Fractional Edgeworth expansion: Corrections to the Gaussian-Lévy central-limit theorem

Hazut, Netanel; Medalion, Shlomi; Kessler, David A.; Barkai, Eli

doi:10.1103/physreve.91.052124

Cited by 9 publications

(7 citation statements)

References 38 publications

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“…Data analyses were performed on SPSS for Mac OS X, Version 22.0 (SPSS Inc., Chicago IL) with a 95% confidence interval (CI) and considering statistically significant differences if P value < 0.05. Parametric tests were used because the sample size (greater than 30 subjects per group) was sufficient to be supported by the central limit theorem [ 29 ]. The continuous variables are presented as mean and standard deviation (SD), and the categorical variables are presented as absolute numbers and relative frequency (i.e., percentages).…”

Section: Methodsmentioning

confidence: 99%

Which Seems to Be Worst? Pain Severity and Quality of Life between Patients with Lateral Hip Pain and Low Back Pain

Ferrer-Peña

Calvo‐Lobo

Aiguadé

et al. 2018

Pain Research and Management

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Purpose The aim of this study was to compare the pain severity, health-related quality of life (HRQoL), and risk of continue having pain with prognostic risk scores (PRS), between patients referring greater trochanteric pain syndrome (GTPS) and chronic low back pain (CLBP). Methods A descriptive, cross-sectional design using nonprobability convenience sampling was performed. A total sample of 102 patients were recruited from two primary health-care centers and divided into GTPS (n = 51) and CLBP (n = 51) groups. The primary outcome was pain severity which was assessed with the Spanish version of the Graded Chronic Pain Scale (GCPS). The secondary outcome was the HRQoL which was measured using the Spanish version of EuroQoL Five Dimensions and Five Levels (EQ-5D-5L) as well as the PRS. Results Significant differences (P<0.05) were found within both groups in the pain severity global score with a medium effect size showing greater values for the CLBP group with regards to the GTPS group. The PRS in both groups did not show statistical differences (P>0.05). Nevertheless, subjects referring CLBP showed greater levels in the PRS than patients with GTPS. Comparing both groups, the HRQoL showed statistical differences (P<0.05) in the “pain/discomfort” domain in the CLBP group with respect to the GTPS group, but not in the other domains. Conclusions Patients who suffered from CLBP showed greater pain severity and HRQoL discomfort with regard to patients with GTPS. Despite greater scores for CLBP, the PRS did not seem to be different between both conditions.

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Section: Methodsmentioning

confidence: 99%

Which Seems to Be Worst? Pain Severity and Quality of Life between Patients with Lateral Hip Pain and Low Back Pain

Ferrer-Peña

Calvo‐Lobo

Aiguadé

et al. 2018

Pain Research and Management

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“…In contrast the Gaussian cannot be matched to the ID for intermediate values of x. To make the matching, one needs to find the correction to the central limit theorem, for example using the fractional Edgeworth expansion [26]. This could yield a power law correction term to the Gaussian which could in principle match the ID.…”

Section: +1mentioning

confidence: 99%

Complementary Densities of Lévy Walks: Typical and Rare Fluctuations

Rebenshtok

Denisov

Hänggi

et al. 2016

Math. Model. Nat. Phenom.

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Strong anomalous di↵usion is a recurring phenomenon in many fields, ranging from the spreading of cold atoms in optical lattices to transport processes in living cells. For such processes the scaling of the moments follows h|x(t)| q i ⇠ t q⌫(q) and is characterized by a bi-linear spectrum of the scaling exponents, q⌫(q). Here we analyze Lévy walks, with power law distributed times of flight (⌧) ⇠ ⌧ (1+↵) , demonstrating sharp bi-linear scaling. When ↵ > 1 we show that the asymptotic behavior is characterized by two complementary densities corresponding to the bi-scaling of the moments of x(t). The first density is the expected generalized central limit theorem which is responsible for the low-order moments 0 < q < ↵. The second one, a nonnormalizable density (also called infinite density) is formed by rare fluctuations and determines the time evolution of higher-order moments. We use the Faà di Bruno formalism to derive the moments of sub-ballistic super-di↵usive Lévy walks and then apply the Mellin transform technique to derive exact expressions for their infinite densities. We find a uniform approximation for the density of particles using Lévy distribution for typical fluctuations and the infinite density for the rare ones. For ballistic Lévy walks 0 < ↵ < 1 we obtain mono-scaling behavior which is quantified.

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“…Descriptive statistics were generated for the sociodemographic data (such as age, BMI, chronicity time, pain intensity, and others). Manuscript to be reviewed showed that the majority of the variables were normally distributed in the sample, so parametric tests were used because of the central limit theorem for samples >50 subjects per group (Mouri, 2013;Hazut et al, 2015). Continuous variables are presented as mean and standard deviation, and the categorical variables are presented as absolute numbers and relative frequency (percentages).…”

Section: Discussionmentioning

confidence: 99%

Peer Review #2 of "Patient-reported outcomes measured with and without dizziness associated with non-specific chronic neck pain: implications for primary care (v0.2)"

2019

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The aim of this study was to compare health-related quality of life (HRQoL) and disability and fear of movement in patients with non-specific chronic neck pain (NSCNP) associated with dizziness with respect to patients with isolated NSCNP in primary care settings. Methods: A cross-sectional study was carried out in a primary care center. A total of 120 patients were divided into two groups and analyzed in this study. One group of patients reported dizziness combined with NSCNP (n=60), and the other reported no dizziness with their NSCNP (n=60). Patient-reported outcome measurements were HRQoL (primary outcome) and disability and kinesiophobia (secondary outcomes) assessed by the EuroQoL Five Dimensions and Five Levels (EQ-5D-5L), neck disability index (NDI) and Tampa Scale of Kinesiophobia (TSK-11), respectively. Results: Statistically significant differences (P < 0.05) for a 95% confidence interval (CI) with a large effect size (Cohen d) were found between both groups with greater values of disability (mean difference = 6.30 points; 95% CI = 3.84-8.75; d = 0.94) and kinesiophobia (mean difference = 8.36 points; 95% CI = 6.07-10.65; d = 1.33), and an impairment of HRQoL (mean difference = 16.16 points; 95% CI = 11.09-21.23; d = 1.16), for patients with NSCNP associated with dizziness with respect to patients with dizziness associated with non-specific chronic neck pain: implications for primary care Running title: Dizziness & neck pain primary care ABSTRACT Background: The aim of this study was to compare health-related quality of life (HRQoL) and disability and fear of movement in patients with non-specific chronic neck pain (NSCNP) associated with dizziness with respect to patients with isolated NSCNP in primary care settings. Methods: A cross-sectional study was carried out in a primary care center. A total of 120 patients were divided into two groups and analyzed in this study. One group of patients reported dizziness combined with NSCNP (n=60), and the other reported no dizziness with their NSCNP (n=60). Patient-reported outcome measurements were HRQoL (primary outcome) and disability and kinesiophobia (secondary outcomes) assessed by the EuroQoL Five Dimensions and Five Levels (EQ-5D-5L), neck disability index (NDI) and Tampa Scale of Kinesiophobia (TSK-11), respectively. Results: Statistically significant differences (P < 0.05) for a 95% confidence interval (CI) with a large effect size (Cohen d) were found between both groups with greater values of disability (mean difference = 6.30 points; 95% CI = 3.84-8.75; d = 0.94) and kinesiophobia (mean difference = 8.36 points; 95% CI = 6.07-10.65; d = 1.33), and an impairment of HRQoL (mean difference = 16.16 points; 95% CI = 11.09-21.23; d = 1.16), for patients with NSCNP associated with dizziness with respect to patients with isolated NSCNP.

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Fractional Edgeworth expansion: Corrections to the Gaussian-Lévy central-limit theorem

Cited by 9 publications

References 38 publications

Which Seems to Be Worst? Pain Severity and Quality of Life between Patients with Lateral Hip Pain and Low Back Pain

Which Seems to Be Worst? Pain Severity and Quality of Life between Patients with Lateral Hip Pain and Low Back Pain

Complementary Densities of Lévy Walks: Typical and Rare Fluctuations

Peer Review #2 of "Patient-reported outcomes measured with and without dizziness associated with non-specific chronic neck pain: implications for primary care (v0.2)"

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