Approximated non parametric confidence regions for the ratio of two percentiles

Huang, Lifei

doi:10.1080/03610926.2015.1076479

Cited by 7 publications

(2 citation statements)

References 13 publications

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“…Therefore, quantiles can be used for comparing the reliability (survivability) of different samples of items; see Malekzadeh and Sabri-Laghaie (2021). Similar cases can be found in biomedical problems (Albers & Löhnberg, 1984), medical diagnoses (Rudolfer & Campbell, 1985), and wood industries (Huang, 2017;Huang & Johnson, 2006). These studies remind us that developing methods, such as constructing SCI, for interpreting and comparing quantiles of several populations can be very advantageous.…”

Section: Introductionmentioning

confidence: 81%

Simultaneous confidence intervals for quantile differences of several heterogeneous normal populations: With application to vitamin D supplement treatment on colorectal cancer patients

Malekzadeh

Kharrati-Kopaei

2023

Biometrical J

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Section: Introductionmentioning

confidence: 81%

Simultaneous confidence intervals for quantile differences of several heterogeneous normal populations: With application to vitamin D supplement treatment on colorectal cancer patients

Malekzadeh

Kharrati-Kopaei

2023

Biometrical J

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“…In economics, it is often used to analyse income or wealth distribution. Additionally, the ratio of percentiles also plays a significant role in academic assessments and educational research; see, e.g., [1]- [2].…”

Section: Introductionmentioning

confidence: 99%

Simultaneous Confidence Intervals for Ratios of the Percentiles of the Delta-Lognormal Distribution

Janthasuwan,

Niwitpong,

Niwitpong

2024

Mal. J. Fund. Appl. Sci.

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Statistical percentiles are extremely important and valuable measurement tools in various contexts. They offer significant advantages when it comes to estimating a wide range of values across different fields, making them essential in statistical analysis and research. This importance motivates researchers to study the construction of simultaneous confidence intervals for ratios of percentiles of the delta-lognormal distribution. This research introduces four distinct methods for constructing such confidence intervals: the fiducial generalized confidence interval, the Bayesian-based highest posterior density credible interval using Jeffreys prior, Jeffreys rule prior, and Uniform prior. All methods are subjected to evaluation and comparison through coverage probabilities and expected lengths in Monte Carlo simulations. The simulation study shows that, overall, the Bayesian-based highest posterior density credible interval works better and more accurately than the fiducial generalized confidence interval. To further validate the findings of the simulation study, these methods are applied to real-world daily rainfall data collected from a river basin in Thailand.

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Test for Changes in the Modeled Solvency Capital Requirement of an Internal Risk Model

Gaigall¹

2021

ASTIN Bull.

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In the context of the Solvency II directive, the operation of an internal risk model is a possible way for risk assessment and for the determination of the solvency capital requirement of an insurance company in the European Union. A Monte Carlo procedure is customary to generate a model output. To be compliant with the directive, validation of the internal risk model is conducted on the basis of the model output. For this purpose, we suggest a new test for checking whether there is a significant change in the modeled solvency capital requirement. Asymptotic properties of the test statistic are investigated and a bootstrap approximation is justified. A simulation study investigates the performance of the test in the finite sample case and confirms the theoretical results. The internal risk model and the application of the test is illustrated in a simplified example. The method has more general usage for inference of a broad class of law-invariant and coherent risk measures on the basis of a paired sample.

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Approximated non parametric confidence regions for the ratio of two percentiles

Cited by 7 publications

References 13 publications

Simultaneous confidence intervals for quantile differences of several heterogeneous normal populations: With application to vitamin D supplement treatment on colorectal cancer patients

Simultaneous confidence intervals for quantile differences of several heterogeneous normal populations: With application to vitamin D supplement treatment on colorectal cancer patients

Simultaneous Confidence Intervals for Ratios of the Percentiles of the Delta-Lognormal Distribution

Test for Changes in the Modeled Solvency Capital Requirement of an Internal Risk Model

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