Weibull Power Research Articles

On the Topp-Leone Generalized Power Weibull Distribution: Properties, Applications and Regression

Abstract The Topp-Leone generalized power Weibull distribution, which is an extension of generalized power Weibull, is proposed and its properties explored. The failure rate of the proposed distribution exhibits increasing, reversed J, upside-down bathtub, and bathtub shapes. Some statistical properties are obtained: quantile function, moments, moment generating function, incomplete moment, mean and median deviations, mean residual life function, and Lorenz as well as Bonferroni curves. The maximum likelihood estimation approach is deployed to estimate the model parameters. Simulation studies are conducted to evaluate the performance and accuracy of the maximum likelihood estimates of the model parameters. Applications of the model to real datasets are presented. A location-scale regression model is also developed for the proposed model and its application has been demonstrated with a real dataset. Keywords: Bonferroni, Deviation, Mimicked, Simulation, and Upside-down Bathtub.

Fitting COVID-19 datasets to a new statistical model

This paper discussed gull alpha power Weibull distribution with a three-parameter. Different statistical inference methods of Gull Alpha Power Weibull distribution parameters have been obtained, estimated, and evaluated. Then, the results are compared to find a suitable model. The unknown parameters of the published Gull Alpha Power Weibull distribution are analyzed. Seven estimation methods are maximum likelihood, Anderson–Darling, right-tail Anderson–Darling, Cramér–von Mises, ordinary least-squares, weighted least-squares, and maximum product of spacing. In addition, the performance of this distribution is computed using the Monte Carlo method, and the limited sample features of parameter estimates for the proposed distribution are analyzed. In light of the importance of heavy-tailed distributions, actuarial approaches are employed. Applying actuarial criteria such as value at risk and tail value at risk to the suggested distribution shows that the model under study has a larger tail than the Weibull distribution. Two real-world COVID-19 infection datasets are used to evaluate the distribution. We analyze the existence and uniqueness of the log-probability roots to establish that they represent the global maximum. We conclude by summarizing the outcomes reported in this study.

Study of Alpha Power Weibull Distribution with Application

Study of Alpha Power Weibull Distribution with Application

A NEW flexible exponent power family of distributions with biomedical data analysis

Probability distributions are widely utilized in applied sciences, especially in the field of biomedical science. Biomedical data typically exhibit positive skewness, necessitating the use of flexible, skewed distributions to effectively model such phenomena. In this study, we introduce a novel approach to characterize new lifetime distributions, known as the New Flexible Exponent Power (NFEP) Family of distributions. This involves the addition of a new parameter to existing distributions. A specific sub-model within the proposed class, known as the New Flexible Exponent Power Weibull (NFEP-Wei), is derived to illustrate the concept of flexibility. We employ the well-established Maximum Likelihood Estimation (MLE) method to estimate the unknown parameters in this family of distributions. A simulation study is conducted to assess the behavior of the estimators in various scenarios. To gauge the flexibility and effectiveness of the NFEP-Wei distribution, we compare it with the AP-Wei (alpha power Weibull), MO-Wei (Marshal Olkin Weibull), classical Wei (Weibull), NEP-Wei (new exponent power Weibull), FRLog-Wei (flexible reduced logarithmic Weibull), and Kum-Wei (Kumaraswamy Weibull) distributions by analyzing four distinct biomedical datasets. The results demonstrate that the NFEP-Wei distribution outperforms the compared distributions.

A novel flexible exponent power-X family of distributions with applications to COVID-19 mortality rate in Mexico and Canada.

This paper aims to introduce a novel family of probability distributions by the well-known method of the T-X family of distributions. The proposed family is called a "Novel Generalized Exponent Power X Family" of distributions. A three-parameters special sub-model of the proposed method is derived and named a "Novel Generalized Exponent Power Weibull" distribution (NGEP-Wei for short). For the proposed family, some statistical properties are derived including the hazard rate function, moments, moment generating function, order statistics, residual life, and reverse residual life. The well-known method of estimation, the maximum likelihood estimation method is used for estimating the model parameters. Besides, a comprehensive Monte Carlo simulation study is conducted to assess the efficacy of this estimation method. Finally, the model selection criterion such as Akaike information criterion (AINC), the correct information criterion (CINC), the Bayesian information criterion (BINC), the Hannan-Quinn information criterion (HQINC), the Cramer-von-Misses (CRMI), and the ANDA (Anderson-Darling) are used for comparison purpose. The comparison of the NGEP-Wei with other rival distributions is made by Two COVID-19 data sets. In terms of performance, we show that the proposed method outperforms the other competing methods included in this study.

McDonald Generalized Power Weibull Distribution: Properties, and Applications

McDonald Generalized Power Weibull Distribution: Properties, and Applications

Classical and Bayesian estimation for the extended odd Weibull power Lomax model with applications

A new continuous distribution called the extended odd Weibull power Lomax (ExOW-POLO) distribution is introduced and studied. Numerous reliability and statistical features are derived. Additionally studied are point estimates using maximum likelihood, maximum product space, least square, weighted least square, and Bayesian estimation techniques. The mean square error and bias of the maximum likelihood and Bayesian parameter estimators are computed using simulation approaches, such as Markov chain Monte Carlo. Two intraocular pressure (IOP) real datasets were conducted between January 2015 and February 2018 on 49 patients (84 eyes) under the age of two who presented with primary congenital glaucoma to the Paediatric Ophthalmology Unit of the Mansoura Ophthalmic Center of Mansoura University in Egypt have been fitted the ExOW-POLO distribution. Comparing the properties of the proposed distribution’s fitting of the data to recognized extensions of the Lomax distribution. The analysis revealed that the most well-known extensions of Lomax distribution were made by the ExOW-POLO distribution outfit. In addition, the correlation measures and independent sample test for the two IOP real datasets are introduced with (A) Levene’s test for equality of variances for the two cases and (B) the t-test for equality of means. For Levene’s test for equality of variances: the null hypothesis is that equal variances are assumed and the alternative hypothesis is that equal variances are not assumed.

A New Type 1 Alpha Power Family of Distributions and Modeling Data with Correlation, Overdispersion, and Zero-Inflation in the Health Data Sets

In the recent era, the introduction of a new family of distributions has gotten great attention due to the curbs of the classical univariate distributions. This study introduces a novel family of distributions called a new type 1 alpha power family of distributions. Based on the novel family, a special model called a new type 1 alpha power Weibull model is studied in depth. The new model has very interesting patterns and it is very flexible. Thus, it can model the real data with the failure rate patterns of increasing, decreasing, parabola-down, and bathtub. Its applicability is studied by applying it to the health sector data, and time-to-recovery of breast cancer patients, and its performance is compared to seven well-known models. Based on the model comparison, it is the best model to fit the health-related data with no exceptional features. Furthermore, the popular models for the data with exceptional features such as correlation, overdispersion, and zero-inflation in aggregate are explored with applications to epileptic seizer data. Sometimes, these features are beyond the probability distribution models. Hence, this study has implemented eight possible models separately to these data and they are compared based on the standard techniques. Accordingly, the zero-inflated Poisson-normal-gamma model which includes the random effects in the linear predictor to handle the three features simultaneously has shown its supremacy over the others and is the best model to fit the health-related data with these features.

A Modified Group Chain Sampling Plan for lifetime following Kumaraswamy Generalized Power Weibull Distribution with Minimum Angle Approach

A Modified Group Chain Sampling Plan for lifetime following Kumaraswamy Generalized Power Weibull Distribution with Minimum Angle Approach

A New Generalized Logarithmic–X Family of Distributions with Biomedical Data Analysis

In this article, an attempt is made to propose a novel method of lifetime distributions with maximum flexibility using a popular T–X approach together with an exponential distribution, which is known as the New Generalized Logarithmic-X Family (NGLog–X for short) of distributions. Additionally, the generalized form of the Weibull distribution was derived by using the NGLog–X family, known as the New Generalized Logarithmic Weibull (NGLog–Weib) distribution. For the proposed method, some statistical properties, including the moments, moment generating function (MGF), residual and reverse residual life, identifiability, order statistics, and quantile functions, were derived. The estimation of the model parameters was derived by using the well-known method of maximum likelihood estimation (MLE). A comprehensive Monte Carlo simulation study (MCSS) was carried out to evaluate the performance of these estimators by computing the biases and mean square errors. Finally, the NGLog–Weib distribution was implemented on four real biomedical datasets and compared with some other distributions, such as the Alpha Power Transformed Weibull distribution, Marshal Olkin Weibull distribution, New Exponent Power Weibull distribution, Flexible Reduced Logarithmic Weibull distribution, and Kumaraswamy Weibull distribution. The analysis results demonstrate that the new proposed model performs as a better fit than the other competitive distributions.

Modeling the Amount of Carbon Dioxide Emissions Application: New Modified Alpha Power Weibull-X Family of Distributions

The use of statistical distributions to model life phenomena has received considerable attention in the literature. Recent studies have shown the potential of statistical distributions in modeling data in applied sciences, especially in environmental sciences. Among them, the Weibull distribution is one of the most well-known models that can be used very effectively for modeling data in the fields of pollution and gas emissions, to name a few. In this paper, we introduce a family of distributions, which we call the modified Alpha-Power Weibull-X family of distributions. Based on the proposed family, we introduce a new model with five parameters, the modified Alpha-Power Weibull–Weibull distribution. Some mathematical properties were determined. Bayesian and maximum likelihood estimates for the model parameters were derived. The MLEs, bootstrap and Bayesian HPD credibility intervals for the unknown parameters were performed. A Monte Carlo simulation study was performed to evaluate the performance of the estimates. A simulation study was performed based on the parameters of the proposed model. An application to the carbon dioxide emissions dataset was performed to predict unique symmetric and asymmetric patterns and illustrate the applicability and potential of the model. For this data set, the proposed model is compared with the modified alpha power Weibull exponential distribution and the two-parameter Weibull distribution. To show which of the competing distributions is the best, we draw on certain analytical tools such as the Kolmogorov–Smirnov test. Based on these analytical measures, we found that the new model outperforms the competing models.

A Novel Modified Alpha Power Transformed Weibull Distribution and Its Engineering Applications

This paper suggests a new modified version of the traditional Weibull distribution by adding a new shape parameter utilising the modified alpha power transformed technique. We refer to the new model as modified alpha power transformed Weibull distribution. The attractiveness and significance of the new distribution lie in its power to model monotone and non-monotone failure rate functions, which are quite familiar in environmental investigations. Its hazard rate function can be decreasing, increasing, bathtub and upside-down then bathtub shaped. Diverse structural properties of the proposed model are acquired including quantile function, moments, entropies, order statistics, residual life and reversed failure rate function. The parameters of the distribution were estimated using the maximum likelihood function. The maximum likelihood method is employed to estimate the model parameters and the approximate confidence intervals are also computed. Via a simulation study, the performance of the point and interval estimates are compared using different criteria. Employing real lifetime data sets, we verify that the offered model furnishes a better fit than some other lifetime models including Weibull, gamma and alpha power Weibull models.

Reliability assessment of transformer insulating oil using accelerated life testing

To improve the reliability and reduce the maintenance cost of transformer oil, a life prediction of transformer oil is needed so that the maintenance of transformer can be performed correctly. However, it is difficult to predict the reliable lifetime of transformer oil accurately because of its unkind operating condition at different environments. To solve this problem, based on the theory of accelerated life testing (ALT), a reliability assessment method for transformer insulating oil on a normal operational conditions is proposed. An inverse power Weibull distribution model for insulating oil lifetime with voltage is built. Numerical procedure of model parameter estimation is presented, the variances of model parameters and reliability indices, which including mean lifetime, reliability, reliable lifetime at given reliability and failure rate, are derived. The feasibility and correctness of the proposed method are validated by real lifetime data of transformer insulating oil in literature. The reliability of transformer insulating oil used at normal usage conditions are predicted by the proposed method, and the point and interval estimations of reliability indices are evaluated. The results show that reliable lifetime and mean lifetime under reliability limit should be considered simultaneously in repair or replacement of transformer insulating oil.

The Proportional Hazard Generalized Power Weibull Distribution: Properties, Applications and Regression Model

We introduce the proportional hazard generalized power Weibull (PHGPW) model in which hazard rate function can assume increasing, decreasing, unimodal or (upside bathtub) and constant. Some of its mathematical properties are studied including the power series for the quantile function. Monte Carlo simulation was performed to determine the finite sample behaviour of the maximum likelihood estimates of the parameters. The flexibility of the PHGPW distribution compared with some other existing distributions is proved empirically by means of two sets of real data related to remission times of bladder cancer patients and strike duration of manufacturing company. A new regression model was defined based on the PHGPW distribution. The performance of the regression model is proved empirically using real data set.

Generalized power Weibull software reliability growth model

Software usage in various industries and homes forms part of our daily lives. Thus, performing quality control checks on developed software by software engineers is essential to both the developer and the users. The general idea of software reliability as a quality control check is very important to both the producer and the consumer. This paper offers a Generalized Power Weibull software reliability growth model that takes environmental factors into account. The applications of the proposed software reliability growth model reveals that it performs better than some of the existing competing models. Finally, a sequential probability ratio test for the proposed model was developed for monitoring of reliability data.

Optimal Test Plan of Step-Stress Model of Alpha Power Weibull Lifetimes under Progressively Type-II Censored Samples

In this study, the estimation of the unknown parameters of an alpha power Weibull (APW) distribution using the concept of an optimal strategy for the step-stress accelerated life testing (SSALT) is investigated from both classical and Bayesian viewpoints. We used progressive type-II censoring and accelerated life testing to reduce testing time and costs, and we used a cumulative exposure model to examine the impact of various stress levels. A log-linear relation between the scale parameter of the APW distribution and the stress model has been proposed. Maximum likelihood estimators for model parameters, as well as approximation and bootstrap confidence intervals (CIs), were calculated. Bayesian estimation of the parameter model was obtained under symmetric and asymmetric loss functions. An optimal test plan was created under typical operating conditions by minimizing the asymptotic variance (AV) of the percentile life. The simulation study is discussed to demonstrate the model’s optimality. In addition, real-world data are evaluated to demonstrate the model’s versatility.

Inferences and Engineering Applications of Alpha Power Weibull Distribution Using Progressive Type-II Censoring

As an extension of the standard Weibull distribution, a new crucial distribution termed alpha power Weibull distribution has been presented. It can model decreasing, increasing, bathtub, and upside-down bathtub failure rates. This research investigates the estimation of model parameters and some of its reliability characteristics using progressively Type-II censored data. To get estimates of unknown parameters, reliability, and hazard rate functions, the maximum likelihood, and Bayesian estimation approaches are studied. To acquire estimated confidence intervals for unknown parameters and reliability characteristics, the maximum likelihood asymptotic properties are used. The Markov chain Monte Carlo approach is used in Bayesian estimation to provide Bayesian estimates under squared error and LINEX loss functions. Furthermore, the highest posterior density credible intervals of the parameters and reliability characteristics are determined. A Monte Carlo simulation study is used to investigate the accuracy of various point and interval estimators. In addition, various optimality criteria are used to choose the best progressive censoring schemes. Two real data from the engineering field are analyzed to demonstrate the applicability and significance of the proposed approaches. Based on numerical results, the Bayesian procedure for estimating the parameters and reliability characteristics of alpha power Weibull distribution is recommended. The analysis of two real data sets showed that the alpha power Weibull distribution is a good model to investigate engineering data in the presence of progressive Type-II censoring.

Statistical Analysis of COVID-19 Data: Using A New Univariate and Bivariate Statistical Model

In this paper, a new distribution named as unit-power Weibull distribution (UPWD) defined on interval (0,1) is introduced using an appropriate transformation to the positive random variable of the Weibull distribution. This work offers quantile function, linear representation of the density, ordinary and incomplete moments, moment-generating function, probability-weighted moments, L -moments, TL-moments, Rényi entropy, and MLE estimation. Additionally, several actuarial measures are computed. The real data applications are carried out to underline the practical usefulness of the model. In addition, a bivariate extension for the univariate power Weibull distribution named as bivariate unit-power Weibull distribution (BIUPWD) is also configured. To elucidate the bivariate extension, simulation analysis and application using COVID-19-associated fatality rate data from Italy and Belgium to conform a BIUPW distribution with visual depictions are also presented.

A GAMLSS approach to predicting growth of Nopalea cochenillifera Giant Sweet clone submitted to water and saline stress

Water and saline stresses are the main factors affecting agricultural production in semiarid regions. The tolerance of forage cactus to water and salt deficit makes it a promising solution, in particular Nopalea cochenillifera. The growth curves for species facing these conditions can provide useful information supporting the cultivation and management of natural populations and carry significant biological importance as growth rate assessment contributes to maintaining species viability. The objective of this study was to estimate the plant height and linear dimensions (length, width, and thickness) of N. cochenillifera Giant Sweet clone growing under water and saline stress. The experiment design was completely randomized, comprising a 4 × 4 factorial, with four water and four salinity levels; there were four replications. In order to estimate plant height in N. cochenillifera Giant Sweet clone as a function of the accumulated thermal sum, generalized additive models for location, scale, and shape (GAMLSS) were used to determine water level, saline level, length, width, and thickness. We constructed models using four distributions: the Weibull, Gumbel, Logistic, and Box-Cox power exponential distributions. The models were evaluated using global deviation and the generalized Akaike criterion. The Box–Cox power exponential proved to be the most effective in estimating N. cochenillifera height. This model enabled information relevant to practical environmental management to be obtained, as it precisely defined the optimum salt application and the required amount of replacement water, together with the cladode width for each plant growth stage using the accumulated thermal sum.

The alpha power Weibull transformation distribution applied to describe the behavior of electronic devices under voltage stress profile

ABSTRACT This paper presents a life-stress methodology that models the failure rate in the form of a bathtub curve. The model consists of the Alpha Power Transformation (APT), which adds an extra parameter to the probability distributions to achieve better flexibility in the representation in the data analysis. To build the life–stress relationship, the APT is combined with the Weibull Distribution (WD) and the Inverse Power Law (IPL) as a stress model to relate the data from the accelerated life tests (ALT), thus presenting the APTW-IPL. Statistical properties of the APTW-IPL are analyzed and discussed. For the parameter estimation of APTW-IPL, the Maximum Likelihood Estimator was used. On the other hand, to test the efficacy of the APTW-IPL, the model is compared with other methodologies that describe the behavior of the bathtub curve in two case studies related to determining the behavior of electronic devices that were subjected to ALT. The results show that the APTW-IPL can be a good option for reliability analysis in electronic devices. It represents the failure times in the form of a bathtub curve, the value of MTTF, and fitting the distribution to the case study data.