On estimating parameters in a discrete Weibull distribution

Khan, Muhammad Shuaib; Khalique, Abdul; Abouammoh, A. M.

doi:10.1109/24.44179

Cited by 103 publications

(65 citation statements)

References 2 publications

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“…(10) coincides and reduces to geometric distribution when c = 1 − q and β = 1. Khan et al (1989) dealt with the estimation of the parameters of this distribution.…”

Section: Discrete Weibullmentioning

confidence: 99%

See 1 more Smart Citation

Generating discrete analogues of continuous probability distributions-A survey of methods and constructions

Chakraborty

2015

J Stat Distrib App

121

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“…(10) coincides and reduces to geometric distribution when c = 1 − q and β = 1. Khan et al (1989) dealt with the estimation of the parameters of this distribution.…”

Section: Discrete Weibullmentioning

confidence: 99%

“…(see also Almalki (2014). Khan et al (1989) and Kulasekara (1994) considered estimation of this distribution. Englehardht and Li (2011) applied this distribution in modeling microbial counts.…”

Section: Discrete Weibull Distributionmentioning

confidence: 99%

Generating discrete analogues of continuous probability distributions-A survey of methods and constructions

Chakraborty

2015

J Stat Distrib App

121

View full text Add to dashboard Cite

show abstract

“…With regard to the issues related to point and interval estimation of the parameters of the discrete Weibull distribution, one can refer to Khan and Khalique and Abouammoh [5], Kulasekera [6], and Barbiero [7].…”

Section: The Discrete Weibull Distributionmentioning

confidence: 99%

A proposal for modeling and simulating correlated discrete Weibull variables

Barbiero

2017

Scientia Iranica

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Abstract. Researchers in the applied sciences are often concerned with multivariate random variables. In particular, multivariate discrete data often arise in many elds (statistical quality control, biostatistics, failure and reliability analysis, etc.) and modeling such data is a relevant task, as well as simulating correlated discrete data satisfying some speci c constraints. Here, we consider the discrete Weibull distribution as an alternative to the popular Poisson random variable and propose a procedure for simulating correlated discrete Weibull random variables with marginal distributions and correlation matrix assigned by the user. The procedure relies upon the Gaussian copula model and an iterative algorithm for recovering the proper correlation matrix for the copula ensuring the desired correlation matrix on the discrete margins. A simulation study is presented, which empirically assesses the performance of the procedure in terms of accuracy and computational burden, and in relation to the necessary (but temporary) truncation of the support of the discrete Weibull random variable. Inferential issues for the proposed model are also discussed and are eventually applied to a dataset taken from the literature, which shows that the proposed multivariate model can satisfactorily t real-life correlated counts even better than the most popular or recent existing ones.

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“…It was only briefly mentioned by few scientists. Khan, Khalique and Abouammoh [3], d iscussed two discrete Weibull distributions (type I and type II), and suggested a simp le method to estimate the unknown parameters for one of them, since the usual methods of estimat ion are not easy to apply. Kulasekera [4] presented approximate maximu m likelihood estimators of the parameters of a discrete Weibull distribution under censoring.…”

Section: Discretizing a Continuous Distributionmentioning

confidence: 99%

Discrete Burr Type Iii Distribution

AL-Huniti¹,

AL-Dayian²

2012

AJMS

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In this paper, the discrete Burr type III distribution is introduced using the general approach of discretizing a continuous distribution and proposed it as a suitable lifetime model. The equivalence of continuous and discrete Burr type III distribution is established. Some important distributional properties and estimat ion of the parameters, reliability, failure rate and the second rate of failure functions are discussed based on the maximu m likelihood method and Bayesian approach.Keywords Burr Type III Distribution, Discrete Lifetime Models, Reliability, Failure Rate, Maximu m Likelihood Estimation, Bayes Estimation Intro ductionAn important aspect of lifetime analysis is to find a lifetime d istribution that can adequately describe the ageing behavior of the device concerned. Most of the lifet imes are continuous in nature and hence many continuous life distributions have been proposed in literature. On the other hand, discrete failure data are arising in several common situations for examp le:· Reports on field failure are collected weekly, monthly and the observations are the number of failures, without a specification of the failure times.· A piece of equip ment operates in cycles and experimenter observes the number of cycles successfully completed prior to failure. A frequently referred examp le is copier whose life length would be the total number of copies it produces. Another example is the number o f on/off cycles of a switch before failure occurs, see Lai and Xie [1].In the last two decades, standard discrete distributions like geometric and negative binomial have been employed to model life time data. Usually, if the discrete model is used with lifet ime data, it is a mu ltino mial distribution. This arises because effectively the continuous data have been grouped, see Lawless [2]. However, there is a need to find mo re plausible discrete lifetime d istributions to fit to various types of lifet ime data. For this purpose, discretizing popular continuous lifetime d istributions can be helpful in this manner, since, it effects on speed, accuracy and understandability of the generated data using these discrete lifetime models. and times are grouped into unit intervals so that the discrete observed variable is dX = [ X ] , the largest integer part of X, the probability mass function (pmf) of d X can be written as p ( x ) = P [ dX = x ] = P [ x ≤ dX < + 1 ] Discretizing a Continuous Distribution

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On estimating parameters in a discrete Weibull distribution

Cited by 103 publications

References 2 publications

Generating discrete analogues of continuous probability distributions-A survey of methods and constructions

Generating discrete analogues of continuous probability distributions-A survey of methods and constructions

A proposal for modeling and simulating correlated discrete Weibull variables

Discrete Burr Type Iii Distribution

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