Modified Weibull Distribution Research Articles

Upper Record Values from Modified Weibull Distribution and Characterization

Upper Record Values from Modified Weibull Distribution and Characterization

Transmuted exponentiated Chen distribution with application to survival data

This article considers an extension of the exponentiated Chen distribution based on the quadratic rank transmutation map technique. Some structural properties of the transmuted exponentiated Chen distribution are discussed. The estimation procedure is performed using the method of maximum likelihood. Finally, the flexibility of the new distribution is illustrated using strengths of glass fibres data and nicotine in cigarettes data. References G. R. Aryal and C. P. Tsokos. Transmuted Weibull distribution: A generalization of the Weibull probability distribution. Euro. J. Pure Appl. Math. , 4(2):89–102, 2011. http://www.ejpam.com/index.php/ejpam/article/view/1170 Z. Chen. A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Stats. Prob. Lett. , 49:155–161, 2000. doi:10.1016/S0167-7152(00)00044-4 Y. P. Chaubey and R. Zhang. An extension of Chen's family of survival distributions with bathtub shape or increasing hazard rate function. Commun. Stat. A: Theor. , 44(19):4049–4064, 2015. doi:10.1080/03610926.2014.997357 M. S. Khan and R. King. Transmuted modified Weibull distribution: A generalization of the modified Weibull probability distribution. Euro. J. Pure Appl. Math. , 6(1):66–88, 2013. http://www.ejpam.com/index.php/ejpam/article/view/1606 M. S. Khan, R. King and I. Hudson. Characterizations of the transmuted inverse Weibull distribution. ANZIAM J , 55:C197–C217, 2014. doi:10.21914/anziamj.v55i0.7785 M. S. Khan and R. King. A new class of transmuted inverse Weibull distribution for reliability analysis. Am. J. Math. Manage. Sci. . 33(4):261–286, 2014. doi:10.1080/01966324.2014.929989 M. S. Khan, R. King and I. Hudson. A new three parameter transmuted Chen lifetime distribution with application. J. Appl. Stat. Sci. , 21(3) 2015. https://www.novapublishers.com/catalog/product_info.php?products_id=54720 F. Merovci. Transmuted Rayleigh distribution. Austrian J. Stat. , 42(1):21–31, 2013. http://www.ajs.or.at/index.php/ajs/article/view/vol42,%20no1-2 R. L. Smith and J. C. Naylor. A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. J. Roy. Stat. Soc. C–App. , 36:358–369, 1987. doi: 10.2307/2347795 W. T. Shaw and I. R. C. Buckley. The alchemy of probability distributions: Beyond Gram–Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. Technical report, 2009. http://arxiv.org/abs/0901.0434 Federal Trade Commission (USA). Results of tar, nicotine and carbon monoxide testing for 1,249 varieties of domestic cigarettes sold in 1995. File No. 962 3099, Jan. 1998. https://www.ftc.gov/news-events/press-releases/1998/01/results-tar-nicotine-and-carbon-monoxide-testing-1249-varieties

Reliability Estimation of Modified Weibull Distribution with Type-II Hybrid Censored Data

The study deals with the analysis of Type-II hybrid censored data from the modified Weibull distribution. We provide maximum-likelihood estimates of the parameters, reliability, and hazard rate functions along with their standard errors. The confidence intervals along with their widths have also been obtained. Assuming gamma and Jeffrey’s invariant priors for the unknown parameters, Bayes estimates along with its posterior errors and highest posterior density credible intervals are obtained. The Markov Chain Monte Carlo technique has been used to simulate draws from the complicated posterior densities of the parameters. A simulation study is conducted to compare the performances of classical and Bayesian methods of estimation. Finally, a real data analysis is performed for illustrative purpose.

A new flexible Weibull distribution

Many of studies have suggested the modifications on Weibull distribution to model the non-monotone hazards. In this paper, we combine two cumulative hazard functions and propose a new modifiedWeibull distribution function. The newly suggested distribution will be named as a new flexible Weibull distribution. Corresponding hazard function of the proposed distribution shows flexible (monotone or non-monotone) shapes. We study the characteristics of the proposed distribution that includes ageing behavior, moment, and order statistic. We also discuss an estimation method for its parameters. The performance of the proposed distribution is compared with existing modifiedWeibull distributions using various types of hazard functions. We also use real data example to illustrate the efficiency of the proposed distribution.

Inference and prediction for modified Weibull distribution based on doubly censored samples

In this article, inference for the modified Weibull (MW) distribution under type-II doubly censored sample is discussed. Maximum likelihood estimator (MLE) and Bayes estimators (BEs) based on conjugate and discrete priors are derived for three unknown parameters. The BEs are studied under squared error loss and LINEX error loss functions. The Bayesian prediction (BP) of the ℓ-th ordered observation xℓ in a sample of size n from MW distribution is obtained. A real life data set and simulation data are used to illustrate the results derived.

Micro-sized enterprises: vulnerability to flash floods

In the framework of risk assessment for flash floods, vulnerability is a key concept to assess the susceptibility of elements at risk. Vulnerability is defined as expected degree of loss for an element at risk due to a hazard impact of a defined magnitude and frequency. Besides the increasing number of studies on flash floods available, in-depth information on vulnerability was missing so far. In order to close this gap, a vulnerability model was created for micro-sized enterprises exposed to flash floods in Greece. This model was based on a nonlinear regression approach using data from four different events. By means of bootstrapping, different functions were fitted to the data, and a modified Weibull distribution was found to represent the relationship between process magnitude and degree of loss best. Moreover, there is no need to distinguish between different business sectors when computing vulnerability for buildings exposed. The model can be applied on a local scale and may serve as a basis for flash flood risk management.

A Study on Estimation of Wind Speed Distribution by Using the Modified Weibull Distribution

The knowledge of the probability density function of wind speed is key information for determining wind energy potential of the specified region. In literature, the Weibull distribution is widely-used and accepted distribution to express the probability density function of wind speed data. However, the Weibull distribution does not exhibit good fitting for all wind speed data measured at different geographical locations throughout the world. Thus, in this study, it is proposed that a better fitting of wind speed data and a better estimating wind power density is possible with new modified Weibull distribution (MWD). Also, we compare the performance of the MWD relative to the Weibull distribution by using wind speed data measured in the different regions of Turkey. The results point out that the MWD shows good fitting for most of the considered wind speed data cases. Thus, the MWD can be alternative for assessment of wind energy potential.

Exploration of reliability algorithms using modified Weibull distribution: application on gas turbine

The main purpose of the present paper is the exploration of an algorithm for reliability assessment and analysis based on the modified Weibull distribution. Indeed, an original methodology for the monitoring and the evaluation of the a gas turbine system reliability has been proposed and set up. The obtained results in this work show the effectiveness of the used approach for assessing the operational reliability (observed and estimated) for the studied system by providing advantageous performance in minimizing the number of data classes. On the other side; these results allow a better understanding of the studied system behavior based on its reliability and survival function analyzing. Finally, the validation tests on heavily biased data and on incomplete data confirm the effectiveness of the proposed algorithm.

Transmuted New Modified Weibull Distribution

In statistical and reliability theory, the transmuted distributions are the present day researcher’s interest because these distributions will fit the data in a better manner by involving a new parameter namely transmuted parameter. This paper aims to produce another transmuted distribution based on the new modified weibull distribution using the quadratic rank transmutation map. Further, the properties such as moments, moment generating function, Estimation of parameters, order statistics are derived for the proposed distribution along with the hazard and survival functions.

Parameter estimation of the modified Weibull distribution using Monte Carlo Expectation Maximization algorithm

In the present article, the modified Weibull distribution proposed by Sarhan and Zaindin (5) is considered and proposed parameter estimation procedure based on the Monte Carlo Expectation Maximization algorithm to obtain the estimates of un- known parameters. To see the performance of the proposed estimation procedure, we report the simulation results. For illustrative purposes, we have also applied the proposed estimation procedure on a real data set.

Assessing flash flood vulnerability using a multi-vulnerability approach

In the framework of flood risk assessment, while the understanding of hazard and exposure has significantly improved over the last years, knowledge on vulnerability remains one of the challenges. Current approaches in vulnerability research are characterised by a division between social scientists and natural scientists. In order to close this gap, we present an approach that combines information on physical and social vulnerability in order to merge information on the susceptibility of elements at risk and society. With respect to physical vulnerability, the study is based on local-scale vulnerability models using nonlinear regression approaches. Modified Weibull distributions were fit to the data in order to represent the relationship between process magnitude and degree of loss. With respect to social vulnerability we conducted a door-to-door survey which resulted in particular insights on flood risk awareness and resilience strategies of exposed communities. In general, both physical and social vulnerability were low in comparison with other European studies, which may result from (a) specific building regulations in the four Mediterranean test sites as well as general design principles leading to low structural susceptibility of elements at risk, and (b) relatively low social vulnerability of citizens exposed. As a result it is shown that a combination of different perspectives of vulnerability will lead to a better understanding of exposure and capacities in flood risk management.

The odd generalized exponential modified Weibull distribution

The odd generalized exponential modified Weibull distribution

A New Class of Generalized Modified Weibull Distribution with Applications

A new five parameter gamma-generalized modified Weibull (GGMW) distribution which includes exponential, Rayleigh, modified Weibull, Weibull, gamma-modified Weibull, gamma-modified Rayleigh, gamma-modified exponential, gamma-Weibull, gamma-Rayleigh, and gamma-exponential distributions as special cases is proposed and studied. Some mathematical properties of the new class of distributions including moments, distribution of the order statistics, and Renyi entropy are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to a real datasets to illustrates the usefulness of the proposed class of models are presented.

An additive modified Weibull distribution

A new five-parameter lifetime distribution with increasing, decreasing and bathtub-shaped hazard function is proposed in this paper. An important property of the new distribution is that it is very flexible to model the bathtub-shaped hazard rate data. For a bathtub-shaped hazard rate with sharp change in the initial and wear-out phase, the new distribution can provide a better fit than many other modified Weibull distributions. The properties of the new distribution including moments, order statistics and the Weibull type probability plot (WPP) are studied. The estimation of parameters is discussed by using the method of maximum likelihood. Finally, the superiority of the proposed distribution and its four-parameter sub-model are tested by analyzing two well-known lifetime data sets.

On the Exponentiated Generalized Modified Weibull Distribution

In this paper, we study a generalization of the modified Weibull distribution. The generalization follows the recent work of Cordeiro et al. (2013) and is based on a class of exponentiated generalized distributions that can be interpreted as a double construction of Lehmann. We introduce a class of exponentiated generalized modified Weibull (EGMW) distribution and provide a list of some well-known distributions embedded within the proposed distribution. We derive some mathematical properties of this class that include ordinary moments, generating function and order statistics. We propose a maximum likelihood method to estimate model parameters and provide simulation results to assess the model performance. Real data is used to illustrate the usefulness of the proposed distribution for modeling reliability data.

Prediction and reconstruction of future and missing unobservable modified Weibull lifetime based on generalized order statistics

Abstract When a system consisting of independent components of the same type, some appropriate actions may be done as soon as a portion of them have failed. It is, therefore, important to be able to predict later failure times from earlier ones. One of the well-known failure distributions commonly used to model component life, is the modified Weibull distribution ( MWD ). In this paper, two pivotal quantities are proposed to construct prediction intervals for future unobservable lifetimes based on generalized order statistics (gos) from MWD . Moreover, a pivotal quantity is developed to reconstruct missing observations at the beginning of experiment. Furthermore, Monte Carlo simulation studies are conducted and numerical computations are carried out to investigate the efficiency of presented results. Finally, two illustrative examples for real data sets are analyzed.

The Kumaraswamy-transmuted exponentiated modified Weibull distribution

ABSTRACTThis article introduces a new generalization of the transmuted exponentiated modified Weibull distribution introduced by Eltehiwy and Ashour in 2013, using Kumaraswamy distribution introduced by Cordeiro and de Castro in 2011. We refer to the new distribution as Kumaraswamy-transmuted exponentiated modified Weibull (Kw-TEMW) distribution. The new model contains 54 lifetime distributions as special cases such as the KumaraswamyWeibull, exponentiated modified Weibull, exponentiated Weibull, exponentiated exponential, transmuted Weibull, Rayleigh, linear failure rate, and exponential distributions, among others. The properties of the new model are discussed and the maximum likelihood estimation is used to evaluate the parameters. Explicit expressions are derived for the moments and examine the order statistics. This model is capable of modeling various shapes of aging and failure criteria.

Characterizations of New Modified Weibull Distribution

Several characterizations of a New Modified Weibull distribution, introduced by Doostmoradi et al. (2014), are presented. These characterizations are based on: (i) truncated moment of a function of the random variable (ii) the hazard function (iii) a single function of the random variable (iv) truncated moment of certain function of the 1st order statistic.

A new generalization of lifetime distributions

In the current study, we set out to extend the three-parameter Modified Weibull (MW) distribution in an attempt to propose a four-parameter distribution named the Modified Weibull Poisson (MWP) distribution including such noticeable submodels as Exponential Poisson, Weibull Poisson, and Rayleigh Poisson known as the distributions subsumed under the umbrella term MWP. Depending on its parameter values, this overarching distribution was demonstrated by this work to exhibit some hazard rates like decreasing, increasing, bathtub, and upside-down bathtub ones. In addition to the hazard rates of the MWP, the mathematical properties as well as the properties of maximum likelihood estimations were brought to the forefront, and the very capability of the quantile measures to be explicitly expressed in terms of the Lambert W function was vigorously discussed. To shed light on the functioning of the maximum likelihood estimators and their asymptomatic results for the finite sample sizes, some numerical experiments were carried out leading to two data sets intended chiefly to illustrate or explicate the higher levels of importance and flexibility of the MWP in comparison with its standard counterparts, namely the Weibull, Gamma, and MW distributions.

Modified Weibull Distribution for Analyzing the Tensile Strength of Bamboo Fibers

There is growing evidence that the standard Weibull strength distribution is not always accurate for the description of variability in tensile strength and its dependence on the gauge size of brittle fibers. In this work, a modified Weibull model by incorporating the diameter variation of bamboo fiber is proposed to investigate the effect of fiber length and diameter on the tensile strength. Fiber strengths are obtained for lengths ranging from 20 to 60 mm and diameters ranging from 196.6 to 584.3 μm through tensile tests. It is shown that as the within-fiber diameter variation increases, the fracture strength of the bamboo fiber decreases. In addition, the accuracy of using weak-link scaling predictions based on the standard and modified Weibull distribution are assessed, which indicates that the use of the modified distribution provides better correlation with the experimental data than the standard model. The result highlights the accuracy of the modified Weibull model for characterizing the strength and predicting the size dependence of bamboo fiber.