Single Moments Research Articles

Exact Moments of Order Statistics and Parameter Estimation for Sushila Distribution

In this paper, we have obtained the exact expression and recurrence relations for single moments of order statistics arising from Sushila distribution. We have also obtained L-moments, TL-moments of Sushila distribution and used them to find the L-moment and TL-moment estimators of the parameters of the distribution. The estimators of the parameters are also obtained using the method of moments and maximum likelihood. Further, by using these maximum likelihood estimators (MLEs), we have also obtained the MLEs of the measures of reliability of the considered distribution. Monte Carlo simulation has been carried out to investigate the performance of the estimators.

Analytic and numerical bootstrap for one-matrix model and “unsolvable” two-matrix model

We propose the relaxation bootstrap method for the numerical solution of multi-matrix models in the large N limit, developing and improving the recent proposal of H. Lin. It gives rigorous inequalities on the single trace moments of the matrices up to a given “cutoff” order (length) of the moments. The method combines usual loop equations on the moments and the positivity constraint on the correlation matrix of the moments. We have a rigorous proof of applicability of this method in the case of the one-matrix model where the condition of positivity of the saddle point solution appears to be equivalent to the presence of supports of the eigenvalue distribution only on the real axis and only with positive weight. We demonstrate the numerical efficiency of our method by solving the analytically “unsolvable” two-matrix model with tr[A, B]2 interaction and quartic potentials, even for solutions with spontaneously broken discrete symmetry. The region of values for computed moments allowed by inequalities quickly shrinks with the increase of the cutoff, allowing the precision of about 6 digits for generic values of couplings in the case of ℤ2 symmetric solutions. Our numerical data are checked against the known analytic results for particular values of parameters.

On the Generalized Bilal Distribution: Some Properties and Estimation under Ranked Set Sampling

The generalized Bilal (GB) distribution can be defined as the distribution of the median of three independent random variables drawn from the Weibull distribution. Its failure rate function can be monotonic (decreasing or increasing) or upside-down bathtub-shaped. In this study, we aim to reveal some important properties of the GB distribution that have not been considered before. The findings are both theoretical and practical. From the theoretical viewpoint, we present explicit expressions for both single and product moments of order statistics from the GB distribution. The L-moments are derived as well. From the practical viewpoint, the parameter estimations are accomplished using the maximum likelihood (ML) method, which is based on two different sampling schemes: simple random sampling (SRS) and ranked set sampling (RSS) schemes. Furthermore, the asymptotic confidence intervals for the SRS and RSS estimators are discussed. For the sake of comparison and illustration, a simulation study and a real data example are presented. Concluding remarks are given at the end.

On Relations for Moments of Generalized Order Statistics for Lindley–Weibull Distribution

Moments of generalized order statistics appear in several areas of science and engineering. These moments are useful in studying properties of the random variables which are arranged in increasing order of importance, for example, time to failure of a computer system. The computation of these moments is sometimes very tedious and hence some algorithms are required. One algorithm is to use a recursive method of computation of these moments and is very useful as it provides the basis to compute higher moments of generalized order statistics from the corresponding lower-order moments. Generalized order statistics provides several models of ordered data as a special case. The moments of generalized order statistics also provide moments of order statistics and record values as a special case. In this research, the recurrence relations for single, product, inverse and ratio moments of generalized order statistics will be obtained for Lindley–Weibull distribution. These relations will be helpful for obtained moments of generalized order statistics from Lindley–Weibull distribution recursively. Special cases of the recurrence relations will also be obtained. Some characterizations of the distribution will also be obtained by using moments of generalized order statistics. These relations for moments and characterizations can be used in different areas of computer sciences where data is arranged in increasing order.

The first-passage area of Ornstein-Uhlenbeck process revisited

For Ornstein-Uhlenbeck process starting from we highlight some results about the first-passage time of X(t) through zero and its first-passage area, that is the random area swept out by till its first-passage through zero. We study single and joint moments of the first-passage time and first-passage area, and their behaviors, as and moreover, we investigate the expected value of the time average of X(t) till the FPT, and the maximum displacement of

On the record values and its predictions from Exponentiated Inverted Weibull distribution and associated inference

This paper deals with the lowest record values from the Exponentiated Inverted Weibull distribution. We establish exact expression for moments of lower record values and also derive the recurrence relations for single and product moments of the same. Then we estimate the location and scale parameters as well as obtain confidence intervals for location and scale parameters from location-scale Exponentiated Inverted Weibull distribution. We also worked on future lower record values. We discuss linear predictor and prediction interval for the future record values. Finally, with the help of real rainfall data, we presented all the methods discussed here.

Relationships for moments of the progressively Type-II right censored order statistics from the power Lomax distribution and the associated inference

Abstract In this paper, we establish several recurrence relations between single and product moments of progressively Type-II right censored order statistics from the power Lomax distribution. The relations enable the computation of all the single and product moments of progressively Type-II right censored order statistics for all sample sizes n and all censoring schemes (R 1, R 2,..., R m ), m ≥ n, in a simple recursive manner. The maximum likelihood approach is used for the estimation of the parameters and the reliability characteristic. A Monte Carlo simulation study has been conducted to compare the performance of the estimates for different censoring schemes.

The Moment Properties of Order, Reversed Order and Upper Record Statistics for the Power Ailamujia Distribution

The power Ailamujia distribution has been successfully developed in statistics, both theoretically and practically, performing well in the fitting of various types of data. This paper investigates the moment properties of the associated order, reversed order and upper record statistics, which are indeed unexplored aspects of this distribution. In particular, the exact expressions for the single moments of the order and reversed order statistics are provided. Some recurrence relationships for both single and product moments for the order and upper record statistics are proved. For additional goals, certain joint distributions are also given.

On the order statistics of exponentiated moment exponential distribution and associated inference

Explicit algebraic expressions for both single and product moments of order statistics from the exponentiated moment exponential (EME) distribution are derived. By using these expressions, we have computed the means, variances and covariances of order statistics for and for arbitrarily chosen parameter values. Further, these moments are used to determine the best linear unbiased estimators (BLUEs) and best linear invariant estimators (BLIEs) of the location and scale parameters based on complete as well as Type-II right censored samples. Prediction of unobserved order statistics in Type-II right censored samples is also discussed. A simulation study and a real data example are presented for the sake of comparison and illustration. The concluding remarks are given at the end.

Ankle muscles drive mediolateral center of pressure control to ensure stable steady state gait

During steady-state walking, mediolateral gait stability can be maintained by controlling the center of pressure (CoP). The CoP modulates the moment of the ground reaction force, which brakes and reverses movement of the center of mass (CoM) towards the lateral border of the base of support. In addition to foot placement, ankle moments serve to control the CoP. We hypothesized that, during steady-state walking, single stance ankle moments establish a CoP shift to correct for errors in foot placement. We expected ankle muscle activity to be associated with this complementary CoP shift. During treadmill walking, full-body kinematics, ground reaction forces and electromyography were recorded in thirty healthy participants. We found a negative relationship between preceding foot placement error and CoP displacement during single stance; steps that were too medial were compensated for by a lateral CoP shift and vice versa, steps that were too lateral were compensated for by a medial CoP shift. Peroneus longus, soleus and tibialis anterior activity correlated with these CoP shifts. As such, we identified an (active) ankle strategy during steady-state walking. As expected, absolute explained CoP variance by foot placement error decreased when walking with shoes constraining ankle moments. Yet, contrary to our expectations that ankle moment control would compensate for constrained foot placement, the absolute explained CoP variance by foot placement error did not increase when foot placement was constrained. We argue that this lack of compensation reflects the interdependent nature of ankle moment and foot placement control. We suggest that single stance ankle moments do not only compensate for preceding foot placement errors, but also assist control of the subsequent foot placement. Foot placement and ankle moment control are ‘caught’ in a circular relationship, in which constraints imposed on one will also influence the other.

Multi-scale spatialtemporal information deep fusion network with temporal pyramid mechanism for video action recognition

In the deep learning-based video action recognitio, the function of the neural network is to acquire spatial information, motion information, and the associated information of the above two kinds of information over an uneven time span. This paper puts forward a network extracting video sequence semantic information based on deep integration of local Spatial-Temporal information. The network uses 2D Convolutional Neural Network (2DCNN) and Multi Spatial-Temporal scale 3D Convolutional Neural Network (MST_3DCNN) respectively to extract spatial information and motion information. Spatial information and motion information of the same time quantum receive 3D convolutional integration to generate the temporary Spatial-Temporal information of a certain moment. Then, the Spatial-Temporal information of multiple single moments enters Temporal Pyramid Net (TPN) to generate the local Spatial-Temporal information of multiple time scales. Finally, bidirectional recurrent neutral network is used to act on the Spatial-Temporal information of all parts so as to acquire the context information spanning the length of the entire video, which endows the network with video context information extraction capability. Through the experiments on the three video action recognitio common experimental data sets UCF101, UCF11, UCFSports, the Spatial-Temporal information deep fusion network proposed in this paper has a high correct recognition rate in the task of video action recognitio.

Moments of generalized order statistics for Pareto-Rayleigh distribution

In this paper, we derive the explicit expressions for single and product moments of generalized order statistics from Pareto-Rayleigh distribution using hypergeometric functions. Also, some interesting remarks are presented.

The effect of a medial knee thrust gait modification on single plane and 3D peak moments

The effect of a medial knee thrust gait modification on single plane and 3D peak moments

Moment properties of lower record values from generalized inverse Weibull distribution and characterization

In this paper, the exact expressions as well as recurrence relations for single and product moments of the generalized lower record values from generalized inverse Weibull distribution are obtained. Further, the characterization of the given distribution is carried out through recurrence relations and conditional moment.

Inferences for generalized Topp-Leone distribution under dual generalized order statistics with applications to Engineering and COVID-19 data

This article accentuates the estimation of a two-parameter generalized Topp-Leone distribution using dual generalized order statistics (dgos). In the part of estimation, we obtain maximum likelihood (ML) estimates and approximate confidence intervals of the model parameters using dgos, in particular, based on order statistics and lower record values. The Bayes estimate is derived with respect to a squared error loss function using gamma priors. The highest posterior density credible interval is computed based on the MH algorithm. Furthermore, the explicit expressions for single and product moments of dgos from this distribution are also derived. Based on order statistics and lower records, a simulation study is carried out to check the efficiency of these estimators. Two real life data sets, one is for order statistics and another is for lower record values have been analyzed to demonstrate how the proposed methods may work in practice.

Generalized Exponential Power Distribution with Application to Complete and Censored Data

The exponential power distribution (EP) is a lifetime model that can exhibit increasing and bathtub hazard rate function. This paper proposed a generalization of EP distribution, named generalized exponential power (GEP) distribution. Some properties of GEP distribution will be investigated. Recurrence relations for single moments of generalized ordered statistics from GEP distribution are established and used for characterizing the GEP distribution. Estimation of the model parameters are derived using maximum likelihood method based on complete sample, type I, type II and random censored samples. A simulation study is performed in order to examine the accuracy of the maximum likelihood estimators of the model parameters. Three applications to real data, two with censored data, are provided in order to show the superiority of the proposed model to other models.

On the Omega Distribution: Some Properties and Estimation

We obtain explicit expressions for single and product moments of the order statistics of an omega distribution. We also discuss seven methods to estimate the omega parameters. Various simulation results are performed to compare the performance of the proposed estimators. Furthermore, the maximum likelihood method is adopted to estimate the omega parameters under the type II censoring scheme. The usefulness of the omega distribution is proven using a real data set.

Information Measures for Generalized Order Statistics and Their Concomitants under General Framework from Huang-Kotz FGM Bivariate Distribution.

In this paper, we study the concomitants of dual generalized order statistics (and consequently generalized order statistics) when the parameters are assumed to be pairwise different from Huang–Kotz Farlie–Gumble–Morgenstern bivariate distribution. Some useful recurrence relations between single and product moments of concomitants are obtained. Moreover, Shannon’s entropy and the Fisher information number measures are derived. Finally, these measures are extensively studied for some well-known distributions such as exponential, Pareto and power distributions. The main motivation of the study of the concomitants of generalized order statistics (as an important practical kind to order the bivariate data) under this general framework is to enable researchers in different fields of statistics to use some of the important models contained in these generalized order statistics only under this general framework. These extended models are frequently used in the reliability theory, such as the progressive type-II censored order statistics.

On concomitants of dual generalized order statistics from Bairamov–Kotz–Becki Farlie–Gumbel–Morgenstern bivariate distributions

In this paper, we study the concomitants of [Formula: see text]-dual generalized order statistics ([Formula: see text]-DGOS) from Bairamov–Kotz–Becki Farlie–Gumbel–Morgenstern bivariate distributions as an extension of several recent papers. This study can also be applied to the model of [Formula: see text]-generalized order statistics ([Formula: see text]-GOS) as a parallel model of [Formula: see text]-DGOS. Furthermore, the joint distribution of [Formula: see text]-DGOS of concomitants for this family is studied. Some useful recurrence relations between single and product moments of concomitants are obtained. Moreover, most of the paper results are extended to any arbitrary distribution. Finally, an application of these results is given for bivariate generalized exponential distribution.

Relations for moments of progressively Type-II censored order statistics from the exponential-geometric distribution and associated inference

In this paper, we derive the recurrence relations for the single and product moments of progressively Type-II right censored order statistics from the exponential-geometric distribution. For a particular case, these results are reduced to the corresponding results for the usual order statistics. Next, we use these moments to obtain the best linear unbiased estimators of the scale and location-scale parameters of the exponential-geometric distribution based on progressively Type-II right censored samples. The best linear unbiased predictors of future failure times are then discussed. Finally, an illustrative example is presented.