Exponentiated Weibull Distribution Research Articles

THE COMPARISON SOME EXTENDED WEIBULL DISTRIBUTION (WEIBULL (W), EXPONENTIATED WEIBULL (EW), EXPONENTIATED EXPONENTIAL WEIBULL (EEW) AND ADDITIVE WEIBULL (AW)) FOR THE WIND SPEED PROBABILITY MODELLING

Accurate wind speed modeling is critical in estimating wind energy potential for harnessing wind power effectively. One of the bases for assessment of wind energy potential for a specified region is the probability distribution of wind speed, therefore wind speed data is needed to produce statistical modeling, especially in determining the best probability distribution. For this purpose, several modified weibull distributions will be used and tested to determine the best model to describe wind speed in Pekanbaru. The main goal of this study is to find the best fitting distribution to the daily wind speed measured over Pekanbaru region for the years 1999-2020 by using the four modified weibull distributions, namely Weibull (W), Exponentiated Weibull (EW), Additive Weibull (AW) and Exponentiated Exponential Weibull (EEW). The maximum likelihood method will be used to get the estimated parameter value from the distribution used in this study. Furthermore, the graphical inspection (density-density plot and cumulative plot) and numerical criteria (Akaike’s information criterion (AIC), Bayesian Information Criteria (BIC), - log likelihood (- l) ) were used to determine the best fit model. In most cases, the results produced by the graphical inspection were similar, and differed from the numerical criteria . The best fit result was chosen as the distribution with the lowest values of AIC, BIC and - l. In general, the Exponentiated Exponential Weibull (EEW) distribution has been selected as the best model.

Bayesian Estimation of Exponentiated Exponential Strength and Exponentiated Weibull Stress Reliability Model for Real Data

Stress-strength reliability is an important concept in reliability analysis, quantifies the probability that the strength of a system surpasses its applied stress. This paper focuses on the reliability analysis for exponentiated exponential distribution strength variable and the exponentiated Weibull distribution stress variable. The study explores the estimation of the parameters in stress-strength reliability model using maximum likelihood estimation and Bayesian estimation. In particular, the Bayesian estimator of stress-strength reliability is obtained by utilizing Lindley’s approximation by considering both linear exponential loss function and squared error loss function for informative and non-informative priors. A comprehensive simulation study is conducted and the performances of estimators are compared using mean squared errors. The stress-strength reliability for real datasets is also investigated for real-time data sets.

Modelling auto insurance Size-of-Loss distributions using Exponentiated Weibull distribution and de-grouping methods

Rate regulation plays an important role in the financial service of the auto insurance industry. Modelling the Size of Loss distributions, particularly the large loss distribution at the aggregate level, is a key component of rate regulation to produce a benchmark for the industry. However, traditionally actuarial practice is constructing the group-based Size of Loss with irregular intervals. The frequency values associated with each group are counted to form a frequency distribution. However, this approach is limited by lacking a parametric distribution that can capture the underlying randomness of the Size of Loss. In this work, we propose a de-grouping method based on the simulation of the uniform random variate, with and without constraint on knowing the average incurred loss per claim count. Using the de-grouping method, we simulate the individual observation based on the limited information available from the grouped Size of Loss. We have successfully identified the Exponentiated Weibull distribution as a good candidate as it outperforms other heavy-tailed distributions being considered. Our findings provide critical guidance and direction for the practical use of the proposed de-grouping method in auto insurance rate regulation practice and other fields in business and economics.

A Novel Version of the Exponentiated Weibull Distribution: Copulas, Mathematical Properties and Statistical Modeling

In this study, the authors of the current work describe a novel exponentiated Weibull distribution that they have invented. The study was written by the writers of the current work. It is required to analyze those properties once the pertinent mathematical properties have been derived. In addition to the dispersion index, the anticipated value, variance, skewness, and kurtosis are also statistically examined. The dispersion index is likewise examined. Other beneficial shapes that the new density can assume include "bathtub," "right skewed," "bimodal and left skewed," "unimodal and left skewed," and "bimodal and right skewed." Additionally, these forms can be merged to create a "bathtub." The term "bathtub (U-HRF)," "constant," "monotonically increasing," "upside down-increasing (reversed U-increasing)," "J-HRF," "upside down-constant," "increasing-constant," or "upside down (reversed U)" may be used to describe the new rate of failure. The greatest likelihood method's efficiency is assessed via graphical analysis. The main measures for this procedure’s evaluation are biases and mean squared errors. The reader is given a scenario that graphically displays the adaptability and value of the innovative distribution through the use of three separate sets of actual data.

Variational Bayesian Inference for Exponentiated Weibull Right Censored Survival Data

The exponential, Weibull, log-logistic and lognormal distributions represent the class of light and heavy-tailed distributions that are often used in modelling time-to-event data. The exponential distribution is often applied if the hazard is constant, while the log-logistic and lognormal distributions are mainly used for modelling unimodal hazard functions. The Weibull distribution is on the other hand well-known for modelling monotonic hazard rates. Recently, in practice, survival data often exhibit both monotone and non-monotone hazards. This gap has necessitated the introduction of Exponentiated Weibull Distribution (EWD) that can accommodate both monotonic and non-monotonic hazard functions. It also has the strength of adapting unimodal functions with bathtub shape. Estimating the parameter of EWD distribution poses another problem as the flexibility calls for the introduction of an additional parameter. Parameter estimation using the maximum likelihood approach has no closed-form solution, and thus, approximation techniques such as Newton-Raphson is often used. Therefore, in this paper, we introduce another estimation technique called Variational Bayesian (VB) approach. We considered the case of the accelerated failure time (AFT) regression model with covariates. The AFT model was developed using two comparative studies based on real-life and simulated data sets. The results from the experiments reveal that the Variational Bayesian (VB) approach is better than the competing Metropolis-Hasting Algorithm and the reference maximum likelihood estimates.

Modeling Bivariate Data Using Linear Exponential and Weibull Distributions as Marginals

ABSTRACT Modeling bivariate data with different marginals is an important problem and have numerous applications in diverse disciplines. This paper introduces a new family of bivariate generalized linear exponential Weibull distribution having generalized linear and exponentiated Weibull distributions as marginals. Some important quantities like conditional distributions, conditional moments, product moments and bivariate quantile functions are derived. Concepts of reliability and measures of dependence are also discussed. The methods of maximum likelihood and Bayesian estimation are considered to estimate model parameters. Monte Carlo simulation experiments are performed to demonstrate the performance of the estimators. Finally, a real data application is also discussed to demonstrate the usefulness of the proposed distribution in real-life situations.

A Novel Bivariate Generalized Weibull Distribution with Properties and Applications

Univariate Weibull distribution is a well known lifetime distribution and has been widely used in reliability and survival analysis. In this paper, we introduce a new family of bivariate generalized Weibull (BGW) distributions, whose univariate marginals are exponentiated Weibull distribution. Different statistical quantiles like marginals, conditional distribution, conditional expectation, product moments, correlation and a measure component reliability are derived. Various measures of dependence and statistical properties along with aging properties are examined. Further, the copula associated with BGW distribution and its various important properties are also considered. The methods of maximum likelihood and Bayesian estimation are employed to estimate unknown parameters of the model. A Monte Carlo simulation and real data study are carried out to demonstrate the performance of the estimators and results have proven the effectiveness of the distribution in real-life situations.

Families of Extended Exponentiated Generalized Distributions and Applications of Medical Data Using Burr III Extended Exponentiated Weibull Distribution

In this article, four new families named as Weibull extended exponentiated-X (WEE-X), Lomax extended exponentiated-X (LEE-X), Logistic extended exponentiated-X (LGCEE-X), and Burr III extended exponentiated-X (BIIIEE-X) with their quantile functions are proposed. The expressions for distribution function and density function of BIIIEE-X family are written in terms of linear combinations of the exponentiated densities based to parent model. New models, i.e., Weibul extended exponentiated Weibull (WEEW), Lomax extended exponentiated Weibull (LEEW), Logistic extended exponentiated Weibull (LGCEEW), and Burr III extended exponentiated-Weibull (BIIIEEW) distributions are derived, were plotted for functions of probability density and hazard rate at different levels of parameters. Some mathematical properties of the BIIIEEW model are disclosed. The maximum likelihood method for the BIIIEEW model are described. Numerical applications of the BIIIEEW model to disease of cancer datasets are provided.

New prediction method for reliability analysis of ocean sustainable energy systems

With the aim of overcoming the shortcomings of traditional approaches, in this paper, an exponential Weibull distribution for fitting the significant wave height data is proposed in order to calculate more accurately the sea-state parameter distribution tails and to extrapolate well. This proposal is applied in predicting the probability distribution tails of a measured ocean wave dataset, and its accuracy is clearly demonstrated. The proposal is subsequently utilised in combination with Monte Carlo sampling to form a new environmental contour method for deriving a 50 year contour line based on the aforementioned measured ocean wave dataset. The derived environmental contour line is compared with that predicted by using a traditional contour line approach. Additionally, the engineering significance of using a more reliable environmental contour line, such as the one derived using the proposed new method for predicting the long-term design force values for an ocean sustainable energy system is highlighted. In conclusion, the newly proposed environmental contour method is recommended to be used when predicting the extreme dynamic response values for the safe and successful design of ocean sustainable energy systems.

Bayesian Estimation for Exponentiated Weibull Distribution using Lindleys Approximation on Record Data

Bayesian Estimation for Exponentiated Weibull Distribution using Lindleys Approximation on Record Data

A New Probability Distribution: Model, Theory and Analyzing the Recovery Time Data

Probability models are frequently used in numerous healthcare, sports, and policy studies. These probability models use datasets to identify patterns, analyze lifetime scenarios, predict outcomes of interest, etc. Therefore, numerous probability models have been studied, introduced, and implemented. In this paper, we also propose a novel probability model for analyzing data in different sectors, particularly in biomedical and sports sciences. The probability model is called a new modified exponential-Weibull distribution. The heavy-tailed characteristics along with some other mathematical properties are derived. Furthermore, the estimators of the new modified exponential-Weibull are derived. A simulation study of the new modified exponential-Weibull model is also provided. To illustrate the new modified exponential-Weibull model, a practical dataset is analyzed. The dataset consists of seventy-eight observations and represents the recovery time after the injuries in different basketball matches.

Different estimation methods for the unit inverse exponentiated weibull distribution

Different estimation methods for the unit inverse exponentiated weibull distribution

The properties of Type II Half-Logistic Exponentiated Weibull Distribution with Applications

Recent research has demonstrated the utility of extending continuous distributions in fitting data of all kinds. This paper proposes the Type II Half-Logistic Exponentiated Weibull (TIIHLEtW) Distribution as a new distribution. For the Type II Half-Logistic Exponentiated Weibull distribution, we obtain precise expressions for the quantile function, probability-weighted, moments, moments generating function, reliability function, hazards function, and order statistics. The maximum likelihood estimation approach is used to estimate the parameters of the new distribution, and a simulation study is presented. Two real data sets are used to demonstrate the new distribution's applicability and flexibility. The findings indicated that the new distribution is a better fit for the data compared to the other models that were examined.

Modelling the Wind Speed Using Exponentiated Weibull Distribution: Case Study of Poprad-Tatry, Slovakia

In the paper, we statistically analysed data on the average hourly wind speed obtained from the meteorological station Poprad (located at the Poprad-Tatry airport, the Prešov region, Northern Slovakia) for the period 2005–2021. High altitude and rough mountainous terrain influence the weather conditions considerably and are a source of occasional weather risks. Finding an appropriate wind speed distribution for modelling the wind speed data is therefore important to determine the wind profile at this particular location. In addition to the commonly used two- and three-parameter Weibull distribution, a more flexible exponentiated Weibull (EW) distribution was applied to model the wind speed. Based on the results of the goodness-of-fit criteria (the Kolmogorov–Smirnov test, the Anderson–Darling test, Akaike’s and Bayesian information criteria, the root mean square error, and the coefficient of determination), the EW distribution obtained a significantly better fit to seasonal and monthly wind speed data, especially around the peaks of the data. The EW distribution also proved to be a good model for data with high positive skewness. Therefore, we can recommend the EW distribution as a flexible distribution for modelling a dataset with extremely strong winds or outliers in the direction of the right tail. Alongside the wind speed analysis, we also provided the wind direction analysis, finding out that the most prevailing direction was west (W)—with an occurrence rate of 34.99%, and a mean wind speed of 3.91 m/s, whereas the northern (N) direction featured the lowest occurrence rate of only 4.45% and the mean wind speed of 1.99 m/s.

On Predictive Modeling Using a New Three-Parameters Modification of Weibull Distribution and Application

In this article, a new modification of the Weibull model with three parameters, the new exponential Weibull distribution (E-WD), is defined. The new model has many statistical advantages, the heavy-tailed behavior and the regular variation property were offered. Many of the important statistical functions of the modified model are presented in closed forms. The flexibility of E-WD has been improved. The proposed model can be used to fit data with different shapes, it can be right-skewed, left-skewed, decreasing, curved and symmetric. Some distribution properties of the proposed model, including moment generating function, characteristic function, moment, quantile and identifiability property, have been derived. In addition to the information generating function, the Shannon entropy and information energy are also discussed. The maximum likelihood approach and Bayesian estimation are used to estimate the distribution parameters. In the Bayesian method, three different loss functions are used. The calculations show the biases and estimated risks to obtain the best estimator. The bootstrap confidence intervals, the asymptotic confidence intervals and the observed variance-covariance matrix are obtained. Metropolis Hastings’ MCMC procedure is used for the calculations. We apply the composite distribution to stock data for four variables. The goodness-of-fit results show that the model performs well compared to its competitors. The proposed model can be used for forecasting and decision making.

Integer-valued Autoregressive Model Based on Innovations with Discrete Exponential-Weibull Distribution

Integer-valued Autoregressive Model Based on Innovations with Discrete Exponential-Weibull Distribution

Study on the Wind and Wave Environmental Conditions of the Xisha Islands in the South China Sea

Wind and waves are the main factors of environmental loading on ships and offshore structures. Thus, detailed understanding of wind and wave conditions can improve the design and maintenance of these structures. This paper developed a validated long-term wind and wave hindcast database covering the recent 32 years from 1988 to 2019. The spatial distribution of wind and wave characteristics for the whole Xisha Islands’ domain were analyzed. Frequency and directional distributions of wind speeds and significant wave heights were investigated at several locations around typical islands. Extreme value models were used to estimate the wind speed for 100-year return levels, whereas environmental contour approaches were utilized to establish the extreme sea-state parameters for 50- and 100-year return periods. It was found that the Weibull distribution was better fitted to the significant wave heights of the Xuande Atoll’s sites in the open sea, while the exponential Weibull distribution provided a better fit at the Yongle Atoll’s sites where waves are sheltered.

Performance Analysis of Mixed PLC-FSO Dual-Hop Communication Systems

In this article, we analyze the performance of a mixed dual-hop power line communication/free-space optical communication (PLC-FSO) transmission system supporting both decode-and-forward (DF) and fixed-gain amplify-and-forward (AF) relaying protocols. Further, it is assumed that the PLC link experiences log-normal fading under the effects of additive background and impulsive noise, while the free-space optical (FSO) channel obeys an exponentiated Weibull distribution with pointing errors. On this basis, we derive the probability density function (PDF) and cumulative distribution function (CDF) of the end-to-end (e2e) signal-to-noise ratio (SNR). To evaluate the system performance, the closed-form expressions for the outage probability (OP) and average bit-error rate (BER) are derived. Additionally, to gain more insights, the asymptotic analysis of OP and average BER, and the upper bound of the average capacity are presented.

Optical Intelligent Reflecting Surface for Mixed Dual-Hop FSO and Beamforming-Based RF System in C-RAN

Optical intelligent reflecting surface (IRS) is an emerging and low-cost technology that can establish a stable communication route in free space optical (FSO) transmission environment with obstacles. In this work, optical IRS-aided dual-hop mixed FSO and RF system is first proposed for cloud radio access network (C-RAN). Specifically, polar codes are introduced to combat turbulence and building sway induced fading in FSO link, and transmit beamforming (TBF) technique is designed to achieve optimal data-rate for RF link. Supposing that the IRS-aided FSO link is subject to exponentiated Weibull distribution with geometric and misalignment loss, whereas the RF link experiences the Fisher-Snedecor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {F}$ </tex-math></inline-formula> composite fading, the analytical closed-form outage probability expression is derived in terms of Meijer G and Lauricella multivariate hypergeometric functions with decode-and-forward strategy. Exact closed-form average bit error rate expressions are obtained when the relay of C-RAN adopts single antenna and multiantenna beamforming techniques. On the basis of moment generating function of end-to-end signal-to-noise ratio, the ergodic capacity is obtained in terms of univariate and multivariate Fox H-functions over independent but not identically distributed Fisher-Snedecor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {F}$ </tex-math></inline-formula> fading channels. The correctness of the analytical results is verified through Monte-Carlo simulations. We further provide an asymptotic analysis and discuss the achievable diversity orders.

The Extended Exponential Weibull Distribution: Properties, Inference, and Applications to Real-Life Data

A novel version of the exponential Weibull distribution known as the extended exponential Weibull (ExEW) distribution is developed and examined using the Lehmann alternative II (LAII) generating technique. The new distributions basic mathematical properties are derived. The maximum likelihood estimation (MLE) technique is used to estimate the unknown parameters of the proposed distribution. The estimators’ performance is further assessed using the Monte Carlo simulation technique. Eventually, two real-world data sets are utilized to show the applicability of the new distribution.