Moments of order statistics of the standard two-sided power distribution

Çetinkaya, Çağatay; Genç, Alі İ.

doi:10.1080/03610926.2017.1373818

Cited by 7 publications

(6 citation statements)

References 23 publications

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“…Explicit expressions for order statistics moments were determined by [6]. For more results in this context, one may also refer to [7][8][9][10] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

On the Omega Distribution: Some Properties and Estimation

et al. 2021

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We obtain explicit expressions for single and product moments of the order statistics of an omega distribution. We also discuss seven methods to estimate the omega parameters. Various simulation results are performed to compare the performance of the proposed estimators. Furthermore, the maximum likelihood method is adopted to estimate the omega parameters under the type II censoring scheme. The usefulness of the omega distribution is proven using a real data set.

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“…Explicit expressions for order statistics moments were determined by [6]. For more results in this context, one may also refer to [7][8][9][10] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

On the Omega Distribution: Some Properties and Estimation

et al. 2021

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“…Mance et al [13] first considered the TSP distribution under reliability properties. Recently, moments of order statistics and stress-strength reliability estimation under the STSP distribution were studied by C ¸etinkaya and Genç [8], [9]. In this study, the STSP distribution is considered as a further research in statistical reliability analysis.…”

Section: Discussionmentioning

confidence: 99%

“…( 1) and F (.|α, β) denotes the distribution function of the STSP distribution. C ¸etinkaya and Genç [8] studied the STSP distribution in detailed in terms of its order statistics. The density of the s th order statistics is given as…”

Section: Mle Selfmentioning

confidence: 99%

“…where F s:m (y|α, β) denotes the distribution function of the s th order statistics, i.e. where µ s:m is the first moment of s th order statistics of the STSP distribution and it was given by C ¸etinkaya and Genç [8] as in the following…”

Section: Mle Selfmentioning

confidence: 99%

“…Using analytical estimation procedure, they obtained the TSP parameters and compared the distribution with the Weibull distribution. Recently, C ¸etinkaya and Genç [8], [9] studied the STSP distribution under moments of order statistics and stress-strength reliability.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the reliability characteristics of the standard two-sided power distribution

Çetinkaya¹,

Genç²

2021

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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In this study, the standard two-sided power (STSP) distribution is considered with regard to statistical reliability analysis in detail. For this purpose, along with the reliability and hazard functions of the distribution, particular reliability indices that are useful in maintenance and replacement policies are obtained and they are evaluated with their plots. The STSP distribution is classified based on aging according to various cases of its parameters. Then, we studied the classical and Bayesian estimations of the reliability and hazard functions. In Bayesian estimation, symmetric and different asymmetric loss functions are considered. For obtaining the Bayes estimates, Monte Carlo Markov Chain simulation using the Gibbs algorithm is performed. Various simulation schemes are performed for comparing the performances of the estimators. Further, the Bayesian predictions of the future observations based on the observed samples are obtained. A real data example is used to illustrate the theoretical outcomes.

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A Note on Bias Correction for the Standard Two‐Sided Power Distribution

Lemonte

2023

Advcd Theory and Sims

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It is verified that the maximum likelihood (ML) estimators of the standard two‐sided power distribution (STSP) parameters introduced by van Dorp and Kotz on the interval (0,1) can be severely biased. Since the usual analytical methods of bias correction cannot be applied in such a parametric distribution, bootstrap bias correction methods are proposed. The numerical study favors a particular bootstrap estimator based on parametric resampling. Real data applications are also considered to illustrate the impact of bias correction of the usual maximum likelihood estimators of the standard two‐sided power distribution parameters when the sample size is small.

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Moments of order statistics of the standard two-sided power distribution

Cited by 7 publications

References 23 publications

On the Omega Distribution: Some Properties and Estimation

On the Omega Distribution: Some Properties and Estimation

On the reliability characteristics of the standard two-sided power distribution

A Note on Bias Correction for the Standard Two‐Sided Power Distribution

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