Lottery Numbers and Ordered Statistics

The lottery has long captivated the imagination of players worldwide, offering the tantalizing possibility of life-changing wins. While winning the lottery is largely a matter of chance, as lottery drawings are typically random and unpredictable. Some people use the lottery terminal randomly generates numbers for them, some players choose numbers that hold personal significance to them, such as birthdays, anniversaries, or other important dates, some enthusiasts have turned to statistical analysis as a means to analyze past winning numbers identify patterns or frequencies. In this paper, we use order statistics to estimate the probability of specific order of numbers or number combinations being drawn in future drawings.

The asymptotic relation between the first crossing point and the last exit time of Gaussian order statistics sequences

In this paper,we study the asymptotic relation between the first crossing point and the last exit time for Gaussian order statistics which are generated by stationary weakly and strongly dependent Gaussian sequences.It is shown that the first crossing point and the last exit time are asymptotically independent and dependent for weakly and strongly dependent cases,respectively.The asymptotic relations between the first crossing point and the last exit time for stationary weakly and strongly dependent Gaussian sequences are also obtained.

Nearly best linear estimates of logistic parameters based on complete ordered statistics

Deals with the determination of the nearly best linear estimates of location and scale parameters of a logistic population, when both parameters are unknown, by introducing Blom’s semi empirical ’α,β correction’ into the asymptotic mean and covariance formulae with complete and ordered samples taken into consideration and various nearly best linear estimates established and points out the high efficiency of these estimators relative to the best linear unbiased estimators (BLUEs) and other linear estimators makes them useful in practice.

Performance analysis of multi-channel order statistics detector for range-spread target

The problem of two order statistics detection schemes for the detection of a spatially distributed target in white Gaussian noise are studied.When the number of strong scattering cells is known,we first show an optimal detector,which requires many processing channels.The structure of such optimal detector is complex.Therefore,a simpler quasi-optimal detector is then introduced.The quasi-optimal detector,called the strong scattering cells’ number dependent order statistics（SND-OS） detector,takes the form of an average of maximum strong scattering cells with a known number.If the number of strong scattering cells is unknown in real situation,the multi-channel order statistics（MC-OS） detector is used.In each channel,a various number of maximums scattered from target are averaged.Then,the false alarm probability analysis and thresholds sets for each channel are given,following the detection results presented by means of Monte Carlo simulation strategy based on simulated target model and three measured targets.In particular,the theoretical analysis and simulation results highlight that the MC-OS detector can efficiently detect range-spread targets in white Gaussian noise.

Target detection for low angle radar based on multi-frequency order-statistics

For radar targets flying at low altitude, multiple pathways produce fade or enhancement relative to the level that would be expected in a free-space environment. In this paper, a new detec- tion method based on a wide-ranging multi-frequency radar for low angle targets is proposed. Sequential transmitting multiple pulses with different frequencies are first applied to decorrelate the cohe- rence of the direct and reflected echoes. After receiving all echoes, the multi-frequency samples are arranged in a sort descending ac- cording to the amplitude. Some high amplitude echoes in the same range cell are accumulated to improve the signal-to-noise ratio and the optimal number of high amplitude echoes is analyzed and given by experiments. Finally, simulation results are presented to verify the effectiveness of the method.

Analysis of linear weighted order statistics CFAR algorithm

CFAR technique is widely used in radar targets detection fields. Traditional algorithm is cell averaging (CA), which can give a good detection performance in a relatively ideal environment. Recently, censoring technique is adopted to make the detector perform robustly. Ordered statistic (OS) and trimmed mean (TM) methods are proposed. TM methods treat the reference samples which participate in clutter power estimates equally, but this processing will not realize the effective estimates of clutter power. Therefore, in this paper a quasi best weighted (QBW) order statistics algorithm is presented. In special cases, QBW reduces to CA and the censored mean level detector (CMLD).

Prediction Based on Generalized Order Statistics from a Mixture of Rayleigh Distributions Using MCMC Algorithm

This article considers the problem in obtaining the maximum likelihood prediction (point and interval) and Bayesian prediction (point and interval) for a future observation from mixture of two Rayleigh (MTR) distributions based on generalized order statistics (GOS). We consider one-sample and two-sample prediction schemes using the Markov chain Monte Carlo (MCMC) algorithm. The conjugate prior is used to carry out the Bayesian analysis. The results are specialized to upper record values. Numerical example is presented in the methods proposed in this paper.

Passive Steganalysis Based on Higher Order Image Statistics of Curvelet Transform

Steganographic techniques accomplish covert communication by embedding secret messages into innocuous digital images in ways that are imperceptible to the human eye. This paper presents a novel passive steganalysis strategy in which the task is approached as a pattern classification problem. A critical part of the steganalyser design depends on the selection of informative features. This paper is aimed at proposing a novel attack with improved performance indices with the following implications： 1） employing higher order statistics from a curvelet sub-band image representation that offers better discrimination ability for detecting stego anomalies in images, as compared to other conventional wavelet transforms; 2） increasing the sensitivity and specificity of the system by the feature reduction phase; 3） realizing the system using an efficient classification engine, a neuro-C4.5 classifier, which provides better classification rate. An extensive experimental evaluation on a database containing 5600 clean and stego images shows that the proposed scheme is a state-of-the-art steganalyser that outperforms other previous steganalytic methods.

On-line blind source separation algorithm based on second order statistics

An on-line blind source separation （BSS） algorithm is presented in this paper under the assumption that sources are temporarily correlated signals. By using only some of the observed samples in a recursive calculation, the whitening matrix and the rotation matrix could be approximately obtained through the measurement of only one cost function. SimNations show goad performance of the algorithm.

Higher-Order Statistics for Automatic Weld Defect Detection

Image processing and image analysis are the main aspects for obtaining information from digital image owing to the fact that this techniques give the desired details in most of the applications generally and Non-Destructive testing specifically. This paper presents a proposed method for the automatic detection of weld defects in radiographic images. Firstly, the radiographic images were enhanced using adaptive histogram equalization and are filtered using mean and wiener filters. Secondly, the welding area is selected from the radiography image. Thirdly, the Cepstral features are extracted from the Higher-Order Spectra (Bispectrum and Trispectrum). Finally, neural networks are used for feature matching. The proposed method is tested using 100 radiographic images in the presence of noise and image blurring. Results show that in spite of time consumption, the proposed method yields best results for the automatic detection of weld defects in radiography images when the features were extracted from the Trispectrum of the image.

DOA Estimation Based on Sparse Representation of the Fractional Lower Order Statistics in Impulsive Noise

This paper is mainly to deal with the problem of direction of arrival(DOA) estimations of multiple narrow-band sources impinging on a uniform linear array under impulsive noise environments. By modeling the impulsive noise as α-stable distribution, new methods which combine the sparse signal representation technique and fractional lower order statistics theory are proposed. In the new algorithms, the fractional lower order statistics vectors of the array output signal are sparsely represented on an overcomplete basis and the DOAs can be effectively estimated by searching the sparsest coefficients. To enhance the robustness performance of the proposed algorithms,the improved algorithms are advanced by eliminating the fractional lower order statistics of the noise from the fractional lower order statistics vector of the array output through a linear transformation. Simulation results have shown the effectiveness of the proposed methods for a wide range of highly impulsive environments.

Identification of the Wave-Particles Interaction in Space Plasma Using Higher-Order Statistics

The interaction of wave-particles and wave-wave in the space plasmas are essentially non-linear or non-Gaussian processes. Using the higher-order statistical analyses methods (higher-order moments and bi-tri correlation or bi-tri spectrum), its physical properties can be described. The question addressed in this paper is that of the usefulness of higher-order statistical analysis for identification of the wave-particles interaction in space plasmas. The signals handled are from the ARCAD-3 ISOPROBE experiment on ELF frequency range, then strong electrostatic turbulence and electron density irregularities. Second and third order statistical analyses are applied: first, on time series associated with each type of measurement, then, on the two types. All results are presented for one typical case. Correlation functions estimated over the corresponding time intervals point out the existence of a, non-linear interaction between these fluctuations and electrostatic filed.

SOME COMPARISONS BETWEEN GENERALIZED ORDER STATISTICS

Some stochastic comparisons of generalized order statistics under the right spread order, the location independent riskier order and the total time transform order are investigated in this paper. The underlying distributions and parameters on which generalized order statistics are based are also surveyed to obtain the conditions for increasing the expectations of spacings between the first two generalized order statistics and between the last two generalized order statistics.

Generalized Entropy of Order Statistics

In this communication, we consider and study a generalized two parameters entropy of order statistics and derive bounds for it. The generalized residual entropy using order statistics has also been discussed.

On Moment Generating Function of Generalized Order Statistics from Erlang-Truncated Exponential Distribution

In this paper explicit expressions and some recurrence relations are derived for marginal and joint moment generating functions of generalized order statistics from Erlang-truncated exponential distribution. The results for k-th record values and order statistics are deduced from the relations derived. Further, a characterizing result of this distribution on using the conditional expectation of function of generalized order statistics is discussed.

Classification of Multi-User Chirp Modulation Signals Using Wavelet Higher-Order-Statistics Features and Artificial Intelligence Techniques

Higher order statistical features have been recently proved to be very efficient in the classification of wideband communications and radar signals with great accuracy. On the other hand, the denoising properties of the wavelet transform make WT an efficient signal processing tool in noisy environments. A novel technique for the classification of multi-user chirp modulation signals is presented in this paper. A combination of the higher order moments and cumulants of the wavelet coefficients as well as the peaks of the bispectrum and its bi-frequencies are proposed as effective features. Different types of artificial intelligence based classifiers and clustering techniques are used to identify the chirp signals of the different users. In particular, neural networks (NN), maximum likelihood (ML), k-nearest neighbor (KNN) and support vector machine (SVMs) classifiers as well as fuzzy c-means (FCM) and fuzzy k-means (FKM) clustering techniques are tested. The Simulation results show that the proposed technique is able to efficiently classify the different chirp signals in additive white Gaussian noise (AWGN) channels with high accuracy. It is shown that the NN classifier outperforms other classifiers. Also, the simulations prove that the classification based on features extracted from wavelet transform results in more accurate results than that using features directly extracted from the chirp signals, especially at low values of signal-to-noise ratios.

Generalized Order Statistics from Generalized Exponential Distributions in Explicit Forms

The generalized order statistics which introduced by [1] are studied in the present paper. The Gompertz distribution is widely used to describe the distribution of adult deaths, and some related models used in the economic applications [2]. Previous works concentrated on formulating approximate relationships to characterize it [3-5]. The main aim of this paper is to obtain the distribution of single, two, and all generalized order statistics from Gompertz distribution with some special cases. In addition the conditional distribution of two generalized order statistics from the same distribution is obtained. The Gompertz distribution has a continuous probability density function with location parameter a and shape parameter b, , where x restricted by the interval . The nth moment generated function of the Gompertz distributed random variable X is given on the form: where, is the generalized integro-exponential function [6]. In this paper we shall obtain joint distribution, distribution of product of two generalized order statistics from the Gompertz distribution, and then derive some useful formulas of these distributions as special cases.

Inferences under a Class of Finite Mixture Distributions Based on Generalized Order Statistics

The main purpose of this paper is to obtain estimates of parameters, reliability and hazard rate functions of a heterogeneous population represented by finite mixture of two general components. The doubly Type II censoring of generalized order statistics scheme is used. Maximum likelihood and Bayes methods of estimation are used for this purpose. The two methods of estimation are compared via a Monte Carlo Simulation study.

Bayesian Prediction of Future Generalized Order Statistics from a Class of Finite Mixture Distributions

This article is concerned with the problem of prediction for the future generalized order statistics from a mixture of two general components based on doubly?type II censored sample. We consider the one sample prediction and two sample prediction techniques. Bayesian prediction intervals for the median of future sample of generalized order statistics having odd and even sizes are obtained. Our results are specialized to ordinary order statistics and ordinary upper record values. A mixture of two Gompertz components model is given as an application. Numerical computations are given to illustrate the procedures.

Quantile Version of Mathai-Haubold Entropy of Order Statistics

Many researchers measure the uncertainty of a random variable using quantile-based entropy techniques.These techniques are useful in engineering applications and have some exceptional characteristics than their distribution function method.Considering order statistics,the key focus of this article is to propose new quantile-based Mathai-Haubold entropy and investigate its characteristics.The divergence measure of theMathai-Haubold is also considered and some of its properties are established.Further,based on order statistics,we propose the residual entropy of the quantile-based Mathai-Haubold and some of its property results are proved.The performance of the proposed quantile-based Mathai-Haubold entropy is investigated by simulation studies.Finally,a real data application is used to compare our proposed quantile-based entropy to the existing quantile entropies.The results reveal the outperformance of our proposed entropy to the other entropies.