Exponentiated Weibull Research Articles

Modified Average Sample Number for Improved Double Sampling Plan Based on Truncated Life Test Using Exponentiated Distributions

The reliability of the product has developed a dynamic issue in a worldwide business market. Generally acceptance sampling guarantees the superiority of the product. In acceptance sampling plan, increasing the sample size may lead to minimization of customers' risk of accepting bad lots and producers' risk of rejecting good lots to a certain level but will increase the cost of inspection. Hence truncation of life test time may be introduced to reduce the cost of inspection. Modified Average Sample Number (MASN) for Improved Double Sampling Plan (IDSP) based on truncated life test for popular exponentiated family such as exponentiated gamma, exponentiated lomax and exonentiated Weibull distribution are considered. The modified ASN creates a band width for average sample number which is much useful for the consumer and producer. The interval for average sample number makes the choice of consumer with a maximum and minimum sample size which is of much benefit without any loss for the producer. The probability of acceptance and average sample number based on modified double sampling plan for lower and upper limit is computed for the exponentiated family. Optimal parameters of IDSP under various exponentiated families with different shape parameters were computed. The proposed plan is compared over traditional double sampling and modified double sampling using Gamma distribution, Weibull distribution and Birnbaum-Saunders distribution and shows that the proposed plan with respect to exponentiated family performs better than all other plans. The tables were provided for all distributions. Comparative study of tables based on proposed exponentiated family and earlier existing plan are also done.

Bayesian Inference on Progressive-Stress Accelerated Life Testing for the Exponentiated Weibull Distribution under Progressive Type-II Censoring

Bayesian Inference on Progressive-Stress Accelerated Life Testing for the Exponentiated Weibull Distribution under Progressive Type-II Censoring

Estimation of the Parameters for the Exponentiated Weibull Distribution Based on Progressive Type-II Censoring Scheme

The main objective of the present study is to find the estimation of the two Exponentiated Weibull distribution parameters, based on progressive Type II censored samples. The maximum likelihood and Bayes estimators for the two shape parameters and the scale parameter of the exponentiated Weibull lifetime model were derived. Bayes estimators was obtained by using both the symmetric and asymmetric loss functions via squared error loss and linex loss functions This was done with respect to the conjugate priors for two shape parameters. We used an approximation based on the Lindley (Trabajos de Estadistca) method for obtaining Bayes estimates under these loss functions. The different proposed estimators have been compared through an extensive simulation studies. Bayes ratings also turned out to be better than MLE. Whatever the sample sizes are, we get the same results.

On the performance of AF full FSO two-way relay networks over exponentiated Weibull fading channels

This work implements free space optical communication (FSO) in an amplify-and-forward (AF) two-way relay network (TWRN) to exploit the advantages of spectral efficiency, full-duplex Gigabit throughput, license-free spectrum, easy installation and to overcome the limitations of free space optical communication due to distance dependent turbulence induced fading. To quantify the performance of the proposed scheme, overall outage probability (OOP) and ergodic sum rate (ESR) expressions are derived over Exponentiated Weibull (EW) fading channels. The simple theoretical results which are validated with the Monte-Carlo simulations show that a system designer can get a quick idea about the FSO TWRN without resorting to complex prototypes or simulations.

Statistical Learning of the Worst Regional Smog Extremes with Dynamic Conditional Modeling

This paper is concerned with the statistical learning of the extreme smog (PM 2.5 ) dynamics of a vast region in China. Differently from classical extreme value modeling approaches, this paper develops a dynamic model of conditional, exponentiated Weibull distribution modeling and analysis of regional smog extremes, particularly for the worst scenarios observed in each day. To gain higher modeling efficiency, weather factors will be introduced in an enhanced model. The proposed model and the enhanced model are illustrated with temporal/spatial maxima of hourly PM 2.5 observations each day from smog monitoring stations located in the Beijing–Tianjin–Hebei geographical region between 2014 and 2019. The proposed model performs more precisely on fittings compared with other previous models dealing with maxima with autoregressive parameter dynamics, and provides relatively accurate prediction as well. The findings enhance the understanding of how severe extreme smog scenarios can be and provide useful information for the central/local government to conduct coordinated PM 2.5 control and treatment. For completeness, probabilistic properties of the proposed model were investigated. Statistical estimation based on the conditional maximum likelihood principle is established. To demonstrate the estimation and inference efficiency of studies, extensive simulations were also implemented.

The Generalized Gamma – Exponentiated Weibull Distribution with its Properties

In this paper, we present the Generalized Gamma-Exponentiated Weibull distribution as a special case of new generated Generalized Gamma - G family of probability distribution. The cumulative distribution, probability density, reliability and hazard rate functions are introduced. Furthermore, the most vital statistical properties, for instance, the r-th moment, characteristic function, quantile function, simulated data, Shannon and relative entropies besides the stress-strength model are obtained.

Computational Testing Procedure of the Measure of Performance for Exponentiated Weibull Products under Progressive Type II Right Censoring Scheme

Abstract In this study, we consider the quality characteristics of two products, X and Y, to follow the independent exponentiated Weibull distribution under progressive type II right censored sample in order to construct the maximum likelihood estimator (MLE) of the measure of performance R(=P[X > Y]). Moreover, we also use the MLE to construct a new hypothesis testing procedures for R in order to assess the quality performance of product and compare the superiority-inferiority of two products. Finally, two numerical examples and the Monte Carlo simulation study are utilized to illustrate the use of the testing procedure.

Bayesian Estimation of Inverted Exponentiated Weibull Distribution under Progressive Type II Censoring with Binomial Removal

Bayesian Estimation of Inverted Exponentiated Weibull Distribution under Progressive Type II Censoring with Binomial Removal

Exponentiated models preserve stochastic orderings of parallel and series systems

In this paper, we establish that the usual stochastic, hazard rate, reversed hazard rate, likelihood ratio, dispersive and star orders are all preserved for parallel systems under exponentiated models for lifetimes of components. We then use the multiple-outlier exponentiated gamma models to illustrate this result. Finally, we consider the dual family with exponentiated survival function and establish similar results for series systems. The results established here extend some well-known results for series and parallel systems arising from different exponentiated distributions such as generalized exponential and exponentiated Weibull, established previously in the literature.

Exponentiated Exponential Weibull Distribution: Mathematical Properties and Application

An Exponentiated Exponential Weibull Distribution (EEWD) is proposed. Some statistical properties of the proposed distribution are studied. The Maximum Likelihood method (ML) is applied to estimate the model parameters. The efficiency of the ML estimates of the proposed model is demonstrated using a Monte Carlo simulation study with different samples sizes. Moreover, real data set application is provided to show the flexibility of the proposed model in comparison to some selected distributions.

Performance analysis for mixed [formula omitted] shadowed and exponentiated Weibull distributed dual-hop system with multiuser diversity in C-RAN

This paper investigates the performance of mixed radio-frequency/free-space optical (RF/FSO) system with multiuser diversity over mixed fading channels suitable for the Cloud Radio Access Network (C-RAN). Specifically, the considered system consists of K users, a decode-and-forward (DF) relay and a destination. The relay receives the data from the user with best channel conditions and forwards it to the destination. Furthermore, supposing that the RF link experiences κ−μ shadowed fading which combines small-scale multipath fading with line-of-sight shadowing, whereas the FSO link is subject to Exponentiated Weibull (EW) distributed turbulence. We first derived a novel probability density function (PDF) expression for the κ−μ shadowed fading so that the κ, m and can be equal to the arbitrary positive real value. Then, analytical expressions for the end-to-end outage probability (OP) and average bit error rate (ABER) of the overall network are derived assuming an intensity modulation with direct detection (IM/DD) scheme. The closed-form asymptotic expressions at high signal-to-noise (SNR) regimes are also presented. Capitalizing on the asymptotic analysis, we can obtain the diversity gain and discuss the bottlenecks in the mixed RF/FSO systems. Additionally, the impact of several parameters, including the number of users, atmospheric turbulence conditions and pointing errors on the overall system are studied. The simulation results are provided to prove the feasibility of deployment of the system in real-life scenarios.

Performance analysis of circle polarization shift keying modulation over the exponentiated Weibull distribution

The average bit error rate (BER) and outage probability of circle polarization shift keying (CPOLSK) modulation in free-space optical (FSO) system operating under exponentiated Weibull (EW) distribution are studied. The closed expression of the average BER is derived by generalized Gauss–Laguerre polynomials. The analytical results show the relationship between the average BER and average signal to noise ratio (SNR) of CPOLSK modulation with the effect of aperture averaging under different turbulence strengths and it is compared with on–off keying (OOK) modulation. The relationship between the outage probability and normalized threshold SNR of CPOLSK modulation is studied as well. All the analytical results are verified by the Monte Carlo simulation.

Comparison of wind speed distributions: a case study for Aegean coast of Turkey

ABSTRACT The determination of wind speed characteristics is extremely important for estimating the wind power output. In this context, Weibull distribution is one of the most commonly used statistical distributions for modeling wind speed. However, despite its widespread usage, it may not be accurate for modeling all wind regimes. For this reason, alternative distributions are utilized for modeling wind speed data. In this study, we use Rayleigh, Inverse Weibull (IW), Burr Type III, Extreme Value (EV), Gamma, Inverse Gamma (IG), Marshall–Olkin extended Lindley (MOEL), generalized Extreme Value (GEV) and exponentiated Weibull (EW) distributions as alternatives to Weibull. Our aim is to determine the distribution which provides the best fit for different wind regimes encountered in nature. In the application part, data sets are taken from stations located on Turkey’s Aegean coast and the fitting performances of the above-mentioned distributions are compared. In order to determine the appropriate wind speed distributions. Different model selection criteria are utilized.

On the Exponentiated Weibull Rayleigh Distribution

A new four-parameter probability model, referred to the exponentiated Weibull Rayleigh (EWR) distribution, is introduced. Essential statistical properties of the distribution are considered. The maximum likelihood estimators of population parameters are given in case of complete sample. Simulation study is carried out to estimate the model parameters of EWR distribution. Additionally, parameter estimators are given in case of Type II censored samples. We come up with two applications to confirm the usefulness of the proposed distribution.

On the performance of transmit antenna selection in multiuser asymmetric RF/FSO system under generalized order user scheduling

In this paper, the performance analysis of transmit antenna selection on a multiuser asymmetric RF/FSO system under generalized order user scheduling is investigated. A dual-hop system with one source, one relay and multiple FSO users at destination is considered without direct link between the source and destination. The RF link is subjected to Nakagami-m fading and FSO links follow Exponential Weibull (EW) distribution. Using the amplify-and-forward (AF) channel-state-information (CSI) based gain relay protocol, the equivalent cumulative distribution function (CDF) end-to-end SNR at the destination is derived and used to obtain the analytical expression for the system outage probability. By utilizing the derived statistics, the closed-form expression for the system average bit error rate (ABER) is then derived through the Gauss–Laguerre quadrature rule and second kind Stirling number. Moreover, the results demonstrate that the atmospheric turbulence significantly degrades the system performance and increase in the number of source transmit antenna offers the system better performance. Also, the system performance is deteriorated by increasing the orders N or decreasing the number of user K. The accuracy of the derived expressions is validated through Montel-Carlo Simulations.

Bayesian Survival Analysis of Type I General Exponential Distributions

This article aims at generalizing two distribution by means of, exponentiated exponential and Weibull distribution. The researchers have employed three and four parameters life model called the Type I General Exponential exponentiated exponential distribution and Type I General Exponential Weibull distribution. Survival and hazard rate functions were provided for these two models. To fit these models into survival and hazard rate functions, we adopted the Bayesian approach. For illustration, a real survival data set has been employed. Application is carried out by R and Stan. Finally,a comparison between these two models is made by using loo package to find the best model and simulation.

Generalized X-Exponential Bathtub Shaped Failure Rate Distribution

Generalized Lindley, Generalized Gamma, Exponentiated Weibull and X-Exponential distributions are proposed for modelling lifetime data having bathtub shaped failure rate model. These distributions have several desirable properties. In this paper, we introduce a new distribution which generalizes the X-Exponential distribution. Several properties of the distribution are derived including the hazard rate function, moments, moment generating function etc. Moreover, we discussed the maximum likelihood estimation of this distribution. The usefulness of the new distribution is illustrated by means of two real data set. We hope that the new distribution will serve as an alternative model to bathtub models available in the literature.

Discrete Bivariate Distributions Generated By Copulas: DBEEW Distribution

Copulas are the most powerful tools in constructing continuous multivariate distributions given marginals and certain dependence structures. In this paper, we shall propose a general and novel method of generating discrete bivariate distributions using copulas. The advantage of our method is that, contrary to the standard methods, we do not need to have the joint distribution of the base variables, but we only need the marginal distributions. In particular, we shall concentrate on generating a new family of discrete bivariate exponentiated extended Weibull (DBEEW) distribution by a Cuadras–Auge copula. We shall study several mathematical properties of a DBEEW distribution. Three special submodels of our new proposed distribution are studied in more detail. Finally, estimation of parameters for these three submodels is investigated and their potential and flexibility are examined using a real data set.

On the performance of cognitive underlay RF/FSO communication systems with limited feedback

In this work, we consider an underlay cognitive radio (CR) RF/free space optical (FSO) network where the unlicensed secondary user (SU) wishes to communicate with a specific destination node with the aid of an optical path over a selected relay terminal without causing any interference to the primary user (PU). The proposed structure can be viable for metropolitans where an unlicensed user wishes to transfer its information to a specific destination node which is connected to the backbone network over an optical path. For the proposed structure, closed form and approximate outage probability and ergodic capacity expressions are derived for Nakagami-m/ Exponentiated Weibull fading channels. The results show that the transmission capacity of the SU depends on the weather conditions and the number of relays in the system.

The Burr X Exponentiated Weibull Model: Characterizations,Mathematical Properties and Applications to Failure and Survival Times Data

In this article, we introduce a new three-parameter lifetime model called the Burr X exponentiated Weibull model. The major justification for the practicality of the new lifetime model is based on the wider use of the exponentiated Weibull and Weibull models. We are motivated to propose this new lifetime model because it exhibits increasing, decreasing, bathtub, J shaped and constant hazard rates. The new lifetime model can be viewed as a mixture of the exponentiated Weibull distribution. It can also be viewed as a suitable model for fitting the right skewed, symmetric, left skewed and unimodal data. We provide a comprehensive account of some of its statistical properties. Some useful characterization results are presented. The maximum likelihood method is used to estimate the model parameters. We prove empirically the importance and flexibility of the new model in modeling two types of lifetime data. The proposed model is a better fit than the Poisson Topp Leone-Weibull, the Marshall Olkin extended-Weibull, gamma-Weibull , Kumaraswamy-Weibull , Weibull-Fréchet, beta-Weibull, transmuted modified-Weibull, Kumaraswamy transmuted- Weibull, modified beta-Weibull, Mcdonald-Weibull and transmuted exponentiated generalized-Weibull models so it is a good alternative to these models in modeling aircraft windshield data as well as the new lifetime model is much better than the Weibull-Weibull, odd Weibull-Weibull, Weibull Log-Weibull, the gamma exponentiated-exponential and exponential exponential-geometric models so it is a good alternative to these models in modeling the survival times of Guinea pigs. We hope that the new distribution will attract wider applications in reliability, engineering and other areas of research.