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Showing 12 results for Weibull Distribution
Amal Saki Malehi, Ebrahim Hajizadeh, Kambiz Ahmadi,
Volume 6, Issue 1 (8-2012)
Abstract
The survival analysis methods are usually conducted based on assumption that the population is homogeneity. However, generally, this assumption in most cases is unrealistic, because of unobserved risk factors or subject specific random effect. Disregarding the heterogeneity leads to unbiased results. So frailty model as a mixed model was used to adjust for uncertainty that cannot be explained by observed factors in survival analysis. In this paper, family of power variance function distributions that includes gamma and inverse Gaussian distribution were introduced and evaluated for frailty effects. Finally the proportional hazard frailty models with Weibull baseline hazard as a parametric model used for analyzing survival data of the colorectal cancer patients.
Ghobad Barmalzan, Abedin Heidari,
Volume 7, Issue 1 (9-2013)
Abstract
Suppose there are two groups of random variables, one with independent and non-identical distributed and another with independent and identical distributed. In this paper, for the case when the size of groups are not equal, and all of the underlying random variables have exponential distribution, the necessary and sufficient conditions are obtained for establishing the mean residual life, hazard rate and dispersive orders between the second order statistics of two groups. Moreover, when random variables follow the Weibull distribution, the hazard rate, dispersive and likelihood ratio order between the second order statistics from two groups are investigated.
Ali Doostmoradi, Mohammadreza Zadkarami, Mohammadreza Akhoond, Aref Khanjari Idenak,
Volume 8, Issue 2 (3-2015)
Abstract
In this paper a new distribution function based on Weibull distribution is introduced. Then the characteristics of this new distribution are considered and a real data set is used to compare this distribution with some of the generalized Weibull distributions.
Shahram Yaghoubzadeh, Ali Shadrokh, Masoud Yarmohammadi,
Volume 9, Issue 1 (9-2015)
Abstract
In this paper, we introduce a new five-parameters distribution with increasing, decreasing, bathtub-shaped failure rate, called as the Beta Weibull-Geometric (BWG) distribution. Using the Sterling Polynomials, the probability density function and several properties of the new distribution such as its reliability and failure rate functions, quantiles and moments, Renyi and Shannon entropies, moments of order statistics, mean residual life, reversed mean residual life are obtained. The maximum likelihood estimation procedure is presented in this paper. Also, we compare the results of fitting this distribution to some of their sub-models, using to a real data set. It is also shown that the BWG distribution fits better to this data set.
Ghobad Barmalzan, Abedin Haidari, Khaled Masomifard,
Volume 9, Issue 2 (2-2016)
Abstract
In this paper, series and parallel systems, when the lifetimes of their components following the scale model are studied and different stochastic orderings between them are discussed. Moreover, we apply these results to the series and parallel systems consisting of exponentiated Weibull or generalized gamma components. The presented results in this paper complete and extend some known results in the literature.
Ali Doostmoradi, Mohammadreza Zadkarami, Aref Khanjari Idenak, Zahara Fereidooni,
Volume 10, Issue 1 (8-2016)
Abstract
In this paper we propose a new distribution based on Weibull distribution. This distribution has three parameters which displays increasing, decreasing, bathtub shaped, unimodal and increasing-decreasing-increasing failure rates. Then consider characteristics of this distribution and a real data set is used to compared proposed distribution whit some of the generalized Weibull distribution.
Elham Basiri, Seyed Mahdi Salehi,
Volume 14, Issue 1 (8-2020)
Abstract
Nowadays inference based on censored samples has been studied by many researchers. One of the most common censoring methods is progressively type II censoring. In this model, n items are put on the test. At each failure times some of the remaining items randomly withdrawn from the test. This process continues until for a pre-fixed value as m, failure times of m items are observed. For determining the best number for the items on the test different criteria can be considered. One of the most important factors that can be considered is the cost criterion. In this paper, by considering cost function and Weibull distribution for the lifetime of items, we find the optimal value for the sample size, i.e. n. In order to evaluate, the obtained results one example based on real data is given.
Mehran Naghizadeh Qomi,
Volume 14, Issue 2 (2-2021)
Abstract
In classical statistics, the parameter of interest is estimated based on sample information and using natural estimators such as maximum likelihood estimators. In Bayesian statistics, the Bayesian estimators are constructed based on prior knowledge and combining with it sample information. But, in some situations, the researcher has information about the unknown parameter as a guess. Bayesian shrinkage estimators can be constructed by Combining this non-sample information with sample information together with the prior knowledge, which is in the area of semi-classical statistics. In this paper, we introduce a class of Bayesian shrinkage estimators for the Weibull scale parameter as a generalization of the estimator at hand and consider the bias and risk of them under LINEX loss function. Then, the proposed estimators are compared using a real data set.
Bahram Tarami, Mohsen Avaji, Nahid Sanjari Farsipour,
Volume 15, Issue 1 (9-2021)
Abstract
In this paper, using the extended Weibull Marshall-Olkin-Nadarajah family of distributions, the exponential, modified Weibull, and Gompertz distributions are obtained, and density, survival, and hazard functions are simulated. Next, an algorithm is presented for the simulation of these distributions. For exponential case, Bayesian statistics under squared error, entropy Linex, squared error loss functions and modified Linex are calculated. Finally, the presented distributions are fitted to a real data set.
Motahare Zaeamzadeh, Jafar Ahmadi, Bahareh Khatib Astaneh,
Volume 15, Issue 2 (3-2022)
Abstract
In this paper, the lifetime model based on series systems with a random number of components from the family of power series distributions has been considered. First, some basic theoretical results have been obtained, which have been used to optimize the number of components in series systems. The average lifetime of the system, the cost function, and the total time on test have been used as an objective function in optimization. The issue has been investigated in detail when the lifetimes of system components have Weibull distribution, and the number of components has geometric, logarithmic, or zero-truncated Poisson distributions. The results have been given analytically and numerically. Finally, a real data set has been used to illustrate the obtained results.
Abedin Haidari, Mostafa Sattari, Ghobad Barmalzan,
Volume 16, Issue 1 (9-2022)
Abstract
Consider two parallel systems with their component lifetimes following a generalized exponential distribution. In this paper, we introduce a region based on existing shape and scale parameters included in the distribution of one of the systems. If another parallel system's vector of scale parameters lies in that region, then the likelihood ratio ordering between the two systems holds. An extension of this result to the case when the lifetimes of components follow exponentiated Weibull distribution is also presented.
Bahram Haji Joudaki, Reza Hashemi, Soliman Khazaei,
Volume 17, Issue 2 (2-2024)
Abstract
In this paper, a new Dirichlet process mixture model with the generalized inverse Weibull distribution as the kernel is proposed. After determining the prior distribution of the parameters in the proposed model, Markov Chain Monte Carlo methods were applied to generate a sample from the posterior distribution of the parameters. The performance of the presented model is illustrated by analyzing real and simulated data sets, in which some data are right-censored. Another potential of the proposed model demonstrated for data clustering. Obtained results indicate the acceptable performance of the introduced model.
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