Weibull Extension Distribution Research Articles

A new flexible Weibull extension model: Different estimation methods and modeling an extreme value data

The word extreme events refer to unnatural or undesirable events. Due to the general destructive effects on society and scientific problems in various applied fields, the study of extreme events is an important subject for researchers. Many real-life phenomena exhibit clusters of extreme observations that cannot be adequately predicted and modeled by the traditional distributions. Therefore, we need new flexible probability distributions that are useful in modeling extreme-value data in various fields such as the financial sector, telecommunications, hydrology, engineering, and meteorology. In this piece of research work, a new flexible probability distribution is introduced, which is attained by joining together the flexible Weibull distribution with the weighted T-X strategy. The new model is named a new flexible Weibull extension distribution. The distributional properties of the new model are derived. Furthermore, some frequently implemented estimation approaches are considered to obtain the estimators of the new flexible Weibull extension model. Finally, we demonstrate the utility of the new flexible Weibull extension distribution by analyzing an extreme value data set.

A New Bivariate Distribution With Applications on Dependent Competing Risks Data

A new bivariate distribution is proposed in this paper using the univariate modified Weibull extension distribution. The proposed distribution is referred to as the bivariate Modified Weibull Extension (BMWE) distribution. The BMWE distribution is of Marshall-Olkin type. We discuss some of the statistical properties of the BMWE  distribution.  Applications of this distribution to dependent competing risks data are discussed.  The maximum likelihood estimators (MLE) of the model parameters using both bivariate data and dependent competing risks data are discussed. These MLE's cannot be obtained in closed form. Therefore, numerical optimization methods are  applied. A simulation study is carried out to investigate the performance of the estimation technique. Two real data sets;  one bivariate data set and another dependent competing risks data set, are analyzed using the proposed distribution for illustrative and comparison purposes.

Multi-component Reliability Inference in Modified Weibull Extension Distribution and Progressive Censoring Scheme.

The statistical inference of multi-component reliability stress-strength system with nonidentical-component strengths is considered for the modified Weibull extension distribution in the presence of progressive censoring samples. For this aim, we study the estimation of multi-component reliability parameter in classical and Bayesian inference. So we derive some point and interval estimates such as maximum likelihood estimation, asymptotic confidence intervals, uniformly minimum variance unbiased estimation, approximate and exact Bayes estimation and highest posterior density intervals. Comparing of different estimates is provided by employing the Monte Carlo simulation, the mean squared error and coverage probabilities. Finally, one real data is utilized to illustrate the applicability of this new model.

On suitability of modified Weibull extension distribution in modeling product lifetimes and reliability

The Weibull distribution (WD) is an important lifetime model. Due to its prime importance in modeling life data, many researchers have proposed different modifications of WD. One of the most recent modifications of WD is Modified Weibull Extension distribution (MWEM). The MWEM has been shown better in modeling lifetime data as compared to WD. However it comparison with other modifications of WD, in modeling product lifetimes and reliability, is missing in the current literature. We have attempted to bridge up this gap. The Bayesian methods have been proposed for the analysis under non-informative (uniform) and informative (gamma) priors. Since the Bayes estimates for the model parameters were not available in closed form, the Lindley’s approximation (LA) has been used for numerical solutions. Based on detailed simulation study and real life analysis, it has been concluded that Bayesian methods performed better as compared to maximum likelihood estimates (MLE) in estimating the model parameters. The MWEM performed better than eighteen other modifications of WD in modeling real datasets regarding electric and mechanical components. The reliability and entropy estimation for the said datasets has also been discussed. The estimates for parameters of MWEM were quite consistent in nature. In case of small samples, the performance of Bayes estimates under ELF and informative prior was the best. However, in case of large samples, the choice of prior and loss function did not affect the efficiency of the results to a large extend.

New Rayleigh Flexible Weibull Extension (RFWE) Distribution with Applications to Real and Simulated Data

The Rayleigh flexible Weibull extension (RFWE) distribution, a new three-parameter model introduced in this paper, is a generalization of the flexible Weibull extension. This model produces best fit for failure time of electronic device obtained from power-linkage voltage spikes during electronic storms. We derive the statistical properties of the RFWE distribution. The parameters of this new distribution are estimated using the maximum likelihood method, which also yielded asymptotic confidence bounds. This model is examined using both real and simulated data. Under various priors, an additional Bayesian estimate is also carried out. The Bayes estimates and other posterior results are calculated using simulations.

Applicability of modified weibull extension distribution in modeling censored medical datasets: a bayesian perspective

There are some contributions analyzing the censored medical datasets using modifications of the conventional lifetime distribution; however most of the said contributions did not considered the modification of the Weibull distribution (WD). The WD is an important lifetime model. Due to its prime importance in modeling life data, many researchers have proposed different modifications of WD. One of the most recent modifications of WD is Modified Weibull Extension distribution (MWED). However, the ability of MWED to model the censored medical data has not yet been explored in the literature. We have explored the suitability of the model in modeling censored medical datasets. The analysis has been carried out using Bayesian methods under different loss functions and informative priors. The approximate Bayes estimates have been computed using Lindley’s approximation. Based on detailed simulation study and real life analysis, it has been concluded that Bayesian methods performed better as compared to maximum likelihood estimates. In case of small samples, the performance of Bayes estimates under ELF and informative prior was the best. However, in case of large samples, the choice of prior and loss function did not affect the efficiency of the results to a large extend. The MWED performed efficiently in modeling real censored datasets relating to survival times of the leukemia and bile duct cancer patients. The MWED was explored to be a very promising candidate model for modeling censored medical datasets.

The Estimation of Survival Function for Modified Weibull Extension Distribution Using Two-Symmetric Pentagonal Fuzzy Numbers with Simulation

In this paper, the parameters of the Modified Weibull Extension Distribution are estimated using the maximum likelihood estimator method and the Monte Carlo method in the simulation procedure to generate many different sample sizes, with many different replicates of the sample sizes. Following that finding, the Survival function’s estimate. Then fuzzify the estimation of the parameters for the same different sample sizes with the same difference in replicated sample sizes that was obtained from the Monte Carlo method in the simulation procedure by the new proposed method of expanding the Confidence Interval of estimated parameters to nine fuzzy numbers. Then, transform all the fuzzy parameters to crisp parameters using the proposed ranking functions with (proposed Linear Two- Symmetric Pentagonal Fuzzy Numbers, and proposed Non Linear Two-Symmetric Pentagonal Fuzzy Numbers). Accordingly, finding the Survival function. The outcome of Survival functions before and after fuzzy work will be compared using mean square error.

On Predictive Modeling Using a New Flexible Weibull Distribution and Machine Learning Approach: Analyzing the COVID-19 Data

Predicting and modeling time-to-events data is a crucial and interesting research area. For modeling and predicting such types of data, numerous statistical models have been suggested and implemented. This study introduces a new statistical model, namely, a new modified flexible Weibull extension (NMFWE) distribution for modeling the mortality rate of COVID-19 patients. The introduced model is obtained by modifying the flexible Weibull extension model. The maximum likelihood estimators of the NMFWE model are obtained. The evaluation of the estimators of the NMFWE model is assessed in a simulation study. The flexibility and applicability of the NMFWE model are established by taking two datasets representing the mortality rates of COVID-19-infected persons in Mexico and Canada. For predictive modeling, we consider two pure statistical models and two machine learning (ML) algorithms. The pure statistical models include the autoregressive moving average (ARMA) and non-parametric autoregressive moving average (NP-ARMA), and the ML algorithms include neural network autoregression (NNAR) and support vector regression (SVR). To evaluate their forecasting performance, three standard measures of accuracy, namely, root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) are calculated. The findings demonstrate that ML algorithms are very effective at predicting the mortality rate data.

Simulation of Two- Asymmetric Pentagonal Fuzzy Numbers to Estimate the Survival Function for Modified Weibull Extension Distribution

Simulation of Two- Asymmetric Pentagonal Fuzzy Numbers to Estimate the Survival Function for Modified Weibull Extension Distribution

Simulation of Two- Asymmetric Pentagonal Fuzzy Numbers to Estimate the Survival Function for Modified Weibull Extension Distribution

Simulation of Two- Asymmetric Pentagonal Fuzzy Numbers to Estimate the Survival Function for Modified Weibull Extension Distribution

Applying Transformer Insulation Using Weibull Extended Distribution Based on Progressive Censoring Scheme

In this paper, the Weibull extension distribution parameters are estimated under a progressive type-II censoring scheme with random removal. The parameters of the model are estimated using the maximum likelihood method, maximum product spacing, and Bayesian estimation methods. In classical estimation (maximum likelihood method and maximum product spacing), we did use the Newton–Raphson algorithm. The Bayesian estimation is done using the Metropolis–Hastings algorithm based on the square error loss function. The proposed estimation methods are compared using Monte Carlo simulations under a progressive type-II censoring scheme. An empirical study using a real data set of transformer insulation and a simulation study is performed to validate the introduced methods of inference. Based on the result of our study, it can be concluded that the Bayesian method outperforms the maximum likelihood and maximum product-spacing methods for estimating the Weibull extension parameters under a progressive type-II censoring scheme in both simulation and empirical studies.

Modified Beta Inverse Flexible Weibull Extension Distribution

In this article, a new five parameter distribution, known as the modified beta flexible Weibull extension distribution, is derived and studied. Several properties of the distribution including the quantile function, moments, moment generating function, entropies and order statistics are derived. The density function and hazard rate function plots for different parameter values are obtained. It is observed that the density function plots of the distribution exhibit varying shapes and degrees of kurtosis. Also, the hazard rate function plots exhibit different shapes including decreasing, increasing, bathtub, J and reserved J shapes. The parameter estimators of the distribution are obtained using maximum likelihood estimation. The estimators are found to be consistent via a simulation study. Finally, three data sets are used to assess the usefulness of the distribution. It is observed that the distribution can serve as an alternative to modelling failure time data with different characteristics.

THE WEIBULL GENERALIZED FLEXIBLE WEIBULL EXTENSION DISTRIBUTION

This paper introduces a new four parameters model called the Weibull Generalized Flexible Weibull extension (WGFWE) distribution which exhibits bathtub-shaped hazard rate. Some of it's statistical properties are obtained including ordinary and incomplete moments, quantile and generating functions, reliability and order statistics. The method of maximum likelihood is used for estimating the model parameters and the observed Fisher's information matrix is derived. We illustrate the usefulness of the proposed model by applications to real data.

The Flexible Weibull Extension-Burr XII Distribution: Model, Properties and Applications

This paper is devoted to study a new four- parameter additive model. The newly suggested model is referred to as the flexible Weibull extension-Burr XII distribution. It is derived by considering a serial system with one component following a flexible Weibull extension distribution and another following a Burr XII distribution. The usefulness of the model stems from the flexibility of its failure rate which accommodates bathtub and modified bathtub among other risk patterns. These two patterns have been widely accepted in several fields, especially reliability and engineering fields. In addition, the importance of the new distribution is that it includes new sub-models which are not known in the literature. Some statistical properties of the proposed distribution such as quantile function, the mode, the rth moment, the moment generating function and the order statistics are discussed. Moreover, the method of maximum likelihood is used to estimate the parameters of the model. Also, to evaluate the performance of the estimators, a simulation study is carried out. Finally, the performance of the proposed distribution is compared through a real data set to some well-known distributions including the new modified Weibull, the additive Burr and the additive Weibull distributions. It is shown that the proposed model provides the best fit for the used real data set.

Lifetime data modelling and reliability analysis based on modified weibull extension distribution and Bayesian approach

Satellite reliability has long been a critical issue in space industry. In-orbit lifetime data modelling and the corresponding reliability analysis are indispensable aspects for satellite reliability. However, limited by available in-orbit lifetime data, these two aspects have not been well studied. Aiming to mitigate this limitation, we conduct a coherent research on satellite reliability analysis based on an in-orbit database of 1584 satellites. A nonparametric reliability analysis is firstly implemented on the data set to identify the characteristics of failure rate. Then, the modified Weibull extension distribution is used to model the satellite reliability. Point estimation and interval estimation are carried out by utilizing a Bayesian method. Posterior distributions of model parameters are obtained and reserved for further reliability analysis of newly launched satellites. The results presented in this paper can provide helpful information to the space industry for design improvement and test planning of new satellites.

Odd Generalized Exponential Flexible Weibull Extension Distribution

In this article we introduce a new four - parameters model called the odd generalized exponential flexible Weibull extension (OGE-FWE) distribution which exhibits bathtub-shaped hazard rate. Some of it’s statistical properties are obtained including ordinary and incomplete moments, quantile and mode, the moment generating functions, reliability and order statistics. The method of maximum likelihood is used for estimating the model parameters and the observed Fisher’s information matrix is given. Moreover, we give the advantage of the OGE-FWE distribution by an application using real data.

On testing the fit of accelerated failure time and proportional hazard Weibull extension models

Characterized by three parameters, the Weibull extension distribution is introduced by Xie et al. as a generalization of the classical Weibull distribution. In this article, we are interested in the construction of modified chi-squared goodness-of-fit tests for both an accelerated failure time and Cox proportional hazards models with the Weibull extension distribution as the baseline distribution. We use the technique introduced by Bagdonavicius and Nikulin for right-censored samples. Besides an important simulation study, the obtained results are applied to illustrative examples from real data sets.

Generalized Flexible Weibull Extension Distribution

In this article, a four parameter generalization of the flexible Weibull extension distribution so-called generalized flexible Weibull extension distribution is studied. The proposed model belongs to T-X family of distributions proposed by Alzaatreh et al. [5]. The suggested model is much flexible and accommodates increasing, unimodal and modified unimodal failure rates. A comprehensive expression of the numerical properties and the estimates of the model parameters are obtained using maximum likelihood method. By appropriate choice of parameter values the new model reduces to four sub models. The proposed model is illustrated by means of three real data sets.

On Transmuted Flexible Weibull Extension Distribution with Applications to Different Lifetime Data Sets

In this article, a three parameters transmuted version of the flexible Weibull extension distribution called transmuted flexible Weibull extension distribution is studied. The proposed model is very flexible and is able to model real phenomena with increasing, unimodal or modified unimodal failure rates. Explicit expressions for mathematical properties are derived. Maximum likelihood estimates and asymptotic confidence bounds for the unknown parameters of the model are also obtained. Four real data sets are analyzed in order to illustrate the flexibility of the proposed distribution.

The Exponential Flexible Weibull Extension Distribution

This paper is devoted to study a new generalization of the flexible Weibull with three parameters. This model is referred to as the exponential flexible Weibull extension (EFWE) distribution which exhibits bathtub-shaped hazard rate function. Some statistical properties such as the mode, median, the moment, quantile function, the moment generating function and order statistics are discussed. Moreover, the maximum likelihood method for estimating the model parameters and the Fisher’s information matrix is given. Finally, the advantage of the EFWE distribution is concluded by an application using real data.