identification. The data base for this study consisted of five male and five female talkers producing all permutations of the stops C epsilon /p,t,k,b,d,g/ and vowels V epsilon /i,e,a,u/ in the sentence frame "please say /h 'CVt/ again." While the results indicate that the acoustic features of burst/formant-onset frequency and voice onset time (VOT) are the two single most salient features for stop identification, several additional features are also shown to provide important redundancy for identification. The often overlooked time-domain features of "double-burst release" and "voicing during stop closure" were found to be particularly useful in providing such redundancy.