Inverse Weibull Research Articles

Asymptotic Confidence Intervals for MRL and TVaR of the Inverse Weibull Distribution with Type II Censored Data

We consider interval estimation for the parameters, the Mean Residual Life (MRL) and the Tail Value at Risk (TVaR) of the inverse Weibull distribution. We constructed the confidence intervals based on the asymptotic normality of the maximum likelihood estimator in addition to intervals based on the asymptotic Chi-Square distribution of the likelihood ratio (LR) statistic under Type II Censoring. The performance of intervals is investigated and compared using the lower, upper, and total error rates, in addition to expected lengths using simulation. We found that LR intervals showed better overall performance and are more accurate than confidence intervals based on the asymptotic normality of maximum likelihood estimator.

Some Properties of the Cosine Lomax Distribution with Applications

This paper introduces a new trigonometric distribution, named the Cosine Lomax (CLM) distribution. This distribution is a combination of the Lomax distribution and the Cosine-G family of distributions. Among the many mathematical moments, moment-generating function, incomplete moments, and the quantile function. We try to determine the model parameters using the maximum likelihood estimation method. Simulation studies evaluate the effectiveness of maximum likelihood estimators using bias and root mean square error. We applied the CLM distribution to two real-world datasets and tested for consistency using the Akaike information criterion, the consistent AIC, the Hannan-Quinn information criterion, the Bayesian information criterion, the Kolmogorov-Smirnov p-value, Cramer Von-Mises, and Andersen-Darling. The CLM model fared better when compared to the following distributions: Lomax, Inverse Lomax, Inverse Weibull, Burr Type X, Rayleigh, and Exponential, as well as measures of data set fit.

Estimation and Analysis of Trigonometric Models under Bayesian Approach

In this study, we explore three innovative trigonometric models within the Bayesian framework, utilizing the inverse Weibull distribution as our foundation. These models—namely the Sine inverse Weibull, Cosine inverse Weibull, and Tan inverse Weibull—are crafted from distinct distribution families. We employ both maximum likelihood estimation and Markov Chain Monte Carlo (MCMC) simulation techniques to estimate parameters, drawing upon a comprehensive dataset. By scrutinizing posterior samples numerically and graphically, we evaluate the efficacy of our models, generating Bayes estimates for parameters, examining reliability and hazard functions, and establishing credible intervals. Furthermore, we assess the predictive capacity of all three models through posterior predictive checks. We also conduct comparative analyses, pitting our models against competing ones using real-world data. Notably, our results reveal that the proposed trio of models exhibit strikingly similar performance in terms of fitting the data.

A New Family of Distributions Based on Amalgamation of Two Methods with an Application to the Rayleigh Model

In this paper, we present the Alpha power generalized odd generalized exponential-G (APGOGE-G) family of distributions and provides the most common shapes of the hazard rate function: increasing, decreasing, bathtub, and inverted bathtub. We provide some of its structural properties. We estimate the parameters by maximum likelihood estimation method, and perform a simulation study to verify the asymptotic properties of the estimator for the inverse Weibull baseline. The practicality of the new APGOGE-Rayleigh model is shown through application to uncensored real dataset.

Estimation of multicomponent system reliability for inverse Weibull distribution using survival signature

Estimation of multicomponent system reliability for inverse Weibull distribution using survival signature

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.

Discrete Extension of the Inverse Weibull Distribution: Theory and Decision-Making for Count Data in Sustainability Analysis

Discrete Extension of the Inverse Weibull Distribution: Theory and Decision-Making for Count Data in Sustainability Analysis

The New Strange Generalized Rayleigh Family: Characteristics and Applications to COVID-19 Data

In this paper, we introduce a novel family of continuous distributions known as the Odd Generalized Rayleigh-G Family. Within this family, we present a special sub-model known as the odd Generalized Rayleigh Inverse Weibull (OGRIW) distribution. The OGRIW distribution is derived by combining the T-X family and the Generalized Rayleigh distribution. We provide a comprehensive expansion of the (PDF) and (CDF) for the OGRIW distribution. Additionally, we investigate several mathematical properties of the OGRIW distribution, including moments, moment-generating function, incomplete moments, quantile function, order statistics and Rényi entropy. To estimate the model parameters, we employ the maximum likelihood method, aiming to identify the parameter values that maximise the likelihood of the observed data. Finally, we apply the proposed OGRIW distribution to two real COVID-19 datasets from Mexico and Canada. The results of these applications demonstrate that the new distribution exhibits remarkable flexibility and outperforms other comparative distributions in terms of accurately modelling the COVID-19 data.

Parameter estimation of inverse Weibull distribution under competing risks based on the expectation–maximization algorithm

AbstractA system consisting of interconnected components in series is under consideration. This research focuses on estimating the parameters of this system for incomplete lifetime data within the framework of competing risks, employing an underlying inverse Weibull distribution. While one popular method for parameter estimation involves the Newton–Raphson (NR) technique, its sensitivity to initial value selection poses a significant drawback, often resulting in convergence failures. Therefore, this paper opts for the expectation–maximization (EM) algorithm. In competing risks scenarios, the precise cause of failure is frequently unidentified, and these issues can be further complicated by potential censoring. Thus, incompleteness may arise due to both censoring and masking. In this study, we present the EM‐type parameter estimation and demonstrate its superiority over parameter estimation based on the NR method. Two illustrative examples are provided. The proposed method is compared with the existing Weibull competing risks model, revealing the superiority of our approach. Through Monte Carlo simulations, we also examine the sensitivity of the initial value selection for both the NR‐type method and our proposed method.

Bayesian inference for the inverse Weibull distribution based on symmetric and asymmetric balanced loss functions with application

In this study, the unified hybrid censored approach is employed to estimate the parameters of the inverse Weibull distribution, as well as the survival and hazard rate functions. Parameter estimates are obtained using both Bayesian and Maximum Likelihood approaches, with Bayesian estimates acquired through Lindley's approximation method using three distinct balanced loss functions. These encompass both symmetric and asymmetric balanced loss functions, specifically the balanced squared error (BSE) loss function, the balanced linear exponential (BLINEX) loss function, and the balanced general entropy (BGE) loss function. We conduct a simulation study to compare the effectiveness of various estimators, and a real-world data analysis is presented to illustrate practical implementation. Ultimately, our findings indicate that Bayesian parameter estimates consistently outperform their Maximum Likelihood counterparts across all methods.

Bayesian and Non-Bayesian Estimation for the Shape Parameters of New Versions of Bivariate Inverse Weibull Distribution based on Progressive Type II Censoring

Bayesian and Non-Bayesian Estimation for the Shape Parameters of New Versions of Bivariate Inverse Weibull Distribution based on Progressive Type II Censoring

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.

A New Expansion of the Inverse Weibull distribution: Properties with Applications

The use of statistical distributions to model life phenomena has received a great deal of attention in various sciences. Recent studies have shown the possibility of statistical distributions in data modeling in applied sciences, especially in environmental sciences. Among them is the inverse Weibull distribution, which is one of the most common statistical models that can be used very effectively in modeling data in the health, engineering, and environmental fields, as well as other fields. This study proposes to present a new generalization for the inverse Weibull distribution, where two new parameters are added to the basic distribution according to the Odd Lomax-G family so that the new generalization is more modern and flexible with real-world data. It is called the Odd Lomax Inverse Weibull (LoIW) distribution. The OLIW distribution comes with an expansion of its pdf and CDF functions by using binomial series, exponential, and Logarithm expansions with many statistical properties such as (Rényi entropy, moments, skewness, kurtosis with the moments generating function (mgf), ordered statistics, as well as the Quantile function), and the four distribution parameters are estimated using the maximum likelihood function (MLEs). To ensure the robustness of the proposed model, a practical application is conducted using the R language on two different types of real data and compared with many other statistical models.

Inference on the reliability of inverse Weibull with multiply Type-I censored data

Inverse Weibull (IW) distribution is widely used due to its non-monotonic hazard function. For the IW distribution, existing research on statistical inference has mostly focused on censored data, but there has been no study on multiply Type-I censoring until now as far as we know. The multiple Type-I censoring, acted as an extended form of Type-I censoring, is frequently encountered in industry and medicine research, which also needs to be paid attention. Thus, this study conducts detailed analyses on the reliability of IW distribution with multiply Type-I censored data, including point estimation and confidence interval (CI) construction. Four methods, including the maximum likelihood estimation (MLE), least square estimation (LSE), and two Bayesian estimations, namely MCMC and Lindley, are adopted in point estimation. Results show that the Lindley method performs best with small mission times, while MLE is optimal for large mission times. Specifically, for the CIs construction, we proposed a pivotal quantity based on LSE to construct the CIs of reliability and compare it with two popular methods, Fisher information matrix (FIM) derivation and MCMC algorithm. Our proposed method shows competitive performance as the MCMC and outperforms FIM. Finally, those estimation methods are applied to an example for illustration.

A New Cubic Transmuted Inverse Weibull Distribution: Theory and Applications

This paper introduces a new cubic transmutation of the inverse Weibull distribution, known as a cubic transmuted inverse Weibull distribution. The model is thought to be useful for the analysis of complex life data, modeling failure times, accessing product reliability, and many other fields like economics, hydrology, biology, and engineering. Some statistical features of the proposed distribution are explored. These include moments, generating functions, quantile functions, reliability functions, and hazard rate functions. The distribution of order statistics for the proposed cubic transmuted inverse Weibull distribution is also studied. The maximum likelihood estimation approach is used to estimate the model parameters. The effectiveness of the estimation is investigated through extensive simulation study. The suitability of the proposed distribution has been studied by using five real-life datasets. It is found that the proposed distribution is the most suitable fit for the used data sets.

Evaluation of Return Period and Occurrence Probability of the Maximum Magnitude Earthquakes in Iraq and Surroundings

It has long been clear that earthquake prediction is important from both social and economic perspectives; therefore, the practical objective of today’s earthquake seismology researchers is an effective earthquake prediction program. The purpose of this study is to estimate earthquake probabilities and return periods using an updated earthquake catalogue (1900-2019) for Iraq and its surroundings. Weibull’s formula and inverse Weibull’s formula were employed to calculate the period of return and the occurrence probability of the maximum magnitude earthquake. The return period for earthquakes magnitudes 5 and 7Mw was 1.1 and 10.54 years, respectively, while the occurrence probability was 93.79% and 9.5%, respectively. The greatest magnitude is 7.7, with a 121-year return period and likelihood of approximately 0.82%. The probability of exceedance increased as the time period increased. The return duration was greater for earthquakes of higher magnitudes.

Analysis of Censored Data Using Dirichlet Process Mixture Model with Generalized Inverse Weibull Distribution as Kernel

Analysis of Censored Data Using Dirichlet Process Mixture Model with Generalized Inverse Weibull Distribution as Kernel

0,1] Truncated Exponentiated Exponential Inverse Weibull Distribution with Applications of Carbon Fiber and COVID-19 Data

In the recent years the modeling of lifetime data is an essential research topic. Several research studies on this subject have appeared, aiming to introduce new statistical methodologies for dealing with lifetime phenomena. In this paper, we extension Inverse Weibull distribution by using the family [0,1] Truncated Exponentiated Exponential-G family. We get [0,1] Truncated Exponentiated Exponential Inverse Weibull distribution ([0,1]TEEIW). We provide explicit expressions for its properties like: hazard function, quantile function, moments, moment generating function, reliability function, and Order statistics. Three data sets are used to provide the flexibility of new distribution, which represents 63 observations and is about the strength of carbon fibers. And two a COVID-19 mortality rates data set from Italy and Canada. Evidence of this distribution to outperform other classes of lifetime models has been noticed.

Alpha power inverse Weibull distribution: A new lifetime distribution with application to gastric cancer data

Lifetime data analysis has an essential role in various fields of science. In general, lifetime data have a skewed distribution pattern. The Weibull distribution is one of the most frequently used distributions for modeling lifetime data. However, the Weibull distribution is not suitable for modeling data with non-monotonous hazard functions, one of which is an upside-down bathtub shape. According to Sharma et al. (2015), the inverse version of several probability distributions can model the data with an upside-down bathtub shape, one of which is the inverse Weibull distribution. This paper explains the Alpha Power Inverse Weibull (APIW) distribution as a generalization version of the inverse Weibull distribution. This distribution is constructed by using the Alpha Power Transformation method. The modification is done by adding a shape parameter to the inverse Weibull distribution to increase flexibility. The characteristics of APIW distribution discussed include probability density function, distribution function, survival function, hazard function, and the r-th moment. The probability density function of APIW distribution is left-skewed and unimodal. In addition, the hazard function of APIW distribution has an upside-down bathtub shape. The parameters of this distribution are estimated by the maximum likelihood method. Finally, for illustration purposes, the data about the time until gastric cancer patients die are modelled with the inverse Weibull distribution, and the APIW distribution is given. The modeling result shows that the Alpha Power Inverse Weibull distribution is better at modeling the time until gastric cancer patients die data than the inverse Weibull distribution.

On the study of the recurrence relations and characterizations based on progressive first-failure censoring

<abstract> <p>In this research, the progressive first-failure censored data (PFFC) from the Kumaraswamy modified inverse-Weibull distribution (KMIWD) were used to obtain the recurrence relations and characterizations for single and product moments. The recurrence relationships allow for a rapid and efficient assessment of the means, variances and covariances for any sample size. Additionally, the paper outcomes can be boiled down to the traditional progressive type-II censoring. Also, some special cases are limited to some lifetime distributions as the exponentiated modified inverse Weibull and Kumaraswamy inverse exponential.</p> </abstract>