Power Generalized Weibull Distribution Based on Generalised Order Statistics

Kumar, Devendra; Jain, Neetu

doi:10.6339/jds.201807_16(3).00010

Journal of Data Science

2021

DOI: 10.6339/jds.201807_16(3).00010

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Power Generalized Weibull Distribution Based on Generalised Order Statistics

Devendra Kumar¹,

Neetu Jain²

Abstract: The power generalized Weibull distribution due to Bagdonovacius and Nikulin (2002) is an alternative,and always provides better fits than the exponentiated Weibull family for modeling lifetime data. In this paper, we consider the generalized order statistics (GOS) from this distribution. We obtain exact explicit expressions as well as recurrence relations for the single, product and conditional moments of generalized order statistics from the power generalized Weibull distribution and then we use these results… Show more

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Cited by 2 publications

References 21 publications

(7 reference statements)

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Robust Assessment on the Developments of Three Extended Exponential Models with Some New Properties and Applications

Ahmadini

Tahir

Alamri

et al. 2021

Mathematical Problems in Engineering

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The extended exponential distribution introduced by Nadarajah and Haghighi in the year 2011, which is nowadays well known as NH distribution, has received increased attention in these days. In this paper, we provide a robust assessment report on the development of three more related extended versions of exponential (or Weibull) distributions. We assessed that which model was published earlier than the other ones and why the pioneer work was not cited properly or overlooked. For example, power generalized Weibull (PGW) introduced by Bagdonavic̆ios and Nikulin (and Nikulin and Haghighi) and extended Weibull by Dimitrakopoulou, Adamidis, and Loukas, which we call here as the DAL model, were published earlier than the NH model. The developments of these three models are stated. A new method for the construction of NH and DAL models is outlined. A literature review on NH and DAL models is presented, and generalized classes from these models are discussed. Furthermore, some corrections in NH moments are suggested, and alternative expressions for moments and incomplete moments of NH and DAL models are also developed.

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Robust Assessment on the Developments of Three Extended Exponential Models with Some New Properties and Applications

Ahmadini

Tahir

Alamri

et al. 2021

Mathematical Problems in Engineering

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Generalized Pareto Distribution Based on Generalized Order Statistics and Associated Inference

Malik

Kumar

2019

Statistics in Transition New Series

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In this paper, we have considered the generalized Pareto distribution. Various structural properties of the distribution are derived including (quantile function, explicit expressions for moments, mean deviation, Bonferroni and Lorenz curves and Renyi entropy). We have provided simple explicit expressions and recurrence relations for single and product moments of generalized order statistics from the generalized Pareto distribution. The method of maximum likelihood is adopted for estimating the model parameters. For different parameter settings and sample sizes, the simulation studies are performed and compared to the performance of the generalized Pareto distribution.

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Power Generalized Weibull Distribution Based on Generalised Order Statistics

Cited by 2 publications

References 21 publications

Robust Assessment on the Developments of Three Extended Exponential Models with Some New Properties and Applications

Robust Assessment on the Developments of Three Extended Exponential Models with Some New Properties and Applications

Generalized Pareto Distribution Based on Generalized Order Statistics and Associated Inference

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