Properties Of Order Statistics Research Articles

An improved voice activity detection using higher order statistics

In this paper, by using the properties of the higher order statistics (HOS) of speech and noise signals, we develop an improved voice activity detection (VAD) scheme. The proposed scheme employs the logarithm of the kurtosis of the LPC residual of a speech signal and is shown to be more effective and efficient in detecting active speech in medium to low signal-to-noise ratio (SNR) conditions without being unduly affected by the variations in the signal energy. To overcome the inability of the HOS in detecting unvoiced speech, another metric (the low band to full band energy ratio) is introduced. Depending on the estimated mean SNR, the proposed scheme works adaptively in two modes: a simple mode using only the SNR, and an enhanced mode using the HOS, the low band to full band energy ratio and the SNR. This scheme is capable of avoiding unnecessary computations, while maintaining the same performance as that working only in the enhanced mode. Simulations results are presented to demonstrate the effectiveness of the proposed voice activity detection scheme.

One property of student?s distribution with two degrees of freedom

Characterizations of Student’s t2-distribution and some related distributions based on regressional properties of order statistics are obtained. Bibliography: 8 titles.

Blind source separation using order statistics

This paper shows the possibility to blindly separate instantaneous mixtures of sources by means of a criterion exploiting order statistics. Properties of higher order statistics and second-order methods are first underlined. Then a brief description of the order statistics shows that they gather all these properties and a new criterion is proposed. Next an iterative algorithm able to simultaneously extract all the sources is developed. The last part is comparison of this algorithm with well-known methods (JADE and SOBI). The most striking result is the possibility to exploit together independence and correlation through the use of order statistics.

Order statistics for some common hazard rate functions with an application

PurposeThe problem is to devise a life‐test acceptance procedure of an electrical item that has a Weibull failure distribution with an increasing hazard rate. The test‐bed facility has some constraints on the number of test samples and testing time.Design/methodology/approachThe life‐test plan is obtained using censoring of experiments and the properties of order statistics. In this article, the author has derived expressions for order statistics and their moments for some commonly used hazard‐rate functions; for example, constant, linearly increasing, exponentially increasing, power function, etc. and the same is used in planning the life‐test acceptance procedure.FindingsResults and findings are discussed in full. It is postulated that further research in this direction will definitely bring some fruitful results that have immense importance in the field of reliability analysis and life‐testing experiments.Originality/valueThe same methodology can be adopted for devising life‐test acceptance procedure using censoring of experiments.

Quantification of the Variance of Estimated Transfer Functions in the Presence of Undermodeling

We study the effect of undermodeling on the parameter variance for prediction error time-domain identification in open loop. We consider linear time-invariant discrete time single-input-single-output systems with known noise model. We examine asymptotic expressions for the variance for large number of data. This quantity depends in general on the fourth order statistical properties of the applied input. However, we establish a sufficient condition under which the asymptotic variance depends on the input power spectrum only. For this case, we deliver exact expressions. For a stochastic input the undermodeling contributes to the parameter variance due to the correlation between the prediction errors and its gradients, while for a deterministic input it has no influence. As an additional contribution, we investigate the parameter variance under the assumptions of the stochastic embedding procedure.

UNIFORM ORDER STATISTICS PROPERTY AND [ell - cursive small l][infty infinity]-SPHERICAL DENSITIES

In this article, we observe that processes with the uniform order statistics property (UOSP) can be characterized by the condition that their first n epoch times have a joint e∞≤-spherical density, n ≥ 1. Some related results, and some further properties of e∞≤-spherical densities, are also given. We also extend some of the results regarding the UOSP to the more general (not necessarily uniform) order statistics property. Finally, we develop a theory of discrete-time discrete-state processes with the UOSP, where the need to consider multiple jumps, at a single time point, arises.

Information Properties of Order Statistics and Spacings

We explore properties of the entropy, Kullback-Leibler information, and mutual information for order statistics. The probability integral transformation plays a pivotal role in developing our results. We provide bounds for the entropy of order statistics and some results that relate entropy ordering of order statistics to other well-known orderings of random variables. We show that the discrimination information between order statistics and data distribution, the discrimination information among the order statistics, and the mutual information between order statistics are all distribution free and are computable using the distributions of the order statistics of the samples from the uniform distribution. We also discuss information properties of spacings for uniform and exponential samples and provide a large sample distribution-free result on the entropy of spacings. The results show interesting symmetries of information orderings among order statistics.

New Characterizations by Properties of Midrange and Related Statistics

New families of distributions are characterized by regressional properties of order statistics. Among equations for regressions based on order statistics X 1:n ,…, X n:n , n = 1, 2,…, we investigate a relation of the form E(λX k:2k+1 + (1 − λ)X k+2:2k+1|X k+1:2k+1 = x) = x, (0 < λ < 1). As a special case, a characterization of Student's t 2 distribution is obtained.

Changing surfaces—a theoretical and experimental approach

This work is concerned with rough surfaces that undergo small random changes in their morphology. These surfaces and their changes are studied by means of the second order statistical properties of the scattered light. Specifically, the speckle correlation method is used. A new theoretical model relating the speckle phenomenon to changes in the surface roughness is studied. A decreasing quadratic exponential relationship of the speckle correlation to the surface variation is found. This model is valid for dielectric or metallic surfaces. However, for the sake of simplicity, a translucent (dielectric) diffuser is studied and some new experimental results are reported. In the experimental work, the transmitted speckle pattern from a translucent rough surface is recorded before and after this surface suffers a change. The correlation between the two speckle patterns is calculated and related to the surface variation. The roughness is varied in a controlled way by immersing it in liquids of different refractive indices. A good agreement between theoretical descriptions and experimental results obtained in quasi-real time is achieved.

Quantification of the Variance of Estimated Transfer Functions in the Presence of Undermodeling

We study the effect of undermodeling on the parameter variance for prediction error time-domain identification with linear model structures. We restrict our consideration to linear time-invariant discrete time single input single output systems. We examine the asymptotic expression for the variance as the number of data tends to infinity. This quantity is known to depend in general on the fourth order statistical properties of the applied input. However, we establish a sufficient condition under which the asymptotic variance is a function of the input power spectrum only. For this case we deliver exact expressions. We show that for a stochastic input the undermodeling contributes to the parameter variance due to the correlation between the prediction errors and its gradients. As an additional contribution we investigate the parameter variance under the assumptions of the stochastic embedding procedure. We show by means of a counterexample that in the framework of stochastic embedding the parameter variance is not necessarily monotonous with respect to the input power spectrum.

Prediction of Progressive Censored Data from the Gompertz Model

Progressive type-II censored sampling is an important scheme of obtaining data in lifetime studies. This article is concerned with the problem of obtaining Bayesian prediction bounds for future order statistics from the two-parameter Gompertz distribution based on progressive type-II censored data using the two-sample prediction technique. An algorithm due to Balakrishnan and Sandhu (Balakrishnan, N., Sandhu, R. A. (1995). A simple algorithm for generating progressive type-II censored samples. American Statistician 49(2):229–230.) and Aggarwala and Balakrishnan (Aggarwala, R., Balakrishnan, N. (1998a). Some properties of progressive censored order statistics from arbitary and uniform distributions with applications to inference and simulation. J. Statist. Plain. Inference 70:35–49.) was used to generate progressive type-II censored samples from the Gompertz distribution and the accuracy of prediction intervals is investigated via Monte Carlo simulation.

Information Aggregation in Common Value Auctions

A key question in information economics and finance is whether prices aggregate information in a competitive environment. That is, when agents are endowed with private information, does competition lead in the limit to prices which would occur if all information were public?. This paper examines the asymptotic properties of prices in common value auctions when the number of bidders becomes large. The main idea in this paper is to separate the issue of information aggregation from the issue of revenue efficiency. We also distinguish between the amount of information prices contain, and the degree to which prices approximate the asset’s value. Using this approach we get a simple characterization of the limiting distribution of prices. We are not only able to answer whether prices converge to the asset’s value, but also get an explicit form for the limiting distribution. Prices converge to the expected value of the asset conditional on the information possessed by what we call the “pivotal bidder.” This provides insights on how the auction format and the information structure influence the limiting behavior of prices. It shows that the limiting distribution of prices can be derived from the statistical properties of certain order statistics. This lets us abstract from the specific equilibrium bidding strategies. For example, we show that while the first and second price auction have different equilibrium strategies they share a similar limiting distribution of prices. These auctions yield different limiting distributions from auctions such as the English auction or kn auction. Our

Exact Non‐parametric Confidence Intervals for Quantiles with Progressive Type‐II Censoring

It is shown how various exact non‐parametric inferences based on order statistics in one or two random samples can be generalized to situations with progressive type‐II censoring, which is a kind of evolutionary right censoring. Ordinary type‐II right censoring is a special case of such progressive censoring. These inferences include confidence intervals for a given parent quantile, prediction intervals for a given order statistic of a future sample, and related two‐sample inferences based on exceedance probabilities. The proposed inferences are valid for any parent distribution with continuous distribution function. The key result is that each observable uncensored order statistic that becomes available with progressive type‐II censoring can be represented as a mixture with known weights of underlying ordinary order statistics. The importance of this mixture representation lies in that various properties of such observable order statistics can be deduced immediately from well‐known properties of ordinary order statistics.

Properties of speckle patterns generated through multiaperture pupils

The characteristics of the image speckles obtained through multiple aperture pupils are theoretically analyzed in terms of the parameters defining the pupils. The possibility of interpreting and synthesizing the image speckle distribution in terms of rather elementary structures is considered, based on the Fourier optics analysis. Then, first and second order statistical properties of the speckle patterns are studied by evaluating both the mutual intensity and the auto-correlation intensity of speckle distributions obtained by means of pupils consisting of identical apertures. Experimental results are presented to confirm the analysis.

Non‐Minimum Phase Seismic Wavelet Reconstruction Based on Higher Order Statistics

AbstractBased on higher order statistics property containing signal phase information, i.e. fourth order cumulant and its fourth order spectral on a received seismic signal, a novel approach for estimating non‐minimum phase seismic wavelets is proposed. This can be fully reconstructed from the fourth order spectrum by using only spectral decomposing of a seismic wavelet into minimum and maximum phases in an arbitrary Gaussian environment. The effectiveness of the method is demonstrated by computer simulation.

The travel time in carousel systems under the nearest item heuristic

A carousel is an automated warehousing system consisting of a large number of drawers rotating in a closed loop. In this paper, we study the travel time needed to pick a list of items when the carousel operates under the nearest item heuristic. We find a closed form expression for the distribution and all moments of the travel time. We also analyse the asymptotic behaviour of the travel time when the number of items tends to infinity. All results follow from probabilistic arguments based on properties of uniform order statistics.

Robust voice activity detection using higher-order statistics in the LPC residual domain

This paper presents a robust algorithm for voice activity detection (VAD) based on newly established properties of the higher order statistics (HOS) of speech. Analytical expressions for the third and fourth-order cumulants of the LPC residual of short-term speech are derived assuming a sinusoidal model. The flat spectral feature of this residual results in distinct characteristics for these cumulants in terms of phase, periodicity and harmonic content and yields closed-form expressions for the skewness and kurtosis. Important properties about these cumulants and their similarity with the autocorrelation function are revealed from this exploratory part. They show that the HOS of speech are sufficiently distinct from those of Gaussian noise and can be used as a basis for speech detection. Their immunity to Gaussian noise makes them particularly useful in algorithms designed for low SNR environments. The proposed VAD algorithm combines HOS metrics with second-order measures, such as SNR and LPC prediction error, to classify speech and noise frames. The variance of the HOS estimators is quantified and used to yield a likelihood measure for noise frames. Moreover, a voicing condition for speech frames is derived based on the relation between the skewness and kurtosis of voiced speech. The performance of the algorithm is compared to the ITU-T G.729B VAD in various noise conditions, and quantified using the probability of correct and false classifications. The results show that the proposed algorithm has an overall better performance than G.729B, with noticeable improvement in Gaussian-like noises, such as street and parking garage, and moderate to low SNR.

The travel time in carousel systems under the nearest item heuristic

A carousel is an automated warehousing system consisting of a large number of drawers rotating in a closed loop. In this paper, we study the travel time needed to pick a list of items when the carousel operates under the nearest item heuristic. We find a closed form expression for the distribution and all moments of the travel time. We also analyse the asymptotic behaviour of the travel time when the number of items tends to infinity. All results follow from probabilistic arguments based on properties of uniform order statistics.

Probability Inequalities for Generalized L-Statistics

where Xn:1 ≤ · · · ≤ Xn:n are the order statistics based on the sample {Xi; i ≤ n} and hni : R → R, i = 1, . . . , n, are measurable functions. In particular, if hni(y) = cnih(y) and h(y) is monotone then Φn represents the classical L-statistics. Functionals (1) in this general form are called generalized L-statistics. For the first time, these statistics were introduced in [1, 2] where asymptotic expansions for the distributions of these statistics were given in some particular cases. The Fourier analysis of the distributions of Φn is contained in [3]. Note that the integral-type statistics (integral functionals of the empirical distribution function, for example, the Anderson–Darling–Cramer statistics) can be represented as (1), but not as the classical L-statistics (see e.g. [1, 3]). The main purpose of this paper is to obtain upper bounds for the tail probability and moments of Φn. Exponential bounds for the tail probabilities of the classical L-statistics were obtained in [4] by means of approximation of L-statistics by U -statistics with nondegenerate kernels, which makes it possible to reduce the problem to analogous problems for sums of independent real-valued random variables. The approach of the present paper illustrates the capabilities of multivariate analysis: the problems in question are reduced to analogous problems for sums of independent random elements taking values in a functional Banach space. In the previous paper [5], containing some moment inequalities for generalized L-statistics, we suggested an analogous approach using a special property of the order statistics based on a sample from an exponential distribution. In the present paper, to study generalized L-statistics we essentially use the properties of order statistics based on a sample from the (0, 1)-uniform distribution, although we impose no additional restrictions on the sample distribution for the so-called L-statistics with separated kernels which are introduced below. Note also that the term “generalized L-statistics” was introduced in [6] where a generalization of the classical L-statistics theory was considered in a somewhat different aspect related to another construction of order statistics.

Structural and Transport Properties of Alumina Porous Membranes from Process-Based and Statistical Reconstruction Techniques

We study the structural and transport properties of two model porous membranes made by compaction of spherical monosize γ-alumina particles. A ballistic deposition process of spherical particles has been employed as a process-based representation method for accurately simulating the pore structure of the membranes. Comparison between the computed and experimental permeability values obtained in the Knudsen regime shows very good agreement for both membranes and indicates that sufficient representation of the original pore structure is achieved with the random sphere packs. In a further step, a medium with the same porosity and autocorrelation function as the sphere pack has been stochastically reconstructed. Comparison between the structural properties of the random sphere pack system (process-based model) and the stochastically reconstructed medium (statistical model) shows nearly identical correlation functions and pore chord length distributions but widely different mass chord length distributions. This is reflected to a significant difference in the prediction of a dynamic property like the Knudsen permeability by a factor of about 4. The results suggest that matching of the porosity and the two-point correlation function alone is not always adequate when pursuing an accurate representation of the structure of a porous material. In such cases, higher order statistical properties of the material contained in the chord length distribution of both pore and solid phase should be satisfied as well. It is also found that proper account of the formation process in the reconstruction of a porous material (process-based model) leads to representations of its structure more accurate than those of statistical reconstruction models.