Moments Of Order Statistics Research Articles

Inferences for the Type-II Exponentiated Log-Logistic Distribution Based on Order Statistics with Application

In this paper, we first derive the exact explicit expressions for the single and product moments of order statistics from the type-II exponentiated log-logistic distribution, and then use these results to compute the means, variances, skewness and kurtosis of rth order statistics. Besides, best linear unbiased estimators (BLUEs) for the location and scale parameters for the type-II exponentiated log-logistic distribution with known shape parameters are studied. Finally, the results are illustrated with a real data set.

Exponentiated Teissier distribution with increasing, decreasing and bathtub hazard functions

This article introduces a two-parameter exponentiated Teissier distribution. It is the main advantage of the distribution to have increasing, decreasing and bathtub shapes for its hazard rate function. The expressions of the ordinary moments, identifiability, quantiles, moments of order statistics, mean residual life function and entropy measure are derived. The skewness and kurtosis of the distribution are explored using the quantiles. In order to study two independent random variables, stress–strength reliability and stochastic orderings are discussed. Estimators based on likelihood, least squares, weighted least squares and product spacings are constructed for estimating the unknown parameters of the distribution. An algorithm is presented for random sample generation from the distribution. Simulation experiments are conducted to compare the performances of the considered estimators of the parameters and percentiles. Three sets of real data are fitted by using the proposed distribution over the competing distributions.

Recurrence relations for moments of order statistics from half logistic-geometric distribution and their applications

The half logistic-geometric (HLG) distribution derived here is a simple distribution with interesting properties and is therefore a useful distribution for analyzing lifetime data. Algorithm is derived for the computation of single and product moments of order statistics from this distribution. These recurrence relations enable the computation of means, variances and covariances of all order statistics for all sample size in a simple and efficient way. The results are of great importance in determining the best linear unbiased estimator of the scale parameter of a scaled-HLG distribution, and those of parameters of the more general location-scale HLG distribution based on complete and Type-II censored samples. Finally, an example is presented to illustrate the developed results.

Skin Disease Classification using Neural Network.

In this study, a novel and fully automatic skin disease classification approach is proposed using statistical feature extraction and Artificial Neural Network (ANN) based classification using first and second order statistical moments, the entropy of different color channels and texture-based features. The basic aim of our study is to develop an automated system for skin disease classification that can help a general physician to automatically detect the lesion and classify it to disease types. The performance of the proposed approach is corroborated by extensive experiments performed on a dataset of 588 images containing 6907 lesion regions. The results show that the proposed methodology can be effectively used to construct a skin disease classification system. Our proposed method is designed for a specific skin tone. Future investigation is needed to analyze the impact of different skin tones on the performance of lesions detection and classification system.

A Note on Exact Moments of Order Statistics from Exponentiated Burr XII Distribution

In this paper, we establish the explicit expressions and some recurrence relations for single and product moments of order statistics from exponentiated Burr XII distribution. By using, these results we can calculate the mean and variances based on order statistics for the given distribution.

Wall pressure fluctuations induced by a single stream jet over a semi-finite plate

This work provides an experimental investigation into the interaction between a jet flow and a semi-finite plate parallel to the jet. Wall pressure fluctuations have been measured in a high compressible subsonic regime and for different distances between the jet and the plate trailing edge. The experiment has been carried out in the ISVR anechoic Doak Laboratory at the University of Southampton, using wall pressure transducers flush mounted on the plate surface. Signals were acquired in the stream-wise direction along the jet centreline and in the span-wise direction in a region close to the trailing edge. The radial position of the flat plate was fixed very close to the jet axis to simulate a realistic jet–wing configuration. The plate was moved axially in order to investigate four different jet-trailing edge distances and to include measurements upstream of the nozzle exhaust. The acquired database was analyzed in both the frequency and the time domains providing an extensive statistical characterization in terms of spectral uni– and multi–variate quantities as well as high order statistical moments. A wavelet analysis was performed as well to investigate the time evolution of the wall pressure events.

Inference for generalized inverse Lindley distribution based on generalized order statistics

This article addresses the problem of deriving the explicit expressions for single and product moments of order statistics, generalized order statistics and dual generalized order statistics from the generalized Lindley distribution. The means and variances of order statistics, lower record values and progressively type-II censored order statistics for various values of the parameters are tabulated. Furthermore, the maximum likelihood estimators for the parameters of the model using generalized order statistics are obtained. The Bayes estimators under squared error and LINEX (Linear exponential) loss functions using Markov Chain Monte Carlo (MCMC) technique are obtained. Finally, three real data examples to lower record values, type-II censored and progressively type-II censored order statistics have been analyzed for illustrative purposes.

Exponentiated quasi power Lindley power series distribution with applications in medical science

Abstract The present paper introduces an advanced five parameter lifetime model which is obtained by compounding exponentiated quasi power Lindley distribution with power series family of distributions. The EQPLPS family of distributions contains several lifetime sub-classes such as quasi power Lindley power series, power Lindley power series, quasi Lindley power series and Lindley power series. The proposed distribution exhibits decreasing, increasing and bathtub shaped hazard rate functions depending on its parameters. It is more flexible as it can generate new lifetime distributions as well as some existing distributions. Various statistical properties including closed form expressions for density function, cumulative function, limiting behaviour, moment generating function and moments of order statistics are brought forefront. The capability of the quantile measures in terms of Lambert W function is also discussed. Ultimately, the potentiality and the flexibility of the new class of distributions has been demonstrated by taking three real life data sets by comparing its sub-models.

On the comparison of several classical estimators of the extreme value index

Due to the fact that for heavy tails the classical Hill estimator of a positive extreme value index is asymptotically biased, new and interesting alternative estimators have appeared in the literature. In this work we compare several classical estimators of the extreme value index based on moments of the upper order statistics. Since several alternative estimators have eventually a null asymptotic bias, for some heavy tailed models, the comparison is performed not only with the Hill and recent generalized means estimators but also with an asymptotically unbiased Hill estimator. The comparison study is performed asymptotically, under a third-order framework, and for finite samples, through a Monte Carlo simulation study.

Power Spectrum in the Conductive Terrestrial Ionosphere

Stochastic differential equation of the phase fluctuations is derived for the collision conductive magnetized plasma in the polar ionosphere applying the complex geometrical optics approximation. Calculating second order statistical moments it was shown that the contribution of the longitudinal conductivity substantially exceeds both Pedersen and Hall’s conductivities. Experimentally observing the broadening of the spatial power spectrum of scattered electromagnetic waves which equivalent to the brightness is analyzed for the elongated ionospheric irregularities. It was shown that the broadening of the spectrum and shift of its maximum in the plane of the location of an external magnetic field (main plane) less than in perpendicular plane for plasmonic structures having linear scale tenth of kilometer; and substantially depends on the penetration angle of an incident wave in the conductive collision turbulent magnetized ionospheric plasma. The angle-of-arrival (AOA) in the main plane has the asymmetric Gaussian form while in the perpendicular plane increases at small anisotropy factors and then tends to the saturation for the power-low spectrum characterizing electron density fluctuations. Longitudinal conductivity fluctuations increase the AOAs of scattered radiation than in magnetized plasma with permittivity fluctuations. Broadening of the temporal spectrum containing the drift velocity of elongated ionospheric irregularities in the polar ionosphere allows to solve the reverse problem restoring experimentally measured velocity of the plasma streams and characteristic linear scales of anisotropic irregularities in the terrestrial ionosphere.

On the record-based transmuted model of balakrishnan and He based on weibull distribution

In this paper, it is investigated that the some statistical properties and the methods of estimation for transmuted record type Weibull (TRTW) distribution.The moments, variance, skewness and kurtosis coefficients, geometric mean, quantile function, median, incomplete moments, Rényi entropy, the moments of order statistics are obtained for TRTW distribution. Six different estimators are considered in order to estimate the parameters of TRTW distribution. Furthermore, Monte Carlo (MC) simulations are performed to evaluate the performances of these estimators. Finally, a real data example is presented to illustrate the usefullness of TRTW distribution.

Alternative approach to moments of order statistics from one-parameter Weibull distribution

Abstract The Weibull distribution is used to describe various observed failures of phenomena and widely used in survival analysis and reliability theory. Sometimes it is very difficult to compute moments of such distributions due to various reasons for e.g. analytical issues, multi parameter cases etc. This study presents the computation of the moments and the expected value of the product of order statistics in the sample from the one-parameter Weibull distribution. An alternative approach in connection to survival function is used to obtain these moments and expected values. In addition the characteristic function of the above distribution is also obtained in the form of gamma functions. Further an illustration is shown to find the first two moments and expected value of the product of order statistics by using this approach.

Moments of Order Statistics from Length-Biased Exponential Distribution and Associated Inference

Dara and Ahmad (Recent advances in moment distribution and their hazard rates, Academic Publishing GmbH KG, Lap Lambert, 2012) proposed the length-biased exponential (LBE) distribution and proved that the LBE distribution is more flexible than the exponential distribution. In this paper, we have obtained new explicit algebraic expressions and some recurrence relations for both single and product moments of order statistics from LBE distribution. Further, these expressions are used to compute the means, variances and covariances of order statistics for different sample of sizes and for arbitrarily chosen parameter values. Next, we use these moments to obtain the best linear unbiased estimates of the location and scale parameters based on complete as well as Type-II right censored samples. Finally, we carried out a simulation study to show the application of our results.

On Moments of Lindley Distribution Based on Generalized Order Statistics

In this paper, we have deduced the exact and explicit expressions for single and product moments of Lindley distribution based on generalized order statistics in terms of Gauss hypergeometric function and Kampé de Fériet series. These results include the exact expression for the single and product moments of order statistics, progressive Type II censoring, record values Pfeifer’s record value and sequential order statistics from Lindley distribution. Further, means and variances of Lindley distribution based on order statistics, progressive type II censored order statistics and for generalized order statistics have been computed. We have also calculated the best linear unbiased estimators for location and scale parameters of Lindley distribution utilizing these results. Finally, a real data application is given.

Moments of order statistics from DNID discrete random variables with application in reliability

In this paper, we present methods of obtaining single moments of order statistics arising from possibly dependent and non-identically distributed discrete random variables. We derive exact and approximate formulas convenient for numerical evaluation of such moments. To demonstrate their use, we tabulate means and second moments of order statistics from random vectors having some typical discrete distributions with selected parameter values. Next, we apply our results in reliability theory. We establish moments of discrete lifetimes of coherent systems consisting of heterogeneous and not necessarily independently working components. In particular, we obtain expression for expectations and variances of lifetimes of such systems. We give some illustrative examples.

A texture based descriptors used for real time tool condition monitoring

Tool Condition Monitoring Systems (TCMs), in the task of tool wear recognition, are highly dependent on the choice of descriptors. It is very important to extract the appropriate marking that contains information on the tool wear condition from the sensor signal. We consider the portions of the Short-Term Discrete Furrier Transform (STDFT) spectrum obtained by speaking from a vibration signal sensor as a 2D textured image. This is achieved by setting the STDFT timeline as the first dimension and the frequency scales as the second dimension of the resulting textured image. We divide the resulting textured image into special particular patches of texture, focusing on a portion of the frequency range of interest. Applying the set filter bank, 2D textons are allocated for each predefined frequency band. From 2D textons, for each frequency band, we extract probability density function (PDF) data in the form of lower order statistical moments. The applied method gives robust descriptors of the Tool wear state.

Relations for Moments of Dual Generalized Order Statistics from Exponentiated Rayleigh Distribution and Associated Inference

In this paper we obtain exact expressions and some recurrence relations satisfied by single and product moments of dual generalized order statistics from exponentiated Rayleigh distribution. These relations are deduced for moments of order statistics and lower record values. Further, conditional expectation, recurrence relations for single moments and truncated moment are used to characterize this distribution.

Recurrence Relations for the Moments of Minimum Order Statistics from Exponential Distribution

In this paper, certain recurrence relations for the moments of minimum order statistics of a random sample of size n arising from exponential distribution are obtained. The usefulness of these relations in evaluating the moments of exponential minimum order statistics is also discussed.

On the Maximum–Minimums Identity: Extension and Applications

For real numbers the maximum–minimums identity allows us to express the maximum of in terms of the minimums of subsets of . In this note, we provide an extension allowing us to express the kth-ranked element in terms of the minimums of subsets of sizes . We also discuss the dual identity, allowing us to express the kth-ranked element in terms of the maximums of subsets of sizes . We present three examples: The first relates to the expected value of order statistics from independent nonidentical geometric distributions, the second to the partial coupon collector’s problem, and the third to relations among moments of order statistics.

Geometric Algebra Correntropy: Definition and Application to Robust Adaptive Filtering

Correntropy is an efficient tool for analyzing higher order statistical moments in non-Gaussian noise environments. Correntropy has been used with real, complex, and quaternion data. However, there is no literature studying the correntropy with geometric algebra data. The geometric algebra has been widely used in the engineering applications including the signal processing and image processing. From the probabilistic view, this brief presents a novel geometric algebra correntropy (GAC) which represents the similarity measure between two random geometric algebra (multivector valued) variables. Then, we develop the adaptive filter based on the maximum GAC criteria (MGACC), which is robust against the non-Gaussian noise. Simulation is conducted to verify the advantages of the proposed adaptive algorithm under the non-Gaussian environment.