Marshall–Olkin q-Weibull distribution and max–min processes

Jose, Kim; Naik, Shanoja R.; Ristić, Miroslav M.

doi:10.1007/s00362-008-0173-9

Cited by 38 publications

(14 citation statements)

References 21 publications

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“…Several authors derived new distributions using the Marshal-Olkin method applied to the theory of minification processes. Some recent results are: the Marshall-Olkin log-logistic minification process [17], Marshall-Olkin q-Weibull distribution and max-min processes [20,21], Marshall-Olkin beta distribution and its applications (Jose et al, 2009), Marshall-Olkin gamma minification process [27] and Marshall-Olkin semi-Weibull minification process (Thomas and Jose, 2005). Cifarelli et al [7] proposed generalized semi-Pareto and semi-Burr distributions and random coefficient minification processes.…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

The Lomax generator of distributions: Properties, minification process and regression model

Cordeiro

Ortega

Popović

et al. 2014

Applied Mathematics and Computation

123

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Section: Maximum Likelihood Estimationmentioning

confidence: 99%

The Lomax generator of distributions: Properties, minification process and regression model

Cordeiro

Ortega

Popović

et al. 2014

Applied Mathematics and Computation

123

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“…The new parameter results in added flexibility of distributions influencing the reliability properties. Jose et al [8] introduced a minification process for the Marshall-Olkin bivariate Weibull distribution. Alice and Jose [1,2] introduced a Marshall-Olkin distribution with semi Weibull and Logistic marginals.…”

Section: Introductionmentioning

confidence: 99%

Marshall–Olkin Morgenstern–Weibull distribution: generalisations and applications

Jose

Sebastian

2013

Economic Quality Control

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In this paper a new bivariate distribution called Marshall-Olkin-Morgenstern-bivariate-Weibull distribution is introduced and studied. Two different models of minification processes with the above bivariate distribution as stationary marginal distribution are developed. It is shown that the process is strictly stationary. The properties of the process are derived. The expressions for reliability under stress-strength analysis when the components are in series and parallel are obtained. The process is extended to ℎ order as well as -variate cases.

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“…Hence, it is a useful generalization of the Weibull distribution [11]. The q-Weibull distribution was considered with the autoregressive conditional duration model [12,13], stress-strength model [14] and maxmin processes [15]. Besides, it has been used to analyse data for dielectric breakdown regime of ultra-thin oxides [16], natural gas recovery plants [17] and robotic welding stations [18].…”

Section: Introductionmentioning

confidence: 99%

Inference on q-Weibull parameters

Jia

Nadarajah

2017

Stat Papers

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The q-Weibull distribution is a generalization of the Weibull distribution and could describe complex systems. We firstly point out how to derive the maximum likelihood estimates (MLEs) and least-squares estimates (LSEs) of the q-Weibull parameters. Next, three confidence intervals (CIs) for the q-Weibull parameters are constructed based on bootstrap methods and asymptotic normality of the MLEs. Explicit expressions for the Fisher information matrix necessary for the asymptotic CIs are derived. A Monte Carlo simulation study is conducted to compare the performances of the MLEs and LSEs as well as the different CIs. The simulation results show that the MLEs are superior to the LSEs in terms of both bias and mean squared error. The bootstrap CIs based on the MLEs are shown to have good coverage probabilities and average interval widths. Finally, a real data example is provided to illustrate the proposed methods.

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Marshall–Olkin q-Weibull distribution and max–min processes

Cited by 38 publications

References 21 publications

The Lomax generator of distributions: Properties, minification process and regression model

The Lomax generator of distributions: Properties, minification process and regression model

Marshall–Olkin Morgenstern–Weibull distribution: generalisations and applications

Inference on q-Weibull parameters

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