Taylor's law, via ratios, for some distributions with infinite mean

2017 ◽  
Vol 54 (3) ◽  
pp. 657-669 ◽  
Author(s):  
Mark Brown ◽  
Joel E. Cohen ◽  
Victor H. de la Peña
Keyword(s):  
Population Density ◽  
Probability Distributions ◽  
Branching Processes ◽  
Population Variance ◽  
Classical Probability ◽  
Birth And Death Processes ◽  
Taylor’S Law ◽  
The Mean ◽  
Fluctuation Scaling ◽  
First Time

Abstract Taylor's law (TL) originated as an empirical pattern in ecology. In many sets of samples of population density, the variance of each sample was approximately proportional to a power of the mean of that sample. In a family of nonnegative random variables, TL asserts that the population variance is proportional to a power of the population mean. TL, sometimes called fluctuation scaling, holds widely in physics, ecology, finance, demography, epidemiology, and other sciences, and characterizes many classical probability distributions and stochastic processes such as branching processes and birth-and-death processes. We demonstrate analytically for the first time that a version of TL holds for a class of distributions with infinite mean. These distributions, a subset of stable laws, and the associated TL differ qualitatively from those of light-tailed distributions. Our results employ and contribute to the methodology of Albrecher and Teugels (2006) and Albrecher et al. (2010). This work opens a new domain of investigation for generalizations of TL.

Neutrosophic Perspective of Neutrosophic Probability Distributions and its Application

2021 ◽  
pp. 96-109
Author(s):  
M. Lathamaheswari ◽  
◽  
◽  
◽  
◽  
...  
Keyword(s):  
Stochastic Process ◽  
Uniform Distribution ◽  
Binomial Distribution ◽  
Probability Distributions ◽  
Statistical Distributions ◽  
Classical Probability ◽  
Numerical Examples ◽  
Limiting Case ◽  
First Time

Neutrosophical probability is concerned with inequitable and defective topics and processes. This is a subset of Neutrosophic measures that includes a prediction of an event (as opposed to indeterminacy) as well as a prediction of some unpredictability. When there is no such thing as a non-stochastic occurrence, the Neutrosophic probability is the probability of determining a stochastic process. It is a generalisation of classical probability, which states that the probability of correctly predicting an occurrence is zero. Until now, neutrosophic probability distributions have been derived directly from conventional statistical distributions, with fewer contributions to the determination of the for statistical distribution. We introduced the Poission distribution as a limiting case of the Binomial distribution for the first time in this study, and we also proposed Neutrosophic Exponential Distribution and Uniform Distribution for the first time. With numerical examples, the validity and soundness of the proposed notions were also tested.

SQUARED COEFFICIENT OF VARIATION OF TAYLOR'S LAW FOR RANDOM ABSOLUTE DIFFERENCES

2017 ◽  
Vol 32 (4) ◽  
pp. 483-494
Author(s):  
Mark Brown ◽  
Joel E. Cohen
Keyword(s):  
Coefficient Of Variation ◽  
Random Variables ◽  
Vector Spaces ◽  
Human Populations ◽  
Population Variance ◽  
Taylor’S Law ◽  
And Migration ◽  
Fluctuation Scaling ◽  
Constant Coefficient Of Variation ◽  
Normed Vector

In a family, parameterized by θ, of non-negative random variables with finite, positive second moment, Taylor's law (TL) asserts that the population variance is proportional to a power of the population mean as θ varies: σ2 (θ) = a[μ(θ)]b, a > 0. TL, sometimes called fluctuation scaling, holds widely in science, probability theory, and stochastic processes. Here we report diverse examples of TL with b = 2 (equivalent to a constant coefficient of variation) arising from a difference of random variables in normed vector spaces of dimension 1 and larger. In these examples, we compute a exactly using, in some cases, a simple, new technique. These examples may prove useful in future models that involve differences of random variables, including models of the spatial distribution and migration of human populations.

scholarly journals Scaling of Measure Fluctuations on a Flapping Flag Device in the Open Channel Around a Cylinder At $Re=10^4$ : Taylor's Law Approach

2021 ◽  
Author(s):  
Samuele De Bartolo ◽  
Massimo De Vittorio ◽  
Antonio Francone ◽  
Francesco Guido ◽  
Elisa LEONE ◽  
...  
Keyword(s):  
Thin Films ◽  
Flow Field ◽  
Open Channel ◽  
Scaling Law ◽  
Time History ◽  
Cylindrical Shape ◽  
Order Analysis ◽  
Taylor’S Law ◽  
Fluctuation Scaling ◽  
First Time

Experimental evidence showed how various complex systems, characterized by a fluctuation scaling, satisfy the well-known Taylor's law. The present work aims to apply for the first time Taylor's law, given its general treatment, for a flow field at $Re$ around $10^4$, since activity of each fluid particle is highly fluctuating, especially in the context of vortex shedding. In addition, the further element of innovation is the use of an innovative thin-films based device consisting of an elastic piezoelectric flapping flag that is proposed as a measuring instrument of the flow field. The oscillations of the flapping flag, due to the vortexes release downstream to an obstacle of cylindrical shape, generate an alternating piezoelectric voltage whose time history is similar to the chaotic components of the fully developed turbulent speed. Preliminary experimental results about the use of thin-films based device in a flume channel are reported together with a second order analysis on the voltage difference and a scaling law of the exponent scale.

scholarly journals Random sampling of skewed distributions implies Taylor’s power law of fluctuation scaling

2015 ◽  
Vol 112 (25) ◽  
pp. 7749-7754 ◽  
Author(s):  
Joel E. Cohen ◽  
Meng Xu
Keyword(s):  
Population Density ◽  
Power Law ◽  
Random Sampling ◽  
Basal Area ◽  
Least Squares Regression ◽  
Skewed Distributions ◽  
Underlying Distribution ◽  
Species Population ◽  
The Mean ◽  
Fluctuation Scaling

Taylor’s law (TL), a widely verified quantitative pattern in ecology and other sciences, describes the variance in a species’ population density (or other nonnegative quantity) as a power-law function of the mean density (or other nonnegative quantity): Approximately, variance = a(mean)b, a > 0. Multiple mechanisms have been proposed to explain and interpret TL. Here, we show analytically that observations randomly sampled in blocks from any skewed frequency distribution with four finite moments give rise to TL. We do not claim this is the only way TL arises. We give approximate formulae for the TL parameters and their uncertainty. In computer simulations and an empirical example using basal area densities of red oak trees from Black Rock Forest, our formulae agree with the estimates obtained by least-squares regression. Our results show that the correlated sampling variation of the mean and variance of skewed distributions is statistically sufficient to explain TL under random sampling, without the intervention of any biological or behavioral mechanisms. This finding connects TL with the underlying distribution of population density (or other nonnegative quantity) and provides a baseline against which more complex mechanisms of TL can be compared.

Asteroid and Comet Impact Speeds upon Mars: Significance for Panspermia and the Supply of Organics

1997 ◽  
Vol 161 ◽  
pp. 197-201 ◽  
Author(s):  
Duncan Steel
Keyword(s):  
Probability Distributions ◽  
Regions Of Interest ◽  
Significant Fraction ◽  
Organic Chemicals ◽  
Impact Speed ◽  
The Mean ◽  
The Impact

AbstractWhilst lithopanspermia depends upon massive impacts occurring at a speed above some limit, the intact delivery of organic chemicals or other volatiles to a planet requires the impact speed to be below some other limit such that a significant fraction of that material escapes destruction. Thus the two opposite ends of the impact speed distributions are the regions of interest in the bioastronomical context, whereas much modelling work on impacts delivers, or makes use of, only the mean speed. Here the probability distributions of impact speeds upon Mars are calculated for (i) the orbital distribution of known asteroids; and (ii) the expected distribution of near-parabolic cometary orbits. It is found that cometary impacts are far more likely to eject rocks from Mars (over 99 percent of the cometary impacts are at speeds above 20 km/sec, but at most 5 percent of the asteroidal impacts); paradoxically, the objects impacting at speeds low enough to make organic/volatile survival possible (the asteroids) are those which are depleted in such species.

RESULTS OF INTRALESIONAL TRIAMCINOLONE ACETONIDE FOR CHALAZION TREATMENT

2011 ◽  
pp. 100-104
Author(s):  
Thi Thu Nguyen ◽  
Viet Hien Vo ◽  
Thi Em Do
Keyword(s):  
Success Rate ◽  
Key Words ◽  
Triamcinolone Acetonide ◽  
Lower Eyelid ◽  
Upper Eyelid ◽  
Interventional Trial ◽  
The Mean ◽  
First Time

The study use intralesional triamcinolone acetonide injection proceduce for chalazion treatment.1. Objectives: To evaluate results of intralesional triamcinolone acetonide injection for chalazion treatment. 2. Method: This noncomparative prospective interventional trial included 72 chalazions of 61 patients. 3. Results: 61 patients (72 chalazions) with 19 males (31.1%) và 42 females (68.9%), the mean age was 24 ± 9,78 years. 31.1% patients was the first time chalazion and 68.9% patients was more than one times chalazion including 78.6% patients was recurrent at the first position and 21.4% patients occur at new position. 72 chalazions with 16 (22.2%) chalazions was treated before and 56 (77.8%) chalazions wasn’t done that. 72 chalazions with 49 chalazions (68.1%) are local in upper eyelid and 23 chalazions (31.9%) are local in lower eyelid. The mean of chalazion diameter is 6.99 ± 3.03mm. Intralesional triamcinolone acetonide is injected to treat 72 chalazions with 16 (22.2%) chalazions are injected through the route of skin and 56 (77.8%) chalazions are injected through the route of conjunctiva. After 2 weeks follow-up, the success rate was 93.1% and 6.9% failed. 4. Conclusion: intralesional triamcinolone acetonide injection for chalazion treatment is really effective. Key words: chalazion, intralesional triamcinolone acetonide.

Synthesis of a silymarin-gold nanoparticle conjugate and analysis of its liver-protecting activity

2021 ◽  
Vol 22 ◽  
Author(s):  
Sergey Staroverov ◽  
Sergey Kozlov ◽  
Alexander Fomin ◽  
Konstantib Gabalov ◽  
Alexey Volkov ◽  
...  
Keyword(s):  
Gold Nanoparticles ◽  
Liver Disease ◽  
Carbon Tetrachloride ◽  
Glutathione Depletion ◽  
Laboratory Animals ◽  
Experimental Hepatitis ◽  
Acute Liver Disease ◽  
The Mean ◽  
Extent Of Damage ◽  
First Time

Background: The liver disease problem prompts investigators to search for new methods of liver treatment. Introduction: Silymarin (Sil) protects the liver by reducing the concentration of free radicals and the extent of damage to the cell membranes. A particularly interesting method to increase the bioavailability of Sil is to use synthesized gold nanoparticles (AuNPs) as reagents. The study considered whether it was possible to use the silymarin-AuNP conjugate as a potential liver-protecting drug. Method: AuNPs were conjugated to Sil and examine the liver-protecting activity of the conjugate. Experimental hepatitis and hepatocyte cytolysis after carbon tetrachloride actionwere used as a model system, and the experiments were conducted on laboratory animals. Result: For the first time, silymarin was conjugated to colloidal gold nanoparticles (AuNPs). Electron microscopy showed that the resultant preparations were monodisperse and that the mean conjugate diameter was 18–30 nm ± 0.5 nm (mean diameter of the native nanoparticles, 15 ± 0.5 nm). In experimental hepatitis in mice, conjugate administration interfered with glutathione depletion in hepatocytes in response to carbon tetrachloride was conducive to an increase in energy metabolism, and stimulated the monocyte–macrophage function of the liver. The results were confirmed by the high respiratory activity of the hepatocytes in cell culture. Conclusion: We conclude that the silymarin-AuNP conjugate holds promise as a liver-protecting agent in acute liver disease caused by carbon tetrachloride poisoning.

scholarly journals Development of Perceptual Inhibition in Adolescents—a Critical Period?

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 457
Author(s):  
Isabel María Introzzi ◽  
María Marta Richard’s ◽  
Yesica Aydmune ◽  
Eliana Vanesa Zamora ◽  
Florencia Stelzer ◽  
...  
Keyword(s):  
Response Time ◽  
Executive Functions ◽  
Critical Period ◽  
Search Task ◽  
Probability Distributions ◽  
Linear Trajectory ◽  
Gaussian Functions ◽  
Mean Response Time ◽  
The Mean ◽  
One Year

Recent studies suggest that the developmental curves in adolescence, related to the development of executive functions, could be fitted to a non-linear trajectory of development with progressions and retrogressions. Therefore, the present study proposes to analyze the pattern of development in Perceptual Inhibition (PI), considering all stages of adolescence (early, middle, and late) in intervals of one year. To this aim, we worked with a sample of 275 participants between 10 and 25 years, who performed a joint visual and search task (to measure PI). We have fitted ex-Gaussian functions to the probability distributions of the mean response time across the sample and performed a covariance analysis (ANCOVA). The results showed that the 10- to 13-year-old groups performed similarly in the task and differ from the 14- to 19-year-old participants. We found significant differences between the older group and all the rest of the groups. We discuss the important changes that can be observed in relation to the nonlinear trajectory of development that would show the PI during adolescence.

scholarly journals Neutrosophic ratio-type estimators for estimating the population mean

2021 ◽  
Author(s):  
Zaigham Tahir ◽  
Hina Khan ◽  
Muhammad Aslam ◽  
Javid Shabbir ◽  
Yasar Mahmood ◽  
...  
Keyword(s):  
Minimum Mean Square Error ◽  
Auxiliary Information ◽  
Population Parameter ◽  
Uncertain Information ◽  
Population Mean ◽  
Classical Statistics ◽  
Neutrosophic Statistics ◽  
The Mean ◽  
Type Data ◽  
First Time

AbstractAll researches, under classical statistics, are based on determinate, crisp data to estimate the mean of the population when auxiliary information is available. Such estimates often are biased. The goal is to find the best estimates for the unknown value of the population mean with minimum mean square error (MSE). The neutrosophic statistics, generalization of classical statistics tackles vague, indeterminate, uncertain information. Thus, for the first time under neutrosophic statistics, to overcome the issues of estimation of the population mean of neutrosophic data, we have developed the neutrosophic ratio-type estimators for estimating the mean of the finite population utilizing auxiliary information. The neutrosophic observation is of the form $${Z}_{N}={Z}_{L}+{Z}_{U}{I}_{N}\, {\rm where}\, {I}_{N}\in \left[{I}_{L}, {I}_{U}\right], {Z}_{N}\in [{Z}_{l}, {Z}_{u}]$$ Z N = Z L + Z U I N where I N ∈ I L , I U , Z N ∈ [ Z l , Z u ] . The proposed estimators are very helpful to compute results when dealing with ambiguous, vague, and neutrosophic-type data. The results of these estimators are not single-valued but provide an interval form in which our population parameter may have more chance to lie. It increases the efficiency of the estimators, since we have an estimated interval that contains the unknown value of the population mean provided a minimum MSE. The efficiency of the proposed neutrosophic ratio-type estimators is also discussed using neutrosophic data of temperature and also by using simulation. A comparison is also conducted to illustrate the usefulness of Neutrosophic Ratio-type estimators over the classical estimators.

scholarly journals P1398 Echocardiographic continuous monitoring of exercise stress test using probe fixation device

2020 ◽  
Vol 21 (Supplement_1) ◽  
Author(s):  
K Wdowiak-Okrojek ◽  
P Wejner-Mik ◽  
Z Bednarkiewicz ◽  
P Lipiec ◽  
J D Kasprzak
Keyword(s):  
Image Quality ◽  
Physical Exercise ◽  
Stress Test ◽  
Exercise Stress Test ◽  
Bicycle Ergometer ◽  
Exercise Stress ◽  
Fixation Device ◽  
The Mean ◽  
First Time

Abstract Background Stress echocardiography (SE) plays an important role among methods of noninvasive diagnosis of ischemic disease. Despite the advantages of physical exercise as the most physiologic stressor, it is difficult (bicycle ergometer) or impossible (treadmill) to obtain and maintain the acoustic window during the exercise. Recently, an innovative probe fixation device was introduced and a research plan was developed to assess the feasibility of external probe fixation during exercise echocardiography on a supine bicycle and upright treadmill exercise for the first time. Methods 37 subjects (36 men, mean age 39 ± 16 years, 21 healthy volunteers, 16 patients with suspected coronary artery disease) were included in this study. This preliminary testing stage included mostly men due to more problematic probe fixation in women. All subjects underwent a submaximal exercise stress test on a treadmill (17/37) or bicycle ergometer (11/37). Both sector and matrix probes were used. We assessed semi-quantitatively the quality of acquired apical views at each stage – the four-point grading system was used (0-no view, 1-suboptimal quality, 2-optimal quality, 3-very good quality), 2-3 sufficient for diagnosis. Results The mean time required for careful positioning of the probe and image optimization was 12 ± 3 min and shortened from 13,7 to 11,1 minutes (mean) in first vs second half of the cohort documenting learning curve. At baseline, 9 patients had at least one apical view of quality precluding reliable analysis. Those patients were excluded from further assessment. During stress, 17 patients maintained the optimal or very good quality of all apical views, whereas in 11 patients the quality significantly decreased during the stress test and required probe repositioning. The mean image quality score at baseline was 2,61 ± 0,48 and 2,25 ± 0,6 after exercise. Expectedly, good image quality was easier to obtain and maintain in the supine position (score 2,74 ± 0,44) points as compared with upright position (score 2,25 ± 0,57). Conclusion This preliminary, unique experience with external probe fixation device indicates that continuous acquisition and monitoring of echocardiographic images is feasible during physical exercise, and for the first time ever - also on the treadmill. This feasibility data stem from almost exclusively male patients and the estimated rate of sufficient image quality throughout the entire test is currently around 60%. We are hoping, that gaining more experience with the product could increase the success rate on exercise tests. Abstract P1398 Figure. Treadmill and ergometer stress test

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