Structural Properties of Transmuted Weibull Distribution

The transmuted Weibull distribution, and a related special case, is introduced. Estimates of parameters are obtained by using a new method of moments

Some Extended Classes of Distributions: Characterizations and Properties

Based on a simple relationship between two truncated moments and certain functions of the th order statistic, we characterize some extended classes of distributions recently proposed in the statistical literature, videlicet Beta-G, Gamma-G, Kumaraswamy-G and McDonald-G. Several properties of these extended classes and some special cases are discussed. We compare these classes in terms of goodness-of-fit criteria using some baseline distributions by means of two real data sets

Exponentiated Extended Weibull-Power Series Class of Distributions

In this paper, we introduce a new class of distributions by compounding the exponentiated extended Weibull family and power series family. This distribution contains several lifetime models such as the complementary extended Weibull-power series, generalized exponential-power series, generalized linear failure rate-power series, exponentiated Weibull-power series, generalized modified Weibull-power series, generalized Gompertz-power series and exponentiated extended Weibull distributions as special cases. We obtain several properties of this new class of distributions such as Shannon entropy, mean residual life, hazard rate function, quantiles and moments. The maximum likelihood estimation procedure via a EM-algorithm is presented.Comment: Accepted for publication Ciencia e Natura Journa

On Bivariate Exponentiated Extended Weibull Family of Distributions

In this paper, we introduce a new class of bivariate distributions called the bivariate exponentiated extended Weibull distributions. The model introduced here is of Marshall-Olkin type. This new class of bivariate distributions contains several bivariate lifetime models. Some mathematical properties of the new class of distributions are studied. We provide the joint and conditional density functions, the joint cumulative distribution function and the joint survival function. Special bivariate distributions are investigated in some detail. The maximum likelihood estimators are obtained using the EM algorithm. We illustrate the usefulness of the new class by means of application to two real data sets.Comment: arXiv admin note: text overlap with arXiv:1501.03528 by other author

Four generalized Weibull distributions: similar properties and applications

We derive a common linear representation for the densities of four generalizations of the two-parameter Weibull distribution in terms of Weibull densities. The four generalized Weibull distributions briefly studied are: the Marshall-Olkin-Weibull, beta-Weibull, gamma-Weibull and Kumaraswamy-Weibull distributions. We demonstrate that several mathematical properties of these generalizations can be obtained simultaneously from those of the Weibull properties. We present two applications to real data sets by comparing these generalized distributions. It is hoped that this paper encourage developments of further generalizations of the Weibull based on the same linear representation

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

A New Method for Reliability Calculation of the Active Systems with Time-Dependent Failure Rates based on Weibull Distribution

Due to the high sensitivity in applying of electronic and mechanical equipment, creating any conditions to increase the reliability of a system is always one of the important issues for system designers. Hence, making academic models much closer to the real word applications is very attractive. In the most studies in the reliability area, it is assumed that the failure rates of the system components are constant and have exponential distributions. This distribution and its attractive memory less property provide simple mathematical relationships in order to obtain the system reliability. But in real word problems, considering time-dependent failure rates is more realistic to model processes. It means that, the system components do not fail with a constant rate during the time horizon; but this failure rate changes over the time. One of the most useful statistical distributions in order to model the time-dependent failure rates is the Weibull distribution. This distribution is not a memory less one, so it was impossible to apply simple and explicit mathematical relationships as the same as exponential distributions for the reliability of a system. Therefore, researchers in this field have used simulation technique in these circumstances which is not an exact method to get near-optimum solutions. In this paper, for the first time, it is tried to obtain a mathematical equation to calculate the reliability function of a system with time-dependent components based on Weibull distribution. Also, in order to validate the proposed method, the results compared with exact solution that exists in literature