Inverse Weibull Model Research Articles

Divergences based Bayesian inference with censored data

. In this work, we deal with some Bayesian inference problems in the presence of right censored data. First, we propose a dual ϕ−divergence Bayes type estimators for parametric models and we establish their asymptotic normality. To establish this result, we need a uniform strong law of large numbers that we prove as well. Then, we consider the problem of prior distributions construction for model selection using ϕ−divergences. Finally, we consider the problem of the predictive density estimation on the basis of ϕ−divergences. We apply an expansion result of the generalized Bayesian predictive density on two parametric models widely used in survival analysis, namely the Weibull and the inverse Weibull model, under right censoring. We also check the performances of our proposed methods through simulations and real data applications. The results of these studies show that our proposed dual ϕ−divergence Bayes type estimators are more robust than other Bayesian estimators. Moreover, the generalized Bayesian predictive density performs better than the classical estimative density especially for the inverse Weibull model.

Introducing the new arcsine-generator distribution family: An in-depth exploration with an illustrative example of the inverse weibull distribution for analyzing healthcare industry data

The study is about a novel Arcsin-function based generator of new families of distributions. We chose the inverse Weibull distribution as the reference distribution to see if the generator could be employed. This generator helps for developing a distribution called the novel Arcsin inverse Weibull. The main features of the suggested distribution have been taken into account. Some of the indicators used in this class include the density function, complete and incomplete moments, average deviation, and aging indicators. The model's parameters are determined using the maximum likelihood method in both simulations and data analysis. The effectiveness of the suggested model in the healthcare sector is demonstrated by analyzing five sets of data, revealing its superior fit compared to the traditional inverse sine model, which is associated with the inverse Weibull model.

Fuzzy multicomponent stress-strength reliability in presence of partially accelerated life testing under generalized progressive hybrid censoring scheme subject to inverse Weibull model

It typically takes a lot of time to monitor life-testing experiments on a product or material. Units can be tested under harsher conditions than usual, known as accelerated life tests to shorten the testing period. This study's goal is to investigate the issue of partially accelerated life testing that use generalized progressive hybrid censored samples to estimate the stress-strength reliability in the multicomponent case. Also, the fuzziness of the model is considered that gives more sensitive and accurate analyses about the underlying system. Maximum likelihood estimation method under the inverse Weibull distribution and using the generalized progressively hybrid censoring scheme is introduced to obtain an estimator for the fuzzy multicomponent stress-strength reliability. Also, an asymptotic confidence interval is deduced to examine the reliability of the fuzzy multicomponent stress-strength. Simulation study is conducted using maximum likelihood estimates and confidence intervals for the fuzzy multicomponent stress-strength reliability for different values of the parameters and different schemes. A real data application representing the data for the failure times for a certain software model is introduced to obtain the fuzzy multicomponent stress-strength reliability for different schemes.•The fuzzy multicomponent stress-strength reliability is investigated under partially accelerated life testing and the generalized progressively hybrid censored scheme.•An algorithm is introduced to simulate data for the censoring scheme.•A real data application is presented to obtain the fuzzy multicomponent stress-strength reliability at different schemes.

Bayesian and non-Bayesian inference for inverse Weibull model based on jointly type-II hybrid censoring samples with modeling to physics data

In recent years, there has been a lot of interest in the research of cooperative censoring schemes. In this work, we compared the relative benefits of two competing length-of-life products using inverse Weibull lifetime products with a joint type-II hybrid censoring scheme (JHC-Type II). We initially examined the maximum likelihood estimators and their confidence intervals (CIs) for the unknown parameters based on JHC-Type II. Then, under the premise of independent gamma priors, we offer Bayes estimates of the parameters using squared error loss and LINEX loss functions. We used the Markov chain Monte Carlo method to create credible intervals and Bayesian estimates. Based on the parametric bootstrapping techniques known as Boot-p and Boot-t, we create two bootstrapping CIs. In addition, we do a Monte Carlo simulation experiment to track how well the aforementioned approaches work and to determine the corresponding confidence and credible intervals. Finally, to show how the approaches covered in this paper might be used, we consider a real physical dataset.

Fuzzy vs. Traditional Reliability Model for Inverse Weibull Distribution

In this paper, fuzzy stress strengths RF=P(Y≺X) and traditional stress strengths R=P(Y<X) are considered and compared when X and Y are independently inverse Weibull random variables. When axiomatic fuzzy set theory is taken into account in the stress–strength inference, it enables the generation of more precise studies on the underlying systems. We discuss estimating both conventional and fuzzy models of stress strength utilizing a maximum product of spacing, maximum likelihood, and Bayesian approaches. Simulations based on the Markov Chain Monte Carlo method are used to produce various estimators of conventional and fuzzy dependability of stress strength for the inverse Weibull model. To generate both conventional and fuzzy models of dependability, we use the Metropolis–Hastings method while performing Bayesian estimation. In conclusion, we will examine a scenario taken from actual life and apply a real-world data application to validate the accuracy of the provided estimators.

The Generalization Inverse Weibull Distribution Related to X-Gamma Generator Family: Simulation and Application for Breast Cancer

The aim of this paper is to propose the new three-parameter X-Gamma inverse Weibull (XGAIW) distribution which generalizes the inverse Weibull model. The density function of the XGAIW can be expressed as a linear combination of the inverse Weibull densities. Some mathematical quantities (reliability and hazard rate properties) of the proposed XGAIW model are derived. Moreover, four estimation methods, namely, the maximum likelihood, maximum product spacing, least squares, and weighted least squares methods, are utilized to estimate the XGAIW parameters. The Monte Carlo simulation study has been performed to assess the performance of the proposed estimation methods using some criteria. The importance, flexibility, and potentiality of the XGAIW model are studied via a breast cancer data set application. The XGAIW model can produce better fits than some well-known distributions, so the proposed model can be used, as a good alternative to some existing distributions, in modeling several real data.

A New Type I Half-Logistic Inverse Weibull Distribution with an Application to the Relief Times Data of Patients Receiving an Analgesic

This article presents a new extension of the type I half-logistic inverse Weibull distribution. It is used as a base line to construct a new bivariate model that is called bivariate extended type I half-logistic inverse Weibull model. Statistical properties of the proposed distributions are derived in explicit forms. Maximum likelihood estimators are discussed. Simulation is employed to discuss theoretical properties, to investigate the performance of the new models and to elaborate the goodness of fit. The new models are applied to real data sets.

Brand Awareness via Online Media: An Evidence Using Instagram Medium with Statistical Analysis.

Online marketing refers to the practices of promoting a company's brand to its potential customers. It helps the companies to find new venues and trade worldwide. Numerous online media such as Facebook, YouTube, Twitter, and Instagram are available for marketing to promote and sell a company's product. However, in this study, we use Instagram as a marketing medium to see its impact on sales. To carry out the computational process, the approach of linear regression modeling is adopted. Certain statistical tests are implemented to check the significance of Instagram as a marketing tool. Furthermore, a new statistical model, namely a new generalized inverse Weibull distribution, is introduced. This model is obtained using the inverse Weibull model with the new generalized family approach. Certain mathematical properties of the new generalized inverse Weibull model such as moments, order statistics, and incomplete moments are derived. A complete mathematical treatment of the heavy-tailed characteristics of the new generalized inverse Weibull distribution is also provided. Different estimation methods are discussed to obtain the estimators of the new model. Finally, the applicability of the new generalized inverse Weibull model is established via analyzing Instagram advertising data. The comparison of the new distribution is made with two other models. Based on seven analytical tools, it is observed that the new distribution is a better model to deal with data in the business, finance, and management sectors.

New Statistical Approaches for Modeling the COVID‐19 Data Set: A Case Study in the Medical Sector

Statistical distributions have great applicability for modeling data in almost every applied sector. Among the available classical distributions, the inverse Weibull distribution has received considerable attention. In the practice of distribution theory, numerous methods have been studied and suggested/introduced to increase the flexibility level of the traditional probability distributions. In this paper, we implement different distribution methods to obtain five new different versions of the inverse Weibull model. The new modifications of the inverse Weibull model are called the logarithm transformed‐inverse Weibull, a flexible reduced logarithmic‐inverse Weibull, the weighted TX‐inverse Weibull, a new generalized‐inverse Weibull, and the alpha power transformed extended‐inverse Weibull distributions. To illustrate the flexibility and applicability of the new modifications of the inverse Weibull model, a biomedical data set is analyzed. The data set consists of 108 observations and represents the mortality rate of the COVID‐19‐infected patients. The practical application shows that the new generalized‐inverse Weibull is the best modification of the inverse Weibull distribution.

Reliability analysis incorporating exponentiated inverse Weibull distribution and inverse power law

AbstractIn reliability research, electronic devices are an important part of our lives and modelling their lives is the most difficult and fascinating area. To investigate the failure functioning of electronic equipments, reliability monitoring of systems is widely used. However, it is stated in the literature that one in five electronic system collapses are a consequence of degradation and saving energy and forecasting future losses, it is necessary to summarize the data through certain versatile models of probability . In current article, a model of reliability formed on inverse power law and generalized inverse Weibull model is suggested. This current distribution presents a clearer framework to modelling the efficiency and functionality lifespan of electronic equipments. In this article, an empirical analysis is discussed related to life cycle of a surface‐mounted electrolytic capacitor (SMEC). In addition, it has noticed that evaluation of suggested distribution varies from classical model of inverse Weibull and that influences average time to failure (ATTF) of the studied capacitor.

A generalization of the Inverse Weibull model: Properties and applications

A new flexible extension of the Inverse Weibull distribution is proposed and studied. The new density can be “right skewed”, “left skewed” and “unimodal” with various shapes, the new failure rate function can be a “decreasing” or “upside down” or “increasing” shaped. Some of its statistical properties are derived. The importance of the new distribution is shown via three applications to real data sets. The new distribution is better fit than many important competitive models based on three real data sets.

The Extended Inverse Weibull Distribution: Properties and Applications

This paper proposes the new three-parameter type I half-logistic inverse Weibull (TIHLIW) distribution which generalizes the inverse Weibull model. The density function of the TIHLIW can be expressed as a linear combination of the inverse Weibull densities. Some mathematical quantities of the proposed TIHLIW model are derived. Four estimation methods, namely, the maximum likelihood, least squares, weighted least squares, and Cramér–von Mises methods, are utilized to estimate the TIHLIW parameters. Simulation results are presented to assess the performance of the proposed estimation methods. The importance of the TIHLIW model is studied via a real data application.

Lomax inverse Weibull model: properties, applications, and a modified Chi-squared goodness-of-fit test for validation

Lomax inverse Weibull model: properties, applications, and a modified Chi-squared goodness-of-fit test for validation

Imprecise Reliability Analysis for the Robotic Component Based on Limited Lifetime Data

The inverse Weibull (IW) distribution has an ability to model failure rates which are quite common in reliability studies. The three-parameter generalized inverse Weibull (GIW) distribution is a promoted form of the inverse Weibull distribution which is mainly used in reliability lifetime data analysis, such as the wear life of mechanical components. With the limited lifetime data, it is difficult to estimate the accurate parameters of the GIW distribution, but we can get the imprecise ones. According to the imprecise Bayesian inference, this paper proposes a new imprecise model called imprecise Gamma-generalized inverse Weibull model, which can do reliability analysis for the component of the robotic device with incomplete lifetime data. Compared to other methods, this imprecise model can be applied to computing reliability measures when the number of events of interest or observations are very small and can provide the effective way of interval estimation. The detailed theoretical derivations for imprecise Gamma-generalized inverse Weibull model are introduced in this paper. Moreover, the impact of some parameters on the proposed model, such as the parameter s and available lifetime data size N, as well as the scale parameter and the shape parameter are also depicted. Furthermore, some convergences of the proposed model are also introduced and proved. Finally, the experimental using simulation lifetime data for the component of the robotic device validate the availability of the proposed model.

The natural tolerance limit for the inverse weibull model and the optimization of technical systems

The natural tolerance limit for the inverse weibull model and the optimization of technical systems

Kinetic modeling of native Cassava starch thermo‐oxidative degradation using Weibull and Weibull‐derived models

A new approach in kinetic modeling of thermo-oxidative degradation process of starch granules extracted from the Cassava roots was developed. Based on the thermoanalytical measurements, three reaction stages were detected. Using Weibull and Weibull-derived (inverse) models, it was found that the first two reaction stages could be described with the change of apparent activation energy (Ea) on conversion fraction (α(T)) (using "Model-free" analysis). It was found that first reaction stage, which involves dehydration and evaporation of lower molecular mass fractions, can be described with an inverse Weibull model. This model with its distribution of Ea values and derived distribution parameters includes the occurrence of three-dimensional diffusion mechanism. The second reaction stage is very complex, and it was found to contain the system of simultaneous reactions (where depolymerization occurs), and can be described with standard Weibull model. Identified statistical model with its distribution of Ea values and derived distribution parameters includes the kinetic model that gives the variable reaction order values. Based on the established models, shelf-life studies for first two stages were carried out. Shelf-life testing has shown that optimal dehydration time is achieved by a programmed heating at medium heating rate, whereas optimal time of degradation is achieved at highest heating rate.

Impact of Three-Parameter Weibull Models in Probabilistic Assessment of Earthquake Hazards

This paper investigates the suitability of a three-parameter (scale, shape, and location) Weibull distribution in probabilistic assessment of earthquake hazards. The performance is also compared with two other popular models from same Weibull family, namely the two-parameter Weibull model and the inverse Weibull model. A complete and homogeneous earthquake catalog (Yadavet al. in Pure Appl Geophys 167:1331–1342, 2010) of 20 events (M ≥ 7.0), spanning the period 1846 to 1995 from north–east India and its surrounding region (20°–32°N and 87°–100°E), is used to perform this study. The model parameters are initially estimated from graphical plots and later confirmed from statistical estimations such as maximum likelihood estimation (MLE) and method of moments (MoM). The asymptotic variance–covariance matrix for the MLE estimated parameters is further calculated on the basis of the Fisher information matrix (FIM). The model suitability is appraised using different statistical goodness-of-fit tests. For the study area, the estimated conditional probability for an earthquake within a decade comes out to be very high (≥0.90) for an elapsed time of 18 years (i.e., 2013). The study also reveals that the use of location parameter provides more flexibility to the three-parameter Weibull model in comparison to the two-parameter Weibull model. Therefore, it is suggested that three-parameter Weibull model has high importance in empirical modeling of earthquake recurrence and seismic hazard assessment.

Non-informative priors for the inverse Weibull distribution

In this paper, we develop the non-informative priors for the inverse Weibull model when the parameters of interest are the scale and the shape parameters. We develop the first-order and the second-order matching priors for both parameters. For the scale parameter, we reveal that the second-order matching prior is not a highest posterior density (HPD) matching prior, does not match the alternative coverage probabilities up to the second order and is not a cumulative distribution function (CDF) matching prior. Also for the shape parameter, we reveal that the second-order matching prior is an HPD matching prior and a CDF matching prior and also matches the alternative coverage probabilities up to the second order. For both parameters, we reveal that the one-at-a-time reference prior is the second-order matching prior, but Jeffreys’ prior is not the first-order and the second-order matching prior. A simulation study is performed to compare the target coverage probabilities and a real example is given.

Bayesian and Non-Bayesian Estimation of the Inverse Weibull Model Based on Generalized Order Statistics

The concept of generalized order statistics has been introduced as a unified approach to a variety of models of ordered random variables with different interpretations. In this paper, we develop methodology for constructing inference based on n selected generalized order statistics (GOS) from inverse Weibull distribution (IWD), Bayesian and non-Bayesian approaches have been used to obtain the estimators of the parameters and reliability function. We have examined Bayes estimates under various losses such as the balanced squared error (balanced SEL) and balanced LINEX loss functions are considered. We show that Bayes estimate under balanced SEL and balanced LINEX loss functions are more general, which include the symmetric and asymmetric losses as special cases. This was done under assumption of discrete-continuous mixture prior for the unknown model parameters. The parametric bootstrap method has been used to construct confidence interval for the parameters and reliability function. Progressively type-II censored and k-record values as a special case of GOS are considered. Finally a practical example using real data set was used for illustration.

Two sample Bayesian prediction intervals for order statistics based on the inverse exponential-type distributions using right censored sample

Abstract In this paper, two sample Bayesian prediction intervals for order statistics (OS) are obtained. This prediction is based on a certain class of the inverse exponential-type distributions using a right censored sample. A general class of prior density functions is used and the predictive cumulative function is obtained in the two samples case. The class of the inverse exponential-type distributions includes several important distributions such the inverse Weibull distribution, the inverse Burr distribution, the loglogistic distribution, the inverse Pareto distribution and the inverse paralogistic distribution. Special cases of the inverse Weibull model such as the inverse exponential model and the inverse Rayleigh model are considered.