a study of the generalized tukey lambda family

Freimer, Marshall; Kollia, Georgia; Mudholkar, Govind S.; Lin, Chia‐Ju

doi:10.1080/03610928808829820

Cited by 195 publications

(128 citation statements)

References 14 publications

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“…The SLD QB is a quantile-based distribution defined through its quantile function. Akin to other quantile-based distributions such as Tukey's lambda distribution and its generalizations (Tukey, 1960;Ramberg and Schmeiser, 1974;Freimer et al, 1988) and the Davies distribution (Hankin and Lee, 2006), closed-form expressions do not exist for either the cumulative distribution function or the probability density function of the SLD QB , except of course for its special cases mentioned above.…”

Section: Functionsmentioning

confidence: 99%

The quantile-based skew logistic distribution

Staden

King

2015

Statistics & Probability Letters

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Section: Functionsmentioning

confidence: 99%

The quantile-based skew logistic distribution

Staden

King

2015

Statistics & Probability Letters

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“…The "uncertainty of the uncertainty" depends on the underlying measurement error probability density, which is sometimes itself uncertain. Figure 5 plots the familiar normal density and three non-normal densities (uniform, gamma, and generalized lambda, [14]). Figure 6 plots the estimated probability density (using the 10 5 realizations) of the estimated value of d IR using the traditional Grubbs' estimator for each of the four distributions (the true value of d IR is 0.05) and the five true standard deviations are the same as in Section 4.…”

Section: Uncertainty On the Uncertainty On The Uncertaintymentioning

confidence: 99%

The impact of metrology study sample size on uncertainty in IAEA safeguards calculations

Burr

Krieger

Norman

et al. 2016

EPJ Nuclear Sci. Technol.

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Abstract. Quantitative conclusions by the International Atomic Energy Agency (IAEA) regarding States' nuclear material inventories and flows are provided in the form of material balance evaluations (MBEs). MBEs use facility estimates of the material unaccounted for together with verification data to monitor for possible nuclear material diversion. Verification data consist of paired measurements (usually operators' declarations and inspectors' verification results) that are analysed one-item-at-a-time to detect significant differences. Also, to check for patterns, an overall difference of the operator-inspector values using a "D (difference) statistic" is used. The estimated DP and false alarm probability (FAP) depend on the assumed measurement error model and its random and systematic error variances, which are estimated using data from previous inspections (which are used for metrology studies to characterize measurement error variance components). Therefore, the sample sizes in both the previous and current inspections will impact the estimated DP and FAP, as is illustrated by simulated numerical examples. The examples include application of a new expression for the variance of the D statistic assuming the measurement error model is multiplicative and new application of both random and systematic error variances in one-item-at-a-time testing.

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“…For detailed and recent studies on QF, its properties and usefulness in the identification of models we refer to Nair et al (2008Nair et al ( , 2011, Nair and Sankaran (2009), Nair (2009), Sankaran et al (2010) and the references therein. Many of the quantile functions used in applied work like various forms of lambda distributions (Ramberg and Schmeiser, 1974;Freimer et al, 1988;van Staden and Loots, 2009;Gilchrist, 2000), the power-Pareto distribution (Gilchrist, 2000, Hankin andLee, 2006), Govindarajulu distribution (Nair et al, 2011) etc. do not have tractable distributions.…”

Section: Introductionmentioning

confidence: 99%

Quantile based entropy function in past lifetime

Sunoj

Sankaran

Nanda

2013

Statistics & Probability Letters

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a b s t r a c tDi Crescenzo and Longobardi (2002) introduced a measure of uncertainty in past lifetime distributions and studied its relationship with residual entropy function. In the present paper, we introduce a quantile version of the entropy function in past lifetime and study its properties. Unlike the measure of uncertainty given in Di Crescenzo and Longobardi (2002) the proposed measure uniquely determines the underlying probability distribution. The measure is used to study two nonparametric classes of distributions. We prove characterizations theorems for some well known quantile lifetime distributions.

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a study of the generalized tukey lambda family

Cited by 195 publications

References 14 publications

The quantile-based skew logistic distribution

The quantile-based skew logistic distribution

The impact of metrology study sample size on uncertainty in IAEA safeguards calculations

Quantile based entropy function in past lifetime

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