A New Modified Weibull Distribution and Its Applications

Computational Statistics & Data Analysis, 2008

A four parameter generalization of the Weibull distribution capable of modeling a bathtubshaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull distributions, among others. We derive two infinite sum representations for its moments. The density of the order statistics is obtained. The method of maximum likelihood is used for estimating the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the proposed distribution.

2014

The Weibull distribution is a popular and widely used distribution in reliability and in lifetime data analysis. Since 1958, the Weibull distribution has been modified by many researchers to allow for non-monotonic hazard functions. Many modifications of the Weibull distribution have achieved the above purpose. On the other hand, the number of parameters has increased, the forms of the survival and hazard functions have become more complicated and the estimation problems have risen.This thesis provides an extensive review of some discrete and continuous versions of the modifications of the Weibull distribution, which could serve as an important reference and encourage further modifications of the Weibull distribution. Four different modifications of the Weibull distribution are proposed to address some of the above problems using different techniques. First model, with five parameters, is constructed by considering a two-component serial system with one component following a Weibull...

2003

The exponential, Rayleigh, linear failure rate and Weibull distributions are the most commonly used distributions for analyzing lifetime data. These distributions have several desirable properties and nice physical interpretations. This paper introduces a new distribution named modified Weibull distribution. This distribution generalizes the following distributions: (1) exponential, (2) Rayleigh, (3) linear failure rate, and (4) Weibull. The properties of the modified Weibull distribution are discussed. The maximum likelihood estimates of its unknown parameters are obtained. A real data set is analyzed and it observed that the present distribution can provide a better fit than some other known distributions.

FUDMA JOURNAL OF SCIENCES, 2020

A lifetime model called Transmuted Exponential-Weibull Distribution was proposed in this research. Several statistical properties were derived and presented in an explicit form. Maximum likelihood technique is employed for the estimation of model parameters, and a simulation study was performed to examine the behavior of various estimates under different sample sizes and initial parameter values. Through using real-life datasets, it was empirically shown that the new model provides sufficient fits relative to other existing models.

Asian Journal of Probability and Statistics, 2020

This paper convolutes two generalized distributions from the family of generated T-X distribution. The new distribution generated from these distributions is called the Generalized Weibull-generalized Exponential Distribution. The properties of the proposed distribution are derived. Method of maximum likelihood estimation is used to estimate the parameters of the distribution and the information matrix is obtained. Thereafter, the distribution is applied to a real life dataset of failure for the air conditioning system and the obtained results are compared with other existing distributions to illustrate the capability and flexibility of the new distribution.

2009

The exponential, Rayleigh, linear failure rate and Weibull distributions are the most commonly used distributions for analyzing lifetime data. These distributions have several desirable properties and nice physical interpretations. This paper introduces a new distribution named modified Weibull distribution. This distribution generalizes the following distributions: (1) exponential, (2) Rayleigh, (3) linear failure rate, and (4) Weibull. The properties of the modified Weibull distribution are discussed. The maximum likelihood estimates of its unknown parameters are obtained. A real data set is analyzed and it observed that the present distribution can provide a better fit than some other known distributions. M.S.C. 2000: 46N30, 47N30, 65C60.

Quality and Reliability Engineering International, 1995

The complementary Weibull distribution may serve as a lietime model for various applications. A modification of this distribution is introduced. Its purpose is to enable the calculation of the MTBF integral, which does not exist for the regular complementary Weibull function. An efficient quadrature technique is provided. Its utility is validated through some examples.

Saeed Hemeda, El Batel

In this article, a new four-parameter lifetime model named the Weibull quasi Lindley distribution based on the Weibull G-family is introduced. It is more flexible than several recently introduced lifetime distributions. Various structural properties of the new distribution are derived including moments, moment generating function, quantile function, reliability, hazard rate function and mean residual life. Expressions for the R´enyi, q-entropies and density function of order statistics are also obtained. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. Two real data sets are presented to illustrate the advantage of the new distribution. In fact, the new model provides a better fit to this data than some of the most important distributions.

Lifetime Data Analysis, 2006

A simple competing risk distribution as a possible alternative to the Weibull distribution in lifetime analysis is proposed. This distribution corresponds to the minimum between exponential and Weibull distributions. Our motivation is to take account of both accidental and aging failures in lifetime data analysis. First, the main characteristics of this distribution are presented. Then the estimation of its parameters are considered through maximum likelihood and Bayesian inference. In particular the existence of a unique consistent root of the likelihood equations is proved. Decision tests to choose between an exponential, Weibull and this competing risk distribution are presented. And this alternative model is compared to the Weibull model from numerical experiments on both real and simulated data sets, especially in an industrial context.

Wiley Interdisciplinary Reviews: Computational Statistics

The basic Weibull distribution is considered the most fundamental and basic lifetime distribution. Various extensions of the Weibull distribution have been proposed since the 1970s and are useful in the modeling of complex lifetime data that are beyond the capability of the basic Weibull. This article reviews the properties of the basic Weibull distribution and lists the various extensions. It describes the use of Weibull probability plots as a tool for model selection and discusses the parameter estimation and model validation. It concludes with some topics for future research.