Testing the equality of two normal percentiles

Cox, Tony; Jaber, Khalifa H.

doi:10.1080/03610918508812443

Cited by 14 publications

(6 citation statements)

References 2 publications

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“…In practice these estimates have to be found numerically using an iterative scheme similar to that in Cox & Jaber (1985). Hence after some algebra a generalized likelihood ratio (LR) test statistic A can be deduced as:…”

Section: Clustering Methodsmentioning

confidence: 99%

Clustering Population Means Under Heterogeneity of Variance

Cox¹,

Cowpertwait²

1992

The Statistician

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Multiple comparison procedures are commonly used for the investigation of relationships between several population means. An alternative method, which has been less well researched, is to carry out a cluster analysis of the means. Scott & Knott proposed such a clustering method based on the likelihood ratio test. Cox & Spjøtvoll considered a method based on a statistic generalized from the ANOVA F‐test. This paper introduces two different statistics which can be used in a similar manner to cluster the population means without assuming homogeneity of variance. The first is the generalized likelihood ratio test statistic and the second is an extension of Welch's statistic for use in testing the equality of all the population means without assuming homogeneity of variance. Also proposed is a clustering method for partitioning means into the most likely best fitting groups for given random samples. Using this method comparisons are made between the above two statistics, the generalized ANOVA F‐test statistic and with a method due to Calinski & Corsten based on an extension of the studentized range statistic. The statistics are compared by simulation experiments, from which the conclusions are that the two new statistics proposed give the best results in attempting to recover original partitionings of population means.

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Section: Clustering Methodsmentioning

confidence: 99%

Clustering Population Means Under Heterogeneity of Variance

Cox¹,

Cowpertwait²

1992

The Statistician

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“…However, comparing their quantiles may be more efficient and meaningful than comparing their means. In medicines, the comparisons of 90th percentiles are much more meaningful than comparing their means in a medical test; see Cox and Jaber (1985). A motivating example is from Li et al (2012).…”

Section: Introductionmentioning

confidence: 99%

“…For inferences on the quantiles of a normal population, see Chakraborti and Li (2007) and Liu et al (2013). For inference about the quantiles of two normal populations, Rudolfer and Campbell (1985) discussed Welch test statistic, Cox and Jaber (1985) considered the generalized likelihood ratio test, an adjusted generalized likelihood ratio test, and a test statistic based on Cochran's test, and Guo and Krishnamoorthy (2005) proposed a generalized confidence interval and a generalized p-value. For testing the equality of the quantiles of several normal distributions, Krishnamoorthy and Xu (2011) proposed an upper confidence limit for an upper percentile based on the maximum likelihood estimates.…”

Section: Introductionmentioning

confidence: 99%

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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“…Often, normal distributions appear in the limits of the statistics under consideration. The testing problem of the equality of quantiles is treated in Kosorok (1999), Malekzadeh and Jafari (2018), Li et al (2012), and Cox and Jaber (1985). Inference for the distance of two quantiles is the topic in Guo and Krishnamoorthy (2005), Ozturk and Balakrishnan (2009), Baklizi (2018), Bristol (1990), Albers and Löhnberg (1984), Kang, Kim, and Lee (2007), Chakraborti and Desu (2008), and Malekzadeh and Kharrati-Kopaei (2020).…”

Section: Introductionmentioning

confidence: 99%

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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Testing the equality of two normal percentiles

Cited by 14 publications

References 2 publications

Clustering Population Means Under Heterogeneity of Variance

Clustering Population Means Under Heterogeneity of Variance

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

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

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