79 results
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2. Combined class of distributions with an exponentiated Weibull family for reliability application.
- Author
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Park, Minjae
- Subjects
WEIBULL distribution ,MAXIMUM likelihood statistics ,SYSTEM failures ,ORDER statistics ,EXPECTATION-maximization algorithms - Abstract
We develop a novel class of distributions after the exponentiated Weibull family and vtub-shaped failure rate for systems are considered and compounded together. This combined class of distributions can be applied to reliability applications using the data, and we investigate its properties. We study the mathematical properties of combined distributions including order statistics and estimation by maximum likelihood. In addition, we implement an EM algorithm to determine unknown parameters using maximum likelihood estimates, and maximum entropy characterizations are discussed under appropriate constraints. Using maximum likelihood estimation, we obtain point estimates and interval estimation for parameters. We develop a novel approach to measuring the reliability of multi-component systems as well as a single-component system and illustrate the usefulness of the proposed approach. We apply the approach to real data sets and discuss numeric examples to show the statistical properties of the new compounding class of distributions derived in the paper. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
3. Bayesian estimation for geometric process with the Weibull distribution.
- Author
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Usta, Ilhan
- Subjects
- *
WEIBULL distribution , *MARKOV chain Monte Carlo , *BAYES' estimation , *ASYMPTOTIC distribution , *MAXIMUM likelihood statistics , *MOMENTUM transfer - Abstract
In this paper, we focus on Bayesian estimation of the parameters in the geometric process (GP) in which the first occurrence time of an event is assumed to have Weibull distribution. The Bayesian estimators are derived based on both symmetric (Squared Error) and asymmetric (General Entropy, LINEX) loss functions. Since the Bayesian estimators of unknown parameters cannot be obtained analytically, Lindley's approximation and the Markov Chain Monte Carlo (MCMC) methods are applied to compute the Bayesian estimates. Furthermore, by using the MCMC methods, credible intervals of the parameters are constructed. Maximum likelihood (ML) estimators are also derived for unknown parameters. The confidence intervals of the parameters are obtained based on an asymptotic distribution of ML estimators. Moreover, the performances of the proposed Bayesian estimators are compared with the corresponding ML, modified moment and modified maximum likelihood estimators through an extensive simulation study. Finally, analyses of two different real data sets are presented for illustrative purposes. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
4. Analysis of adaptive type-II progressively hybrid censoring with binomial removals.
- Author
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Elshahhat, Ahmed and Nassar, Mazen
- Subjects
BAYES' estimation ,BINOMIAL distribution ,MARKOV chain Monte Carlo ,MONTE Carlo method ,WEIBULL distribution ,CENSORSHIP - Abstract
Adaptive Type-II progressive hybrid censoring scheme has quite popular in a life-testing problem and reliability analysis due to it ensures more efficiency of inference procedures and saves total testing time. In this paper, an adaptive Type-II progressive hybrid censored sampling with random removals is considered, where the removals of the survival units at each stage from a life-test follows a binomial distribution during the execution of the experiment. The classical and Bayesian approaches are used to obtain the point and interval estimates of the unknown parameters of Weibull distribution, when the lifetimes are collected under the proposed censoring scheme. Different Bayesian estimates relative to various balanced type loss functions are obtained. Due to the complexity of the proposed estimators, some numerical techniques are implemented to obtain them. Using Markov chain Monte Carlo methods, the different Bayes estimates and associate credible intervals are developed. Extensive simulation study is performed to examine the efficiency of the proposed estimators. To show the applicability of the proposed methods in a real-life scenario, two real data sets coming from clinical and engineering areas are analysed. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
5. The unit extended Weibull families of distributions and its applications.
- Author
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Guerra, Renata Rojas, Peña-Ramírez, Fernando A., and Bourguignon, Marcelo
- Subjects
WEIBULL distribution ,MAXIMUM likelihood statistics ,RANDOM variables - Abstract
In this paper, two new general families of distributions supported on the unit interval are introduced. The proposed families include several known models as special cases and define at least twenty (each one) new special models. Since the list of well-being indicators may include several double bounded random variables, the applicability for modeling those is the major practical motivation for introducing the distributions on those families. We propose a parametrization of the new families in terms of the median and develop a shiny application to provide interactive density shape illustrations for some special cases. Various properties of the introduced families are studied. Some special models in the new families are discussed. In particular, the complementary unit Weibull distribution is studied in some detail. The method of maximum likelihood for estimating the model parameters is discussed. An extensive Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples. Applications to the literacy rate in Brazilian and Colombian municipalities illustrate the usefulness of the two new families for modeling well-being indicators. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
6. The polynomial-exponential distribution: a continuous probability model allowing for occurrence of zero values.
- Author
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Chesneau, Christophe, Bakouch, Hassan S., Ramos, Pedro L., and Louzada, Francisco
- Subjects
DISTRIBUTION (Probability theory) ,CONTINUOUS distributions ,MAXIMUM likelihood statistics ,WEIBULL distribution ,STATISTICAL reliability ,LOGNORMAL distribution ,BIAS correction (Topology) - Abstract
This paper deals with a new two-parameter lifetime distribution with increasing, decreasing and constant hazard rate. This distribution allows the occurrence of zero values and involves the exponential, linear exponential and other combinations of Weibull distributions as submodels. Many statistical properties of the distribution are derived. Maximum likelihood estimation of the parameters and a bias corrective approach is investigated with a simulation study for performance of the estimators. Four real data sets are analyzed for illustrative purposes and it is noted that the distribution is a highly alternative to the gamma, Weibull, Lognormal and exponentiated exponential distributions. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
7. On transmuted generalized linear exponential distribution.
- Author
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Ghosh, S., Kataria, K. K., and Vellaisamy, P.
- Subjects
DISTRIBUTION (Probability theory) ,HAZARD function (Statistics) ,PARAMETER estimation ,WEIBULL distribution - Abstract
In this paper, we introduce a transmuted generalized linear exponential distribution (TGLED) through the quadratic rank transmutation function studied by Shaw and Buckley (2009). The TGLED includes exponential distribution (ED), linear exponential distribution (LED) and generalized linear exponential distribution (GLED) as sub-models. Various statistical properties like moments, the mode, quantile and hazard rate function are discussed. We also derive the expression for the stress-strength parameter and discuss its estimation procedure. Finally, some properties of the maximum likelihood estimators (MLE's) for the parameters are studied using simulated data and some applications of the proposed model to real data are also provided. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
8. A novel flexible additive Weibull distribution with real-life applications.
- Author
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Khalil, Alamgir, Ijaz, Muhammad, Ali, Kashif, Mashwani, Wali Khan, Shafiq, Muhammad, Kumam, Poom, and Kumam, Wiyada
- Subjects
WEIBULL distribution ,MAXIMUM likelihood statistics ,CHARACTERISTIC functions ,GENERATING functions ,ORDER statistics ,MAXIMUM entropy method - Abstract
This paper introduces a novel model with six parameters called "flexible additive Weibull distribution (FAWD)." The suggested model is capable to model the life time data with a non-monotonic hazard rate. The statistical properties of the new distribution including Renyi entropy, quantile function, maximum likelihood estimation, order statistics, moment generating function, probability generating function, factorial and characteristic function are discussed in details. The flexibility of the proposed distribution is judged based on AIC, CAIC, BIC and HQIC, the smaller is the value of these statistics, and the better is the results. The usefulness of the proposed distribution is illustrated by using two real data sets. The proposed distribution has shown better performance and fits the used data better than some other well-known distributions. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
9. On some properties and applications of intervened cluster negative binomial distribution.
- Author
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Satheesh Kumar, C. and Sreejakumari, S.
- Subjects
NEGATIVE binomial distribution ,LIKELIHOOD ratio tests ,MAXIMUM likelihood statistics ,BINOMIAL distribution ,WEIBULL distribution - Abstract
In this paper, we consider an intervened version of the cluster negative binomial distribution and investigate some of its statistical properties. The parameters of the distribution are estimated by the method of maximum likelihood and by the method of pgf based minimum Hellinger type divergence. Also generalised likelihood ratio test procedure is applied for examining the significance of the intervention parameter. Certain real life data applications are provided for illustrating the usefulness of the model and a brief simulation study is carried out for assessing the performances of the estimators obtained through both the methods of estimation. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
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10. Log-epsilon-skew normal: A generalization of the log-normal distribution.
- Author
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Hutson, Alan D., Mashtare, Terry L., and Mudholkar, Govind S.
- Subjects
LOGNORMAL distribution ,KURTOSIS ,WEIBULL distribution ,MAXIMUM likelihood statistics ,GAUSSIAN distribution ,GENERALIZATION ,PARAMETER estimation - Abstract
The log-normal distribution is widely used to model non-negative data in many areas of applied research. In this paper, we introduce and study a family of distributions with non-negative reals as support and termed the log-epsilon-skew normal (LESN) which includes the log-normal distributions as a special case. It is related to the epsilon-skew normal developed in Mudholkar and Hutson (2000) the way the log-normal is related to the normal distribution. We study its main properties, hazard function, moments, skewness and kurtosis coefficients, and discuss maximum likelihood estimation of model parameters. We summarize the results of a simulation study to examine the behavior of the maximum likelihood estimates, and we illustrate the maximum likelihood estimation of the LESN distribution parameters to two real world data sets. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
11. A bivariate inverse Weibull distribution and its application in complementary risks model.
- Author
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Mondal, Shuvashree and Kundu, Debasis
- Subjects
WEIBULL distribution ,HAZARD function (Statistics) ,BAYESIAN analysis ,SURVIVAL analysis (Biometry) ,MAXIMUM likelihood statistics ,SAMPLING (Process) - Abstract
In reliability and survival analysis the inverse Weibull distribution has been used quite extensively as a heavy tailed distribution with a non-monotone hazard function. Recently a bivariate inverse Weibull (BIW) distribution has been introduced in the literature, where the marginals have inverse Weibull distributions and it has a singular component. Due to this reason this model cannot be used when there are no ties in the data. In this paper we have introduced an absolutely continuous bivariate inverse Weibull (ACBIW) distribution omitting the singular component from the BIW distribution. A natural application of this model can be seen in the analysis of dependent complementary risks data. We discuss different properties of this model and also address the inferential issues both from the classical and Bayesian approaches. In the classical approach, the maximum likelihood estimators cannot be obtained explicitly and we propose to use the expectation maximization algorithm based on the missing value principle. In the Bayesian analysis, we use a very flexible prior on the unknown model parameters and obtain the Bayes estimates and the associated credible intervals using importance sampling technique. Simulation experiments are performed to see the effectiveness of the proposed methods and two data sets have been analyzed to see how the proposed methods and the model work in practice. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
12. Existence, uniqueness and consistency of estimation of life characteristics of three-parameter Weibull distribution based on Type-II right censored data.
- Author
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Nagatsuka, Hideki and Balakrishnan, N.
- Subjects
UNIQUENESS (Mathematics) ,PARAMETER estimation ,CENSORING (Statistics) ,WEIBULL distribution ,MONTE Carlo method ,MEAN square algorithms - Abstract
In this paper, we propose a new method of estimation for the parameters and quantiles of the three-parameter Weibull distribution based on Type-II right censored data. The method, based on a data transformation, overcomes the problem of unbounded likelihood. In the proposed method, under mild conditions, the estimates always exist uniquely, and the estimators are also consistent over the entire parameter space. Through Monte Carlo simulations, we further show that the proposed method of estimation performs well compared to some prominent methods in terms of bias and root mean squared error in small-sample situations. Finally, two real data sets are used to illustrate the proposed method of estimation. [ABSTRACT FROM PUBLISHER]
- Published
- 2016
- Full Text
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13. Reliability estimation in a multicomponent stress–strength model under generalized half-normal distribution based on progressive type-II censoring.
- Author
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Ahmadi, Kambiz and Ghafouri, Somayeh
- Subjects
MONTE Carlo method ,PARETO distribution ,MAXIMUM likelihood statistics ,BAYES' estimation ,WEIBULL distribution ,RELIABILITY in engineering ,CENSORSHIP - Abstract
In this paper, based on progressively Type-II censored samples, the problem of estimation of multicomponent stress–strength reliability under generalized half-normal (GHN) distribution is considered. The reliability of a k-component stress-strength system is estimated when both stress and strength variates are assumed to have a GHN distribution with various cases of same and different shape and scale parameters. Different methods such as the maximum likelihood estimates (MLEs) and Bayes estimation are discussed. The expectation maximization algorithm and approximate maximum likelihood methods are proposed to compute the MLE of reliability. The Lindley's approximation method, as well as Metropolis–Hastings algorithm, are applied to compute Bayes estimates. The performance of the proposed procedures is also demonstrated via a Monte Carlo simulation study and an illustrative example. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
14. Compounded inverse Weibull distributions: Properties, inference and applications.
- Author
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Chakrabarty, Jimut Bahan and Chowdhury, Shovan
- Subjects
WEIBULL distribution ,GEOMETRIC distribution ,POISSON distribution ,STATISTICAL reliability ,EXPECTATION-maximization algorithms ,POTENTIAL distribution - Abstract
In this paper two probability distributions are analyzed which are formed by compounding inverse Weibull with zero-truncated Poisson and geometric distributions. The distributions can be used to model lifetime of series system where the lifetimes follow inverse Weibull distribution and the subgroup size being random follows either geometric or zero-truncated Poisson distribution. Some of the important statistical and reliability properties of each of the distributions are derived. The distributions are found to exhibit both monotone and non-monotone failure rates. The parameters of the distributions are estimated using the expectation-maximization algorithm and the method of minimum distance estimation. The potentials of the distributions are explored through three real life data sets and are compared with similar compounded distributions, viz. Weibull-geometric, Weibull-Poisson, exponential-geometric and exponential-Poisson distributions. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
15. Estimation of reliability of multicomponent stress-strength inverted exponentiated Rayleigh model.
- Author
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Sharma, Vikas Kumar and Dey, Sanku
- Subjects
MONTE Carlo method ,PROBABILITY density function ,RAYLEIGH model ,MARKOV chain Monte Carlo ,RANDOM variables ,MARKOV processes ,WEIBULL distribution ,CUMULATIVE distribution function - Abstract
In this paper, we consider the estimation of the multicomponent reliability by assuming the inverted exponentiated Rayleigh distribution. Both stress and strength are assumed to have an inverted exponentiated Rayleigh distribution with common scale parameter. The random variable representing the stress experienced by the system and representing the strength of system available to overcome the stress. The system works flawlessly only if at least out of strength variables exceed the random stress. The multicomponent reliability of the system is given by. We estimate by using frequentist and Bayesian approaches. Bayes estimates of have been obtained by using Markov Chain Monte Carlo methods since joint posteriors of the parameters does not have the explicit forms. We also construct asymptotic and highest probability density credible intervals for. The behavior of the proposed estimators is studied on the basis of estimated risks through Monte Carlo simulations. Finally, a data set is analyzed for illustrative purposes. Abbreviations: PDF: Probability Density Function; CDF: Cumulative Density Function; IER: Inverted Exponentiated Rayleigh; MLE: Maximum likelihood estimators; HPD: Highest Posterior Density; UBT: Upside down Bathtub; HNC: Head and Neck Cancer data; MCMC: Monte-Carlo Markov Chains; CP: Coverage Probability; KS: Kolmogorov - Smirnov. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
16. Estimation under modified Weibull distribution based on right censored generalized order statistics.
- Author
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Ateya, Saieed F.
- Subjects
WEIBULL distribution ,ORDER statistics ,MAXIMUM likelihood statistics ,MARKOV chain Monte Carlo ,AKAIKE information criterion - Abstract
In this paper, the maximum likelihood (ML) and Bayes, by using Markov chain Monte Carlo (MCMC), methods are considered to estimate the parameters of three-parameter modified Weibull distribution (MWD(β, τ, λ)) based on a right censored sample of generalized order statistics (gos). Simulation experiments are conducted to demonstrate the efficiency of the proposed methods. Some comparisons are carried out between the ML and Bayes methods by computing the mean squared errors (MSEs), Akaike's information criteria (AIC) and Bayesian information criteria (BIC) of the estimates to illustrate the paper. Three real data sets from Weibull(α, β) distribution are introduced and analyzed using the MWD(β, τ, λ) and also using the Weibull(α, β) distribution. A comparison is carried out between the mentioned models based on the corresponding Kolmogorov–Smirnov (K–S) test statistic, {AIC and BIC} to emphasize that the MWD(β, τ, λ) fits the data better than the other distribution. All parameters are estimated based on type-II censored sample, censored upper record values and progressively type-II censored sample which are generated from the real data sets. [ABSTRACT FROM PUBLISHER]
- Published
- 2013
- Full Text
- View/download PDF
17. On MLEs of the parameters of a modified Weibull distribution for progressively type-2 censored samples.
- Author
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Jiang, H., Xie, M., and Tang, L.C.
- Subjects
WEIBULL distribution ,DISTRIBUTION (Probability theory) ,EXTREME value theory ,PROBABILITY theory ,ELECTRONICS - Abstract
Lifetimes of modern mechanic or electronic units usually exhibit bathtub-shaped failure rates. An appropriate probability distribution to model such data is the modified Weibull distribution proposed by Lai et al. [15]. This distribution has both the two-parameter Weibull and type-1 extreme value distribution as special cases. It is able to model lifetime data with monotonic and bathtub-shaped failure rates, and thus attracts some interest among researchers because of this property. In this paper, the procedure of obtaining the maximum likelihood estimates (MLEs) of the parameters for progressively type-2 censored and complete samples are studied. Existence and uniqueness of the MLEs are proved. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
18. Alpha power Weibull distribution: Properties and applications.
- Author
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Nassar, M., Alzaatreh, A., Mead, M., and Abo-Kasem, O.
- Subjects
WEIBULL distribution ,STATISTICAL reliability ,ORDER statistics ,MAXIMUM likelihood statistics ,PARAMETER estimation - Abstract
In this paper, a new lifetime distribution is defined and studied. We refer to the new distribution as alpha power Weibull distribution. The importance of the new distribution comes from its ability to model monotone and non monotone failure rate functions, which are quite common in reliability studies. Various properties of the proposed distribution are obtained including moments, quantiles, entropy, order statistics, mean residual life function, and stress-strength parameter. The maximum likelihood estimation method is used to estimate the parameters. Two real data sets are used to illustrate the importance of the proposed distribution. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
19. Cubic rank transmuted distributions: inferential issues and applications.
- Author
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Granzotto, D. C. T., Louzada, F., and Balakrishnan, N.
- Subjects
WEIBULL distribution ,MAXIMUM likelihood statistics ,COMPUTER simulation ,PARAMETER estimation ,LOGISTIC distribution (Probability) - Abstract
In this paper, we introduce a new family of transmuted distributions, the cubic rank transmutation map distribution. This new proposal increases the flexibility of the transmuted distributions enabling the modelling of more complex data such as ones possessing bimodal hazard rates. In order to illustrate the usefulness of the cubic rank transmutation map, we use two well-known lifetime distributions, namely the Weibull and log-logistic models. Several mathematical properties of these new distributions, namely the cubic rank transmuted Weibull distribution and the cubic rank transmuted log-logistic distribution, are derived. Then, the maximum likelihood estimation of the model parameters is described. A simulation study designed to assess the properties of this estimation procedure is then carried out. Finally, applications of the proposed models and their fit are illustrated with some datasets and the corresponding diagnostic analyses are also provided. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
20. Inference for Weibull distribution under adaptive Type-I progressive hybrid censored competing risks data.
- Author
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Ashour, S. K. and Nassar, M.
- Subjects
WEIBULL distribution ,COMPETING risks ,PARAMETERS (Statistics) ,BAYESIAN analysis ,ESTIMATION theory ,MARKOV chain Monte Carlo - Abstract
In this paper, a competing risks model is considered under adaptive type-I progressive hybrid censoring scheme (AT-I PHCS). The lifetimes of the latent failure times have Weibull distributions with the same shape parameter. We investigate the maximum likelihood estimation of the parameters. Bayes estimates of the parameters are obtained based on squared error and LINEX loss functions under the assumption of independent gamma priors. We propose to apply Markov Chain Monte Carlo (MCMC) techniques to carry out a Bayesian estimation procedure and in turn calculate the credible intervals. To evaluate the performance of the estimators, a simulation study is carried out. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
21. The exponential–Weibull lifetime distribution.
- Author
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Cordeiro, Gauss M., Ortega, Edwin M.M., and Lemonte, Artur J.
- Subjects
WEIBULL distribution ,EXPONENTIAL families (Statistics) ,PARAMETER estimation ,MATHEMATICAL models ,GENERATING functions ,MAXIMUM likelihood statistics - Abstract
In this paper, we propose a new three-parameter model called the exponential–Weibull distribution, which includes as special models some widely known lifetime distributions. Some mathematical properties of the proposed distribution are investigated. We derive four explicit expressions for the generalized ordinary moments and a general formula for the incomplete moments based on infinite sums of Meijer's G functions. We also obtain explicit expressions for the generating function and mean deviations. We estimate the model parameters by maximum likelihood and determine the observed information matrix. Some simulations are run to assess the performance of the maximum likelihood estimators. The flexibility of the new distribution is illustrated by means of an application to real data. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
22. Bayesian and maximum likelihood estimations of the inverse Weibull parameters under progressive type-II censoring.
- Author
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Sultan, K. S., Alsadat, N. H., and Kundu, Debasis
- Subjects
BAYESIAN analysis ,MAXIMUM likelihood statistics ,WEIBULL distribution ,GENERALIZATION ,SIMULATION methods & models ,LOSS functions (Statistics) - Abstract
In this paper, the statistical inference of the unknown parameters of a two-parameter inverse Weibull (IW) distribution based on the progressive type-II censored sample has been considered. The maximum likelihood estimators (MLEs) cannot be obtained in explicit forms, hence the approximate MLEs are proposed, which are in explicit forms. The Bayes and generalized Bayes estimators for the IW parameters and the reliability function based on the squared error and Linex loss functions are provided. The Bayes and generalized Bayes estimators cannot be obtained explicitly, hence Lindley's approximation is used to obtain the Bayes and generalized Bayes estimators. Furthermore, the highest posterior density credible intervals of the unknown parameters based on Gibbs sampling technique are computed, and using an optimality criterion the optimal censoring scheme has been suggested. Simulation experiments are performed to see the effectiveness of the different estimators. Finally, two data sets have been analysed for illustrative purposes. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
23. Comparison of estimation methods for the Weibull distribution.
- Author
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Teimouri, Mahdi, Hoseini, SeyedM., and Nadarajah, Saralees
- Subjects
WEIBULL distribution ,ESTIMATION theory ,STATISTICAL reliability ,HYDROLOGY ,MAXIMUM likelihood statistics ,TELECOMMUNICATION systems ,PERCENTILES - Abstract
Weibull distributions have received wide ranging applications in many areas including reliability, hydrology and communication systems. Many estimation methods have been proposed for Weibull distributions. But there has not been a comprehensive comparison of these estimation methods. Most studies have focused on comparing the maximum likelihood estimation (MLE) with one of the other approaches. In this paper, we first propose anL-moment estimator for the Weibull distribution. Then, a comprehensive comparison is made of the following methods: the method of maximum likelihood estimation (MLE), the method of logarithmic moments, the percentile method, the method of moments and the method ofL-moments. [ABSTRACT FROM PUBLISHER]
- Published
- 2013
- Full Text
- View/download PDF
24. Parameter estimation of three-parameter Weibull distribution based on progressively Type-II censored samples.
- Author
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Ng, H. K.T., Luo, L., Hu, Y., and Duan, F.
- Subjects
PARAMETER estimation ,WEIBULL distribution ,CENSORING (Statistics) ,MAXIMUM likelihood statistics ,LEAST squares ,MONTE Carlo method ,NUMERICAL analysis - Abstract
In this paper, the estimation of parameters for a three-parameter Weibull distribution based on progressively Type-II right censored sample is studied. Different estimation procedures for complete sample are generalized to the case with progressively censored data. These methods include the maximum likelihood estimators (MLEs), corrected MLEs, weighted MLEs, maximum product spacing estimators and least squares estimators. We also proposed the use of a censored estimation method with one-step bias-correction to obtain reliable initial estimates for iterative procedures. These methods are compared via a Monte Carlo simulation study in terms of their biases, root mean squared errors and their rates of obtaining reliable estimates. Recommendations are made from the simulation results and a numerical example is presented to illustrate all of the methods of inference developed here. [ABSTRACT FROM PUBLISHER]
- Published
- 2012
- Full Text
- View/download PDF
25. A Finite Mixture Three-Parameter Weibull Model for the Analysis of Wind Speed Data.
- Author
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Qin, Xu, Zhang, Jiang-She, and Yan, Xiao-Dong
- Subjects
FINITE mixture models (Statistics) ,WEIBULL distribution ,WIND speed ,DATA analysis ,MAXIMUM likelihood statistics ,PARAMETER estimation ,NONLINEAR programming - Abstract
This article presents a mixture three-parameter Weibull distribution to model wind speed data. The parameters are estimated by using maximum likelihood (ML) method in which the maximization problem is regarded as a nonlinear programming with only inequality constraints and is solved numerically by the interior-point method. By applying this model to four lattice-point wind speed sequences extracted from National Centers for Environmental Prediction (NCEP) reanalysis data, it is observed that the mixture three-parameter Weibull distribution model proposed in this paper provides a better fit than the existing Weibull models for the analysis of wind speed data under study. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
26. A new compounding life distribution: the Weibull–Poisson distribution.
- Author
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Lu, Wanbo and Shi, Daimin
- Subjects
WEIBULL distribution ,POISSON distribution ,DISTRIBUTION (Probability theory) ,PARAMETER estimation ,ESTIMATION theory ,ALGORITHMS - Abstract
In this paper, a new compounding distribution, named the Weibull–Poisson distribution is introduced. The shape of failure rate function of the new compounding distribution is flexible, it can be decreasing, increasing, upside-down bathtub-shaped or unimodal. A comprehensive mathematical treatment of the proposed distribution and expressions of its density, cumulative distribution function, survival function, failure rate function, the kth raw moment and quantiles are provided. Maximum likelihood method using EM algorithm is developed for parameter estimation. Asymptotic properties of the maximum likelihood estimates are discussed, and intensive simulation studies are conducted for evaluating the performance of parameter estimation. The use of the proposed distribution is illustrated with examples. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
27. Accelerated life test sampling plans for the Weibull distribution under Type I progressive interval censoring with random removals.
- Author
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Chang Ding, Chunyan Yang, and Siu-Keung Tse
- Subjects
WEIBULL distribution ,DISTRIBUTION (Probability theory) ,MONTE Carlo method ,ACCELERATED life testing ,PROBABILITY theory - Abstract
This paper considers the design of accelerated life test (ALT) sampling plans under Type I progressive interval censoring with random removals. We assume that the lifetime of products follows a Weibull distribution. Two levels of constant stress higher than the use condition are used. The sample size and the acceptability constant that satisfy given levels of producer's risk and consumer's risk are found. In particular, the optimal stress level and the allocation proportion are obtained by minimizing the generalized asymptotic variance of the maximum likelihood estimators of the model parameters. Furthermore, for validation purposes, a Monte Carlo simulation is conducted to assess the true probability of acceptance for the derived sampling plans. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
28. Step partially accelerated life tests under finite mixture models.
- Author
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Abdel-Hamid, Alaa H. and Al-Hussaini, Essam K.
- Subjects
ACCELERATED life testing ,ESTIMATION theory ,MAXIMUM likelihood statistics ,WEIBULL distribution ,DISTRIBUTION (Probability theory) ,TESTING - Abstract
In this paper, step partially accelerated life tests are considered when the lifetime of an item under use condition follows a finite mixture of distributions. The analysis is performed when each of the components follows a general class of distributions, which includes, among others, the Weibull, compound Weibull (or three-parameter Burr type XII), power function, Gompertz and compound Gompertz distributions. Based on type-I censoring, the maximum likelihood estimates (MLEs) of the mixing proportions, scale parameters and acceleration factor are obtained. Special attention is paid to a mixture of two exponential components. Simulation results are obtained to study the precision of MLEs. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
29. Optimal accelerated life tests under interval censoring with random removals: the case of Weibull failure distribution.
- Author
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Tse, Siu-Keung, Ding, Chang, and Yang, Chunyan
- Subjects
ACCELERATED life testing ,WEIBULL distribution ,ANALYSIS of variance ,PROBABILITY measures ,PROBABILITY theory - Abstract
In this paper, optimal accelerated life test (ALT) plans are investigated under progressive Type I interval censoring with random removals when lifetimes are Weibull distributed. The optimal ALT plans which minimize the asymptotic variance of the estimated qth quantile for different combinations of total number of inspections and removal probability are presented. For implementation convenience, the practical plans, which adopt the same optimality criterion but the inspection times are determined based on the ideas of equally spaced or equal probability scheme at each stress level, are also derived. Numerical studies are conducted to evaluate the relative efficiency of a practical plan to the corresponding optimal ALT plan. Some suggestions are given to experimenters for selecting an appropriate practical plan in designing an ALT under the proposed censoring scheme. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
30. Accelerated life tests under finite mixture models.
- Author
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Al-Hussaini, Essam and Abdel-Hamid, Alaa
- Subjects
ESTIMATION theory ,SIMULATION methods & models ,STATISTICS ,WEIBULL distribution ,PROBABILITY theory ,FORECASTING - Abstract
In this paper, the failure time of a device is observed under a higher stress subjected to a general class of stress-response model, when its distribution is a mixture of k components each of which represents a different cause of failure. The problem is studied when each of the components belongs to a general class of distributions which includes, among others, the Weibull, compound Weibull (or three-parameter Burr type XII), power function, Gompertz and compound Gompertz distributions. On the basis of the censored data, the maximum likelihood estimates of the unknown parameters involved under the general stress-response model are obtained. A special attention is paid to the power rule model applied to mixtures of two Weibull components. Mixtures of two exponentials, Rayleigh and Weibull components models are used as illustrative examples. [ABSTRACT FROM AUTHOR]
- Published
- 2006
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31. Analysis of two Weibull populations under joint progressively hybrid censoring.
- Author
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Abo-Kasem, Osama E. and Elshahhat, Ahmed
- Subjects
BAYES' estimation ,MONTE Carlo method ,CENSORSHIP ,FISHER information ,GIBBS sampling ,PARAMETERS (Statistics) ,MARKOV chain Monte Carlo - Abstract
Joint Type-I progressive hybrid censoring scheme has been proposed to terminate the life-test experiment at maximum time that the experimenter can afford to continue. This article deals with the problem of estimating the two Weibull population parameters with the same shape parameter under joint Type-I progressively hybrid censoring scheme on the two samples using maximum likelihood and Bayesian inferential approaches. Using Fisher information matrix, the two-sided approximate confidence intervals of the unknown quantities are constructed. Under the assumption of independent gamma priors, the Bayes estimators are developed using squared-error loss function. Since the Bayes estimators cannot be expressed in closed forms, hence, Gibbs within Metropolis-Hastings algorithm is proposed to carry out the Bayes estimates and also to construct the corresponding credible intervals. Moreover, some popular joint censoring plans are generalized and can be obtained as a special cases from our results. Monte Carlo simulations are performed to assess the performance of the proposed estimators. To determine the optimal progressive censoring plan, two different optimality criteria are considered. Finally, to show the applicability of the proposed methods in real phenomenon, a real-life data set is analyzed. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
32. Comparison of estimators and predictors based on modified weibull records: Bayesian and non-Bayesian approaches.
- Author
-
Kotb, Mohammed S. and Raqab, Mohammad Z.
- Subjects
MONTE Carlo method ,WEIBULL distribution ,MAXIMUM likelihood statistics - Abstract
Based on record statistics from three-parameter modified Weibull distribution, we consider the problem of estimating the unknown parameters using Bayesian and non-Bayesian approaches. Under a continuous-discrete joint prior distribution, Bayesian estimators and confidence intervals for the shape and scale parameters involved in the underlying model are obtained. In addition, maximum likelihood prediction and Bayesian prediction (either point or interval) of future record statistics based on an informative set of records are developed. Data analyses involving records extracted from a machine used to measure burr and times to breakdown of an insulating fluid between electrodes have been performed. Finally, Monte Carlo simulations are performed to compare the methods developed here. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
33. A consistent method of estimation for three-parameter generalized exponential distribution.
- Author
-
Prajapat, Kiran, Mitra, Sharmishtha, and Kundu, Debasis
- Subjects
DISTRIBUTION (Probability theory) ,STANDARD deviations ,MONTE Carlo method ,MAXIMUM likelihood statistics ,WEIBULL distribution ,BIAS correction (Topology) - Abstract
In this article, we provide a consistent method of estimation for the parameters of a three-parameter generalized exponential distribution which avoids the problem of unbounded likelihood function. The method is based on a maximum likelihood estimation of the shape parameter, which uses location and scale invariant statistic, originally proposed by Nagatsuka et al. (A consistent method of estimation for the three-parameter weibull distribution, Computational Statistics & Data Analysis 58:210–26). It has been shown that the estimators are unique and consistent for the entire range of the parameter space. We also present a Monte-Carlo simulation study along with the comparisons with some prominent estimation methods in terms of the bias and root mean square error. For the illustration purpose, the data analysis of a real lifetime data set has been reported. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
34. Destructive cure models with proportional hazards lifetimes and associated likelihood inference.
- Author
-
Balakrishnan, N. and Barui, S.
- Subjects
PROPORTIONAL hazards models ,NEGATIVE binomial distribution ,POISSON distribution ,COMPETING risks ,SURVIVAL analysis (Biometry) - Abstract
In survival analysis, cure models have gained much importance due to rapid advancements in medical sciences. More recently, a subset of cure models, called destructive cure models, have been studied extensively under competing risks scenario wherein initial competing risks undergo a destructive process. In this article, we study destructive cure models by assuming a flexible weighted Poisson distribution (exponentially weighted Poisson, length biased Poisson and negative binomial distributions) for the initial number of competing causes and lifetimes of the susceptible individuals being defined by proportional hazards. The expectation-maximization (EM) algorithm and profile likelihood approach are made use of to estimate the model parameters. An extensive simulation study is carried out under various parameter settings to examine the properties of the models, and accuracy and the robustness of the proposed estimation technique. Effects of model mis-specification on the parameter estimates are also discussed in detail. For further illustration of the proposed methodology, a real-life cutaneous melanoma data set is analyzed. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
35. The Lehmann type II inverse Weibull distribution in the presence of censored data.
- Author
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Tomazella, Vera L. D., Ramos, Pedro L., Ferreira, Paulo H., Mota, Alex L., and Louzada, Francisco
- Subjects
WEIBULL distribution ,CENSORING (Statistics) ,PARAMETER estimation ,AUTOMATIC timers ,BAYES' estimation ,MAXIMUM likelihood statistics - Abstract
In this article, we investigate the mathematical properties of the Lehmann type II inverse Weibull distribution. We show that this model is a reparameterized version of the Kumaraswamy-inverse Weibull distribution without identifiability problems. Parameter estimation is discussed using maximum likelihood (ML) method under a right-censoring scheme. Furthermore, a bootstrap resampling approach is considered to reduce the bias of the ML estimates. In order to illustrate the proposed methodology, we consider a real data set related to the failure time of devices in an aircraft. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
36. Discriminating between some lifetime distributions in geometric counting processes.
- Author
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Pekalp, Mustafa Hilmi, Aydoğdu, Halil, and Türkman, Kamil Feridun
- Subjects
GEOMETRIC distribution ,LOGNORMAL distribution ,WEIBULL distribution ,DATA distribution ,RELIABILITY in engineering ,MAXIMUM likelihood statistics - Abstract
Gamma, lognormal and Weibull distributions are most commonly used in modeling asymmetric data coming from the areas of life testing and reliability engineering. In this study, we deal with the problem of selecting one of these distributions for a given data set which is consistent with the geometric process (GP) model according to T -statistic based on the ratio of the maximized likelihood (RML). First, we show that T -statistic performs better than Kolmogorov- Smirnov (KS), mean square error (MSE) and maximum percentage error (MPE) based on extensive simulation study. Then, by using the T-statistic, we determine the distributions of ten real data sets shown to be consistent with the GP model by Lam et al. (2004). After validating the distribution for these data sets, we calculate the estimators of the parameters by using the suitable method given in Lam and Chan (1998), Chan, Lam, and Leung (2004) or Aydoğdu, Şenoğlu, and Kara (2010). Then, we plot observed and the fitted values of the interarrival and arrival times for comparison. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
37. Statistical inference of generalized progressive hybrid censored step-stress accelerated dependent competing risks model for Marshall-Olkin bivariate Weibull distribution.
- Author
-
Wang, Kexin and Gui, Wenhao
- Subjects
WEIBULL distribution ,MARKOV chain Monte Carlo ,COMPETING risks ,MONTE Carlo method ,INFERENTIAL statistics ,MARKOV processes ,ACCELERATED life testing ,BIVARIATE analysis - Abstract
In this article, a step-stress accelerated life test based on the generalized Khamis-Higgins model in the presence of Marshall-Olkin bivariate Weibull distributed dependent competing risks is considered under generalized progressive hybrid censoring. It is assumed that the stress is changed when a pre-specified number of failures take place, and four different failure causes are discussed. The classical and Bayesian statistical methods are used to estimate the unknown parameters. In addition to the maximum likelihood estimation, the stochastic expectation-maximization algorithm is also applied. The Monte Carlo Markov Chain samples with importance sampling are used to obtain the Bayesian estimates under two loss functions, and the Bayesian highest posterior density credible intervals are constructed. Then the parameters and reliability function under normal use stress level are calculated. The Monte Carlo method is applied to compare the performance of the estimation methods. Finally, a real-life data set is analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
38. Flexible methods for reliability estimation using aggregate failure-time data.
- Author
-
Karimi, Samira, Liao, Haitao, and Fan, Neng
- Subjects
INVERSE Gaussian distribution ,MAXIMUM likelihood statistics ,RANDOM variables ,MATHEMATICAL statistics ,FIX-point estimation ,GAUSSIAN distribution ,FISHER information ,WEIBULL distribution - Abstract
The actual failure times of individual components are usually unavailable in many applications. Instead, only aggregate failure-time data are collected by actual users, due to technical and/or economic reasons. When dealing with such data for reliability estimation, practitioners often face the challenges of selecting the underlying failure-time distributions and the corresponding statistical inference methods. So far, only the exponential, normal, gamma and inverse Gaussian distributions have been used in analyzing aggregate failure-time data, due to these distributions having closed-form expressions for such data. However, the limited choices of probability distributions cannot satisfy extensive needs in a variety of engineering applications. PHase-type (PH) distributions are robust and flexible in modeling failure-time data, as they can mimic a large collection of probability distributions of non-negative random variables arbitrarily closely by adjusting the model structures. In this article, PH distributions are utilized, for the first time, in reliability estimation based on aggregate failure-time data. A Maximum Likelihood Estimation (MLE) method and a Bayesian alternative are developed. For the MLE method, an Expectation-Maximization algorithm is developed for parameter estimation, and the corresponding Fisher information is used to construct the confidence intervals for the quantities of interest. For the Bayesian method, a procedure for performing point and interval estimation is also introduced. Numerical examples show that the proposed PH-based reliability estimation methods are quite flexible and alleviate the burden of selecting a probability distribution when the underlying failure-time distribution is general or even unknown. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
39. On the generalized extended exponential-Weibull distribution: properties and different methods of estimation.
- Author
-
Shakhatreh, Mohammed K., Lemonte, Artur J., and Cordeiro, Gauss M.
- Subjects
WEIBULL distribution ,MAXIMUM likelihood statistics - Abstract
We consider the generalized extended exponential-Weibull distribution, which can be very useful for modelling non-monotonic failure rate function, and provide a detailed study of its structural properties. This model includes at least thirteen sub-models and some of them are very known such as the Weibull, generalized Weibull, exponential-Weibull, and exponentiated generalized linear exponential distributions. We also consider different estimation procedures for estimating the model parameters, namely: maximum likelihood, least-square, weighted least-square, maximum product of spacings, Cramér-von-Mises, and Anderson-Darling methods. We also conduct Monte Carlo simulation experiments to assess the finite sample properties of the proposed estimation methods. The usefulness of the distribution is illustrated by means of two real data sets to prove its versatility in practical applications. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
40. The Weibull Marshall–Olkin family: Regression model and application to censored data.
- Author
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Korkmaz, Mustafa Ç., Cordeiro, Gauss M., Yousof, Haitham M., Pescim, Rodrigo R., Afify, Ahmed Z., and Nadarajah, Saralees
- Subjects
REGRESSION analysis ,CENSORING (Statistics) ,MAXIMUM likelihood statistics ,WEIBULL distribution - Abstract
We introduce a new class of distributions called the Weibull Marshall–Olkin-G family. We obtain some of its mathematical properties. The special models of this family provide bathtub-shaped, decreasing-increasing, increasing-decreasing-increasing, decreasing-increasing-decreasing, monotone, unimodal and bimodal hazard functions. The maximum likelihood method is adopted for estimating the model parameters. We assess the performance of the maximum likelihood estimators by means of two simulation studies. We also propose a new family of linear regression models for censored and uncensored data. The flexibility and importance of the proposed models are illustrated by means of three real data sets. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
41. The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval.
- Author
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Ghitany, M. E., Mazucheli, J., Menezes, A. F. B., and Alqallaf, F.
- Subjects
WEIBULL distribution ,INVERSE Gaussian distribution ,GAUSSIAN distribution ,MAXIMUM likelihood statistics ,MOMENTS method (Statistics) ,PARAMETER estimation - Abstract
A new two-parameter distribution over the unit interval, called the Unit-Inverse Gaussian distribution, is introduced and studied in detail. The proposed distribution shares many properties with other known distributions on the unit interval, such as Beta, Johnson S
B , Unit-Gamma, and Kumaraswamy distributions. Estimation of the parameters of the proposed distribution are obtained by transforming the data to the inverse Gaussian distribution. Unlike most distributions on the unit interval, the maximum likelihood or method of moments estimators of the parameters of the proposed distribution are expressed in simple closed forms which do not need iterative methods to compute. Application of the proposed distribution to a real data set shows better fit than many known two-parameter distributions on the unit interval. [ABSTRACT FROM AUTHOR]- Published
- 2019
- Full Text
- View/download PDF
42. On some life distributions with flexible failure rate.
- Author
-
Lu, Wanbo and Chiang, Jyun-You
- Subjects
WEIBULL distribution ,POWER series ,EXPECTATION-maximization algorithms ,EXPONENTIAL generating functions ,DISTRIBUTION (Probability theory) - Abstract
A new three-parameter distribution family with a flexible failure rate function arising by mixing the Weibull distribution and power-series distribution is introduced. This distribution family includes special cases of some well-used mixing distributions and generalizes the exponential power-series distribution. Various properties of the new distribution family are discussed. Themaximum likelihood estimation and an EM algorithm are presented for finding the estimates of the distribution family parameters, and expressions for their asymptotic variance and covariance are derived. Intensive simulation studies are implemented and experimental results are illustrated with real datasets. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
43. The exponentiated transmuted Weibull geometric distribution with application in survival analysis.
- Author
-
Fattah, Ahmed A., Nadarajah, Saralees, and Ahmed, A-Hadi N.
- Subjects
WEIBULL distribution ,GEOMETRIC distribution ,MAXIMUM likelihood statistics ,ENTROPY ,SIMULATION methods & models ,SURVIVAL analysis (Biometry) - Abstract
This article introduces a new generalization of the transmuted Weibull distribution introduced by Aryal and Tsokos in 2011. We refer to the new distribution as exponentiated transmuted Weibull geometric (ETWG) distribution. The new model contains 22 lifetime distributions as special cases such as the exponentiated Weibull geometric, complementary Weibull geometric, exponentiated transmuted Weibull, exponentiated Weibull, and Weibull 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. To examine the performance of our new model in fitting several data we use two real sets of data, censored and uncensored, and then compare the fitting of the new model with some nested and nonnested models, which provides the best fit to all of the data. A simulation has been performed to assess the behavior of the maximum likelihood estimates of the parameters under the finite samples. This model is capable of modeling various shapes of aging and failure criteria. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
44. Transmuted Weibull distribution: Properties and estimation.
- Author
-
Khan, Muhammad Shuaib, King, Robert, and Hudson, Irene Lena
- Subjects
WEIBULL distribution ,PARAMETER estimation ,QUANTILES ,BONFERRONI correction ,LORENZ curve ,REGRESSION analysis - Abstract
In this article, we investigate the potential usefulness of the three-parameter transmuted Weibull distribution for modeling survival data. The main advantage of this distribution is that it has increasing, decreasing or constant instantaneous failure rate depending on the shape parameter and the new transmuting parameter. We obtain several mathematical properties of the transmuted Weibull distribution such as the expressions for the quantile function, moments, geometric mean, harmonic mean, Shannon, Rényi and q-entropies, mean deviations, Bonferroni and Lorenz curves, and the moments of order statistics. We propose a location-scale regression model based on the log-transmuted Weibull distribution for modeling lifetime data. Applications to two real datasets are given to illustrate the flexibility and potentiality of the transmuted Weibull family of lifetime distributions. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
45. Bias corrected MLEs under progressive type-II censoring scheme.
- Author
-
Teimouri, Mahdi and Nadarajah, Saralees
- Subjects
BIAS correction (Topology) ,SURVIVAL analysis (Biometry) ,MAXIMUM likelihood statistics ,INFORMATION theory ,SIMULATION methods & models ,WEIBULL distribution - Abstract
Censoring frequently occurs in survival analysis but naturally observed lifetimes are not of a large size. Thus, inferences based on the popular maximum likelihood (ML) estimation which often give biased estimates should be corrected in the sense of bias. Here, we investigate the biases of ML estimates under the progressive type-II censoring scheme (pIIcs). We use a method proposed in Efron and Johnstone [Fisher's information in terms of the hazard rate. Technical Report No. 264, January 1987, Stanford University, Stanford, California; 1987] to derive general expressions for bias corrected ML estimates under the pIIcs. This requires derivation of the Fisher information matrix under the pIIcs. As an application, exact expressions are given for bias corrected ML estimates of the Weibull distribution under the pIIcs. The performance of the bias corrected ML estimates and ML estimates are compared by simulations and a real data application. [ABSTRACT FROM PUBLISHER]
- Published
- 2016
- Full Text
- View/download PDF
46. A new compound class of log-logistic Weibull–Poisson distribution: model, properties and applications.
- Author
-
Oluyede, Broderick O., Warahena-Liyanage, Gayan, and Pararai, Mavis
- Subjects
WEIBULL distribution ,POISSON distribution ,LOGISTIC distribution (Probability) ,MAXIMUM likelihood statistics ,HAZARD function (Statistics) ,MOMENTS method (Statistics) - Abstract
A new class of distributions called the log-logistic Weibull–Poisson distribution is introduced and its properties are explored. This new distribution represents a more flexible model for lifetime data. Some statistical properties of the proposed distribution including the expansion of the density function, quantile function, hazard and reverse hazard functions, moments, conditional moments, moment generating function, skewness and kurtosis are presented. Mean deviations, Bonferroni and Lorenz curves, Rényi entropy and distribution of the order statistics are derived. Maximum likelihood estimation technique is used to estimate the model parameters. A simulation study is conducted to examine the bias, mean square error of the maximum likelihood estimators and width of the confidence interval for each parameter and finally applications of the model to real data sets are presented to illustrate the usefulness of the proposed distribution. [ABSTRACT FROM PUBLISHER]
- Published
- 2016
- Full Text
- View/download PDF
47. On an Extension of the Exponentiated Weibull Distribution.
- Author
-
Bidram, H., Alamatsaz, M. H., and Nekoukhou, V.
- Subjects
WEIBULL distribution ,MATHEMATICAL functions ,PARAMETER estimation ,EXPONENTIATION ,MAXIMUM likelihood statistics - Abstract
In this article, the exponentiated Weibull distribution is extended by the Marshall-Olkin family. Our new four-parameter family has a hazard rate function with various desired shapes depending on the choice of its parameters and, thus, it is very flexible in data modeling. It also contains two mixed distributions with applications to series and parallel systems in reliability and also contains several previously known lifetime distributions. We shall study some basic distributional properties of the new distribution. Some closed forms are derived for its moment generating function and moments as well as moments of its order statistics. The model parameters are estimated by the maximum likelihood method. The stress–strength parameter and its estimation are also investigated. Finally, an application of the new model is illustrated using two real datasets. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
48. A generalized linear model approach to seasonal aspects of wind speed modeling.
- Author
-
Bensoussan, Alain, Bertrand, Pierre, and Brouste, Alexandre
- Subjects
WIND speed ,WEIBULL distribution ,DISTRIBUTION (Probability theory) ,MATHEMATICAL models ,GAME theory ,RAYLEIGH model - Abstract
The aim of the article is to identify the intraday seasonality in a wind speed time series. Following the traditional approach, the marginal probability law is Weibull and, consequently, we consider seasonal Weibull law. A new estimation and decision procedure to estimate the seasonal Weibull law intraday scale parameter is presented. We will also give statistical decision-making tools to discard or not the trend parameter and to validate the seasonal model. [ABSTRACT FROM PUBLISHER]
- Published
- 2014
- Full Text
- View/download PDF
49. Bayesian estimation and prediction for Weibull model with progressive censoring.
- Author
-
Huang, Syuan-Rong and Wu, Shuo-Jye
- Subjects
BAYESIAN analysis ,PREDICTION models ,ESTIMATION theory ,WEIBULL distribution ,CENSORING (Statistics) ,MAXIMUM likelihood statistics ,COMPUTER simulation - Abstract
This article presents the statistical inferences on Weibull parameters with the data that are progressively type II censored. The maximum likelihood estimators are derived. For incorporation of previous information with current data, the Bayesian approach is considered. We obtain the Bayes estimators under squared error loss with a bivariate prior distribution, and derive the credible intervals for the parameters of Weibull distribution. Also, the Bayes prediction intervals for future observations are obtained in the one- and two-sample cases. The method is shown to be practical, although a computer program is required for its implementation. A numerical example is presented for illustration and some simulation study are performed. [ABSTRACT FROM PUBLISHER]
- Published
- 2012
- Full Text
- View/download PDF
50. The Weibull-geometric distribution.
- Author
-
Barreto-Souza, Wagner, de Morais, Alice Lemos, and Cordeiro, Gauss M.
- Subjects
WEIBULL distribution ,GEOMETRY ,MONOTONIC functions ,ALGORITHMS ,MATRICES (Mathematics) ,MAXIMUM likelihood statistics ,PARAMETER estimation - Abstract
For the first time, we propose the Weibull-geometric (WG) distribution which generalizes the extended exponential-geometric (EG) distribution introduced by Adamidis et al. [K. Adamidis, T. Dimitrakopoulou, and S. Loukas, On a generalization of the exponential-geometric distribution, Statist. Probab. Lett. 73 (2005), pp. 259-269], the exponential-geometric distribution discussed by Adamidis and Loukas [K. Adamidis and S. Loukas, A lifetime distribution with decreasing failure rate, Statist. Probab. Lett. 39 (1998), pp. 35-42] and the Weibull distribution. We derive many of its standard properties. The hazard function of the EG distribution is monotone decreasing, but the hazard function of the WG distribution can take more general forms. Unlike the Weibull distribution, the new distribution is useful for modelling unimodal failure rates. We derive the cumulative distribution and hazard functions, moments, density of order statistics and their moments. We provide expressions for the Renyi and Shannon entropies. The maximum likelihood estimation procedure is discussed and an EM algorithm [A.P. Dempster, N.M. Laird, and D.B. Rubim, Maximum likelihood from incomplete data via the EM algorithm (with discussion), J. R. Stat. Soc. B 39 (1977), pp. 1-38; G.J. McLachlan and T. Krishnan, The EM Algorithm and Extension, Wiley, New York, 1997] is given for estimating the parameters. We obtain the observed information matrix and discuss inference issues. The flexibility and potentiality of the new distribution is illustrated by means of a real data set. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
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