Order statistics from non-identical right-truncated Lomax random variables with applications

Childs, Aaron; Balakrishnan, N.; Moshref, M.E.

doi:10.1007/s003620100050

Cited by 37 publications

(19 citation statements)

References 12 publications

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“…For example, Ghitany et al (2007) extend it by introducing an additional parameter using the Marshal and Olkin (1997) approach; Al-Awadhi and Ghitany (2001) use the Lomax distribution as a mixing distribution for the Poisson parameter and derive a discrete Poisson-Lomax distribution;and Punathumparambath (2011) introduced the double-Lomax distribution and applied it to IQ data. The record statistics of the Lomax distribution have been studied by Ahsanullah (1991) and by Balakrishnan and Ahsanullah (1994); the implications of various forms of right-truncation and right-censoring are discussed by Myhre and Saunders (1982), Childs et al (2001), Cramer and Schmiedt (2011) and others; and sample size estimation has been discussed by Abd-Elfattah et al (2006).…”

Section: Introductionmentioning

confidence: 99%

On the Bias of the Maximum Likelihood Estimator for the Two-Parameter Lomax Distribution

Giles

Feng

Godwin

2013

Communications in Statistics - Theory and Methods

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The Lomax (Pareto II) distribution has found wide application in a variety of fields. We analyze the second-order bias of the maximum likelihood estimators of its parameters for finite sample sizes, and show that this bias is positive. We derive an analytic bias correction which reduces the percentage bias of these estimators by one or two orders of magnitude, while simultaneously reducing relative mean squared error. Our simulations show that this analytic bias correction outperforms a correction based on the parametric bootstrap. Three examples with actual data illustrate the application of our methods.

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Section: Introductionmentioning

confidence: 99%

On the Bias of the Maximum Likelihood Estimator for the Two-Parameter Lomax Distribution

Giles

Feng

Godwin

2013

Communications in Statistics - Theory and Methods

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“…The posterior of , j j p λ and j β in (24), (25) and (26) is not known, but the plot of it shows that it is similar to normal distribution. Therefore to generate from this distribution, we use the Metropolis {Hastings method ( [51] with normal proposal distribution)}.…”

Section: Mcmc Methodsmentioning

confidence: 99%

“…This distribution was used for modeling size spectra data in aquatic ecology by [24]. [25] considered order statistics from non-identical right-truncated Lomax distributions and provided applications for this situation. [26] used the Pareto distribution as a mixing distribution for the Poisson parameter and obtained the discrete PoissonPareto distribution.…”

Section: Introductionmentioning

confidence: 99%

Inference on Constant-Partially Accelerated Life Tests for Mixture of Pareto Distributions under Progressive Type-II Censoring

Abushal¹,

AL-Zaydi²

2017

OJS

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The main purpose of this paper is to obtain the inference of parameters of heterogeneous population represented by finite mixture of two Pareto (MTP) distributions of the second kind. The constant-partially accelerated life tests are applied based on progressively type-II censored samples. The maximum likelihood estimates (MLEs) for the considered parameters are obtained by solving the likelihood equations of the model parameters numerically. The Bayes estimators are obtained by using Markov chain Monte Carlo algorithm under the balanced squared error loss function. Based on Monte Carlo simulation, Bayes estimators are compared with their corresponding maximum likelihood estimators. The two-sample prediction technique is considered to derive Bayesian prediction bounds for future order statistics based on progressively type-II censored informative samples obtained from constant-partially accelerated life testing models. The informative and future samples are assumed to be obtained from the same population. The coverage probabilities and the average interval lengths of the confidence intervals are computed via a Monte Carlo simulation to investigate the procedure of the prediction intervals. Analysis of a simulated data set has also been presented for illustrative purposes. Finally, comparisons are made between Bayesian and maximum likelihood estimators via a Monte Carlo simulation study.

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“…Childs and Balakrishnan (1998) obtained recurrence relations for moments from non-identical Pareto and truncated Pareto distribution. Childs (2001) gave recurrence relations for the single and product moments from nonidentical right truncated Lomax distribution. Moshref (2000) established recurrence relations for moments from non-identical generalized power function.…”

Section: Outliersmentioning

confidence: 99%

A Monte Carlo Study of the Effects of Variability and Outliers on the Linear Correlation Coefficient

Eledum

2017

J. Mod. App. Stat. Meth.

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Order statistics from non-identical right-truncated Lomax random variables with applications

Abstract: Order statistics, outliers, robustness, single moments, product moments, recurrence relations, Lomax distribution, right-truncated Lomax distribution, permanents, censoring, bias, mean square error, BLUE,

Cited by 37 publications

References 12 publications

On the Bias of the Maximum Likelihood Estimator for the Two-Parameter Lomax Distribution

On the Bias of the Maximum Likelihood Estimator for the Two-Parameter Lomax Distribution

Inference on Constant-Partially Accelerated Life Tests for Mixture of Pareto Distributions under Progressive Type-II Censoring

A Monte Carlo Study of the Effects of Variability and Outliers on the Linear Correlation Coefficient

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