A New Discrete Extended Weibull Distribution

Abstract

In this paper, the discrete extended Weibull distribution is introduced by discretizing a new extended the continuous Weibull distribution. The new model has decreasing, increasing, constant and upside-down bathtub shaped hazard rates. Some of basic distributional and reliability properties are studied. The maximum likelihood method is used to estimate the parameters of the model. The performance of the estimation method is evaluated by a Monte-Carlo simulation. Four-real life data sets are considered for illustrating the advantages of the proposed distribution over some other well-known discrete distributions.INDEX TERMS Discrete extended Weibull distribution, hazard rate, estimation method.

A reliability analysis for electronic devices under an extension of exponentiated perks distribution

“…proposes the Omega distribution with three parameters formulated from the Lambert W‐function; this new distribution has two essential characteristics, it lacks exponential terms, and its domain does not have infinity. Other authors propose the modification of classified reliability distributions such as the Weibull distribution (WD), an example of these works can be seen in Xie et al., 7 Jia et al., 8 Liao et al., 9 Lai et al., 10 Bebbington et al., 11 Nassar et al., 12 Peng and Yan, 13 Abd El‐Monsef et al., 14 Shakhatreh et al 15 …”

Applying User Surveys and Accelerated Tests Data to Estimate Reliability of New Consumer Products Using a Discrete Life Distribution Model

“…It was assumed that the equivalent cycles of all datasets followed discrete Weibull distribution type III. The likelihood of the discrete Weibull distribution type III for an incomplete dataset (i.e., a dataset containing failed and right-censored devices) is shown in (11), where c and β are the distribution parameters, ν i is the equivalent cycles of the i-th device, r is the number of failed devices, and m is the total number of devices.…”

“…Various extensions of discrete Weibull distributions have also been introduced, and different methods for estimating their parameters have been suggested. For instance, Jia et al [11] proposed a discrete extended Weibull distribution and used MLE for estimating its parameters. Barbiero [8] proposed three methods, including the method of proportion, MLE, and the method of moments for estimating the parameters of a discrete Weibull type III distribution.…”

Bayesian Confidence Interval Estimation of Weibull Modulus Under Increasing Failure Rate

“…While there are major differences among classical methods, Bayesian methods basically use the same formulation, as will be discussed later; they differ only by the choice of the prior distribution of the parameters [17,18]. In the general scientific literature, there are many Bayesian point estimation studies on , see for example [42][43][44][45][46][47]; however Bayesian interval estimation studies are limited, see Aron et al [48] as an example. The details of Bayesian Weibull analysis can be found in [49].…”