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NEW EXPRESSIONS FOR REPEATED LOWER TAIL INTEGRALS OF THE NORMAL DISTRIBUTION
Withers, Christopher S.,Nadarajah, Saralees The Korean Statistical Society 2007 Journal of the Korean Statistical Society Vol.36 No.3
The recent work by the authors (see, Withers, 1999; Withers and McGavin, 2006; Withers and Nadarajah, 2006) provided new expressions for repeated upper tail integrals of the univariate normal density and so also for the general Hermite function. Here we derive new expressions for repeated lower tail integrals of the same. The calculations involve the use of Moran's L-function and the Airy function. In particular, the Hermite functions are expressed in terms of Moran's L-function and vice versa.
New Expressions for Repeated Lower Tail Integrals of the Normal Distribution
Christopher S. Withers,Saralees Nadarajah 한국통계학회 2007 Journal of the Korean Statistical Society Vol.36 No.3
The recent work by the authors (see, Withers, 1999; Withers and Mc-Gavin, 2006; Withers and Nadarajah, 2006) provided new expressions forrepeated upper tail integrals of the univariate normal density and so also forthe general Hermite function. Here we derive new expressions for repeatedlower tail integrals of the same. The calculations involve the use of Moran'sL-function and the Airy function. In particular, the Hermite functions areexpressed in terms of Moran'sL-function and vice versa.
James Withers,Robert W. Regenhardt,Adam A. Dmytriw,Justin E. Vranic,Rudolph Marciano,James D. Rabinov 대한뇌혈관외과학회 2023 Journal of Cerebrovascular and Endovascular Neuros Vol.25 No.3
Anterior communicating artery aneurysms are the most common intracranial aneurysm and have a high risk of rupture which can lead to morbidity and mortality. Traditionally, intracranial aneurysms were treated by clipping with neurosurgical access. However, certain patients may prefer less invasive approaches or not represent open surgical candidates. Flow diverters, including flow-redirection endoluminal devices (FRED), are new-generation stents that are placed endovascularly by transfemoral or transradial access. Recent studies have demonstrated that FRED is both safe and effective, with complete occlusion of aneurysms in over 90% of patients. This case highlights an interesting phenomenon of post-flow diversion circulatory remodeling, where flow diverter treatment can alter the circle of Willis anatomy and physiology.
The joint distribution of the sample minimum and maximum from a smooth distribution on [w1,w2]
Christopher S. Withers,Saralees Nadarajah 한국통계학회 2018 Journal of the Korean Statistical Society Vol.47 No.3
Wegive expansions in inverse powers of the sample size n for the joint distribution function of the sample extremes when sampling from any smooth distribution on a finite interval when its density function is positive at its end points.
Adelaide L Withers,Jenny Downs,Andrew Wilson,Graham Hall 대한수면연구학회 2023 Journal of sleep medicine Vol.20 No.1
Objectives: Nocturnal hypoventilation is a complication of neuromuscular disorders. There are various recommendations for measuring pCO<sub>2</sub> during polysomnography and numerous national and international definitions of hypoventilation that could contribute to significant variations in clinical practice. We therefore aimed to determine clinical practices implemented by Australasian pediatric sleep physicians.Methods: Pediatric sleep physicians completed an electronic survey for information regarding pCO<sub>2</sub> measurements and definitions of hypoventilation that are followed for children with neuromuscular disorders.Results: It was found that transcutaneous measurement of pCO<sub>2</sub> was performed in all centers, with 25% of the centers simultaneously performing capnography. Twelve definitions of hypoventilation were used, including published definitions from the American Academy of Sleep Medicine (AASM) manual and recommendations of the pediatric Australasian Sleep Association/Australasian Sleep Technologists Association. The most commonly used definition of hypoventilation (9/17, 53%) was the 2012 pediatric AASM definition (pCO<sub>2</sub> >50 mmHg for >25% of the total sleep time). There was a discrepancy between centers and individuals within the same center when defining hypoventilation. Answers stating the use of the Australasian definitions (rise in pCO<sub>2</sub> ≥10 mmHg from wake to sleep, average rise in pCO<sub>2</sub> ≥3 mmHg from non rapid eye movement to rapid eye movement sleep) were more frequent when asked specifically via a checkbox (yes/no) compared to free text.Conclusions: These results confirm the heterogeneity and lack of standardization of clinical practice within Australasia when measuring pCO<sub>2</sub> during polysomnography and defining hypoventilation. The Australasian definitions were not used as frequently as anticipated.
Canonical regression models for exponential families
Christopher S. Withers,Saralees Nadarajah 한국통계학회 2008 Journal of the Korean Statistical Society Vol.37 No.2
Every canonical exponential family generates a regression model that is also a canonical exponential family. For example, forthe normal it is the set of sayn normal observations, with means and variances of the form N = y.Nw/z.Nw and vN = 1/z.Nwfor 1≤N ≤n, wherew is the canonical regression parameter and{yN,zN}are known vectors of the same dimension. This isa much richer model than the usual linear regression model with means and variances N = x.Nβand vN = v for 1≤N ≤n.We give the rst few terms of the Edgeworth Cornish Fisher expansions for the distribution, density and quantiles of any smoothfunction of the maximum likelihood estimate of w, and the associated expansion for the condence limit of any smooth function of w.