Generalized Order Statistics Research Articles

Recursive Computation of Rayleigh- Rayleigh Distribution via Ordered Random Variates

Ordered random variables (ORVs) are of great importance in statistical science. These random variables are organized in increasing order called generalized order statistics (GOS). It has tremendous applications in engineering and science due to the inclusion of ordered random variables. This article addresses recursive moments of Rayleigh-Rayleigh distribution using order random variables. Such moments are applicable in studying the characteristics of random variables in increasing order such as time to failure of an electronic devices. The characterization result is also obtained by simple moments.

Extropy and statistical features of dual generalized order statistics’ concomitants arising from the Sarmanov family

Abstract In this study, we disclose several statistical properties of concomitants of dual generalized order statistics (DGOSs) under a generic setting from the Sarmanov family of bivariate distributions. For this family, cross-moments and joint distributions of concomitants of DGOSs are explored. These results' implications for order statistics and record values are examined. Extropy and cumulative residual extropy (CRE), two well-known information measures, are also investigated. This study offers a few beautiful symmetrical relationships that these inaccuracy measurements satisfy. In addition, based on the concomitants of DGOSs, the issue of estimating the negative cumulative residual extropy (NCRE), empirical NCRE and NCE are investigated using the empirical technique. Lastly, a set of bivariate data from the real world is examined.

Moments of Powered Rayleigh Distribution by Generalized Order Statistics

Moments of Powered Rayleigh Distribution by Generalized Order Statistics

Predicting future failures in generalized order statistics and related models

Quantile regression predictions are considered for generalized order statistics which extend results previously established for record values and order statistics. In order to derive the results, some (univariate and bivariate) distortion representations of generalized order statistics are established. In particular, prediction of the sth generalized order statistic X ( s ) ∗ based on F given a single (generalized) order statistic X ( r ) ∗ with r<s will be addressed. The presentation includes results for both known and unknown baseline distributions. In the latter case, we consider exponential distributions with unknown mean as well as the proportional hazards model. Using unimodality properties of the marginal density functions (pdf) of generalized order statistics, we find a simple representation of the maximum likelihood prediction of X ( s ) ∗ given X ( r ) ∗ .

On multivariate orderings of some general ordered random vectors

Ordered random vectors are frequently encountered in many problems. The generalized order statistics (GOSs) and sequential order statistics (SOSs) are two general models for ordered random vectors. However, these two models do not capture the dependency structures that may be present in the underlying random variables. In this paper, we study the developed sequential order statistics (D-SOSs) and developed generalized order statistics (D-GOSs) models that incorporate dependency structures among ordered random vectors. We then study various univariate and multivariate ordering properties of D-SOS and D-GOS models under Archimedean copula. We develop corresponding results for both one-sample and two-sample situations. We also present some simulational results and a real data analysis for illustrative purpose.

The generalized order statistics arising from three populations with the lower truncated proportional hazard rate models and its application to the sensitivity to the early disease stage

ABSTRACT In this paper, we present some results to make inference about the parameters of lower truncated proportional hazard rate models with the same baseline distributions based on three independent generalized order statistics samples. Then, especially by considering the results of the diagnostic tests for the non-diseased, early-diseased stage and fully diseased populations, we make inference about sensitivity to the early disease stage parameter. The maximum likelihood estimator, a generalized pivotal estimator and some Bayes estimators are obtained for different structures of prior distributions. The percentile bootstrap confidence interval, a generalized pivotal confidence interval and some Bayesian credible intervals are also presented. A Monte Carlo simulation study is used to evaluate the performances of the obtained point estimators and confidence/credible intervals and two competitors. We use two real datasets to illustrate the proposed methods.

Some New Results on Stochastic Comparisons of Spacings of Generalized Order Statistics from One and Two Samples

Generalized order statistics (GOSs) are often adopted as a tool for providing a unified approach to several stochastic models dealing with ordered random variables. In this contribution, we first recall various useful results based on the notion of total positivity. Then, some stochastic comparisons between spacings of GOSs from one sample, as well as two samples, are developed under the more general assumptions on the parameters of the model. Specifically, the given results deal with the likelihood ratio order, the hazard rate order and the mean residual life order. Finally, an application is demonstrated for sequential systems.

Moments of Generalized Order Statistics from Doubly Truncated Power Linear Hazard Rate Distribution

Moments of Generalized Order Statistics from Doubly Truncated Power Linear Hazard Rate Distribution

Inference and other aspects for $ q- $Weibull distribution via generalized order statistics with applications to medical datasets

&lt;abstract&gt;&lt;p&gt;This work utilizes generalized order statistics (GOSs) to study the $ q $-Weibull distribution from several statistical perspectives. First, we explain how to obtain the maximum likelihood estimates (MLEs) and utilize Bayesian techniques to estimate the parameters of the model. The Fisher information matrix (FIM) required for asymptotic confidence intervals (CIs) is generated by obtaining explicit expressions. A Monte Carlo simulation study is conducted to compare the performances of these estimates based on type Ⅱ censored samples. Two well-established measures of information are presented, namely extropy and weighted extropy. In this context, the order statistics (OSs) and sequential OSs (SOSs) for these two measures are studied based on this distribution. A bivariate $ q $-Weibull distribution based on the Farlie-Gumbel-Morgenstern (FGM) family and its relevant concomitants are studied. Finally, two concrete instances of medical real data are ultimately provided.&lt;/p&gt;&lt;/abstract&gt;

Characterization of Phani Distribution Based on Generalized Order Statistics

Characterization of Phani Distribution Based on Generalized Order Statistics

Some Tsallis entropy measures in concomitants of generalized order statistics under iterated FGM bivariate distribution

&lt;p&gt;Shannon differential entropy is extensively applied in the literature as a measure of dispersion or uncertainty. Nonetheless, there are other measurements, such as the cumulative residual Tsallis entropy (CRTE), that reveal interesting effects in several fields. Motivated by this, we study and compute Tsallis measures for the concomitants of the generalized order statistics (CGOS) from the iterated Farlie-Gumbel-Morgenstern (IFGM) bivariate family. Some newly introduced information measures are also being considered for CGOS within the framework of the IFGM family, including Tsallis entropy, CRTE, and an alternative measure of CRTE of order $ \eta $. Applications of these results are given for order statistics and record values with uniform, exponential, and power marginals distributions. In addition, the empirical cumulative Tsallis entropy is suggested as a method to calculate the new information measure. Finally, a real-world data set has been analyzed for illustrative purposes, and the performance is quite satisfactory.&lt;/p&gt;

Residual and Past Entropies of Concomitants from Lai And Xie Extensions of Case-II of Generalized Order Statistics and its Dual

Residual and Past Entropies of Concomitants from Lai And Xie Extensions of Case-II of Generalized Order Statistics and its Dual

On concomitants of generalized order statistics arising from bivariate generalized Weibull distribution and its application in estimation

&lt;p&gt;In this research, we studied the concomitants of generalized order statistics from the bivariate generalized Weibull distribution. We derived probability density functions and moments of concomitants of generalized order statistics from the bivariate generalized Weibull distribution. Moreover, utilizing the ranked set sample obtained from this distribution, we computed the best linear unbiased (BLU) estimator of the parameter connected with the study variable (variable of primary interest). Also, a real data application was presented.&lt;/p&gt;

Fisher Information, Asymptotic Behavior, and Applications for Generalized Order Statistics and Their Concomitants Based on the Sarmanov Family

In this paper, the Fisher information (FI), relevant to m-generalized order statistics (m-GOSs) and their concomitants of the shape-parameter of the Sarmanov family of bivariate distributions, is investigated. In addition, we study the concomitants of m-GOSs from this family. Furthermore, we look at how those concomitants were distributed collectively. The FI contained in the scale and shape parameters of the exponential and power function distributions, respectively, in concomitants of m-GOSs is obtained. A study of the asymptotic behavior of the concomitants of ordinary order statistics is also provided. Some versatile applications for this study are offered. As a final step, we examined a bivariate real-world data set for illustrative purposes.

Bayesian and non-Bayesian analysis for the lifetime performance index based on generalized order statistics from Pareto distribution

&lt;p&gt;Modern businesses depend on efficient management and evaluation of product quality performance to assure that they are on the right track, and process capability analysis is used to gauge business performance in practice. Consequently, the lifetime performance index (LPI) , where is the lower specification limit, is used to gauge a process potential and performance. This paper examines distinct estimators of under Pareto distribution using generalized order statistics (GOS), which is very helpful in a variety of real-world applications. Results for progressive type II censoring (PTIIC) and first-failure censoring are two particular situations. Using symmetric and asymmetric loss functions, the Bayesian estimator was built, then utilized to produce the hypothesis testing technique. A simulation study and real data analysis have been investigated to study the behavior of different estimates for under different schemes, namely PTIIC and the progressive first failure censored scheme.&lt;/p&gt;

Some Characterizations Based on Generalized Order Statistics from Weibull-Weibull Distribution

Some Characterizations Based on Generalized Order Statistics from Weibull-Weibull Distribution

Bayesian Estimation of the Stress-Strength Reliability Based on Generalized Order Statistics for Pareto Distribution

The aim of this paper is to obtain a Bayesian estimator of stress-strength reliability based on generalized order statistics for Pareto distribution. The dependence of the Pareto distribution support on the parameter complicates the calculations. Hence, in literature, one of the parameters is assumed to be known. In this paper, for the first time, two parameters of Pareto distribution are considered unknown. In computing the Bayesian confidence interval for reliability based on generalized order statistics, the posterior distribution has a complex form that cannot be sampled by conventional methods. To solve this problem, we propose an acceptance-rejection algorithm to generate a sample of the posterior distribution. We also propose a particular case of this model and obtain the classical and Bayesian estimators for this particular case. In this case, to obtain the Bayesian estimator of stress-strength reliability, we propose a variable change method. Then, these confidence intervals are compared by simulation. Finally, a practical example of this study is provided.

Log-Extended Exponential–Geometric Distribution: Moments and Inference Based on Generalized Order Statistics

In this paper, we provide explicit expressions as well as recurrence relations for the single and product moments of generalized order statistics from the log-extended exponential–geometric distribution. These relations are utilized to discuss the special cases of generalized order statistics, and some numerical computations are carried out. Further, we use these results to obtain the best linear unbiased estimators for the location and scale parameters based on progressively Type-II right censored samples. Finally, a real data application is presented.

Statistical inference of the inverted exponentiated Lomax distribution using generalized order statistics with application to COVID-19

In this study, the parameters of the inverted exponentiated Lomax distribution via generalized order statistics are assessed using Bayesian and maximum likelihood approaches. The maximum likelihood estimators along with approximate confidence intervals are calculated. Under the squared error loss function, the Bayesian estimator, percentile bootstrap, and bootstrap-t credible periods are produced. Furthermore, the proposed estimators are dedicated to schemes such as type-II censored ordinary order statistics joint density function. A numerical simulation is used to assess the behavior and sensitivity of the estimates for various sample sizes. From the posterior distributions, the Metropolis–Hastings technique is used to generate Markov chain Monte Carlo samples. We utilize this technique to examine a current dataset of interest: daily cases of COVID-19 instances detected in Saudi Arabia from May 31 to October 28, 2020 (inclusive). In the future, the proposed methodology could be useful for analyzing data on COVID-19 instances in other countries for comparative studies.

Conditions for finiteness and bounds on moments of generalized order statistics

We present necessary and sufficient conditions for the finiteness of moments of a fixed order of generalized order statistics based on an arbitrary life baseline distribution with a finite expectation. The conditions depend on a relation between the moment order and the minimal parameter of the generalized order statistic and its multiplicity. Furthermore, under these conditions we determine sharp upper bounds on the moments of generalized order statistic expressed in the scale units being the respective powers of the mean of the baseline distribution.