scholarly journals Have You Seen the Standard Deviation?

2019 ◽  
Vol 3 ◽  
pp. 1-10
Author(s):  
Jyotirmoy Sarkar ◽  
Mamunur Rashid
Keyword(s):  
Standard Deviation ◽  
Cumulative Distribution Function ◽  
Geometric Method ◽  
Cumulative Distribution ◽  
Mean Deviation ◽  
Similar Data ◽  
Tabular Data ◽  
Empirical Cumulative Distribution Function ◽  
Quadratic Transformation ◽  
The Mean

Background: Sarkar and Rashid (2016a) introduced a geometric way to visualize the mean based on either the empirical cumulative distribution function of raw data, or the cumulative histogram of tabular data. Objective: Here, we extend the geometric method to visualize measures of spread such as the mean deviation, the root mean squared deviation and the standard deviation of similar data. Materials and Methods: We utilized elementary high school geometric method and the graph of a quadratic transformation. Results: We obtain concrete depictions of various measures of spread. Conclusion: We anticipate such visualizations will help readers understand, distinguish and remember these concepts.

scholarly journals The Probability of a Confidence Interval Based on Minimal Estimates of the Mean and the Standard Deviation

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Louis M. Houston
Keyword(s):  
Computer Simulation ◽  
Distribution Function ◽  
Standard Deviation ◽  
Confidence Interval ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Sample Standard Deviation ◽  
The Mean

Using two measurements, we produce an estimate of the mean and the sample standard deviation. We construct a confidence interval with these parameters and compute the probability of the confidence interval by using the cumulative distribution function and averaging over the parameters. The probability is in the form of an integral that we compare to a computer simulation.

Eye Movements Simultaneously Recorded by Electrooculographic and Photoelectric Methods

1979 ◽  
Vol 48 (2) ◽  
pp. 619-624 ◽  
Author(s):  
Jin Ong ◽  
Gene A. Harman
Keyword(s):  
Eye Movements ◽  
Standard Deviation ◽  
Mean Amplitude ◽  
Mean Deviation ◽  
Deviation Index ◽  
Velocity Peak ◽  
The Mean

Three types of eye movements, saccadic, reading, and pursuit, were recorded from 6 college subjects, two in each by the electrooculographic and photoelectric methods simultaneously. A deviation index (DI), which is the standard deviation divided by the mean, was devised to compare the precision of recording amplitude deflection, and a proportion index (PI), which is M1 divided by M2, was devised to compare the mean amplitude indirectly between these two methods. Results showed that the proportion indexes of three types of eye movements were comparable, and the mean index of 0.54 indicated that the amplification in the electrooculographic method was about half as much as that in the photoelectric. The mean deviation index of 0.132 vs 0.135 was, again, comparable, meaning that these two methods of recording amplitude deflections are of about the same degree of magnitude and precision. Certain qualitative differences regarding the amplitude and velocity peak deflection between these two methods were also noted.

Series expansions for the all-time maximum of α-stable random walks

2016 ◽  
Vol 48 (3) ◽  
pp. 744-767
Author(s):  
Clifford Hurvich ◽  
Josh Reed
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Queueing Theory ◽  
Cumulative Distribution Function ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Series Expansions ◽  
Stable Random Variables ◽  
The Mean ◽  
The Stability

AbstractWe study random walks whose increments are α-stable distributions with shape parameter 1<α<2. Specifically, assuming a mean increment size which is negative, we provide series expansions in terms of the mean increment size for the probability that the all-time maximum of an α-stable random walk is equal to 0 and, in the totally skewed-to-the-left case of skewness parameter β=-1, for the expected value of the all-time maximum of an α-stable random walk. Our series expansions generalize previous results for Gaussian random walks. Key ingredients in our proofs are Spitzer's identity for random walks, the stability property of α-stable random variables, and Zolotarev's integral representation for the cumulative distribution function of an α-stable random variable. We also discuss an application of our results to a problem arising in queueing theory.

scholarly journals Classification and Statistical Trend Analysis in Detecting Glaucomatous Visual Field Progression

2019 ◽  
Vol 2019 ◽  
pp. 1-5
Author(s):  
Cristiana Valente ◽  
Elisa D’Alessandro ◽  
Michele Iester
Keyword(s):  
Statistical Analysis ◽  
Standard Deviation ◽  
Visual Field ◽  
Trend Analysis ◽  
Open Angle Glaucoma ◽  
Mean Deviation ◽  
Threshold Strategy ◽  
Visual Field Progression ◽  
The Mean

Aim. To evaluate the agreement between different methods in detection of glaucomatous visual field progression using two classification-based methods and four statistical approaches based on trend analysis. Methods. This is a retrospective and longitudinal study. Twenty Caucasian patients (mean age 73.8 ± 13.43 years) with open-angle glaucoma were recruited in the study. Each visual field was assessed by Humphrey Field Analyzer, program SITA standard 30-2 or 24-2 (Carl Zeiss Meditec, Inc., Dublin, CA). Full threshold strategy was also accepted for baseline tests. Progression was analyzed by using Hodapp–Parrish–Anderson classification and the Advanced Glaucoma Intervention Study visual field defect score. For the statistical analysis, linear regression (r2) was calculated for mean deviation (MD), pattern standard deviation (PSD), and visual field index (VFI), and when it was significant, each series of visual field was considered progressive. We also used Progressor to look for a significant progression of each visual field series. The agreement between methods, based on statistical analysis and classification, was evaluated using a weighted kappa statistic. Results. Thirty-eight visual field series were analyzed. The mean follow-up time was 6.2 ± 1.53 years (mean ± standard deviation). At baseline, the mean MD was −7.34 ± 7.18 dB; at the end of the follow-up, the mean MD was −9.25 ± 8.65 dB; this difference was statistically significant (p<0.001). The agreement to detect progression was fair between all methods based on statistical analysis and classification except for PSD r2. A substantial agreement (κ = 0.698 ± 0.126) was found between MD r2 and VFI r2. With the use of all the statistical analysis, there was a better time-saving. Conclusions. The best agreement to detect progression was found between MD r2 and VFI r2. VFI r2 showed the best agreement with all the other methods. GPA2 can help ophthalmologists to detect glaucoma progression and to help in treatment decisions. PSD r2 was the worse method to detect progression.

scholarly journals Results of the Verification of the Statistical Distribution Model of Microseismicity Emission Characteristics

2016 ◽  
Vol 61 (3) ◽  
pp. 489-496
Author(s):  
Aleksander Cianciara
Keyword(s):  
Distribution Function ◽  
Weibull Distribution ◽  
Goodness Of Fit ◽  
Cumulative Distribution Function ◽  
Statistical Distribution ◽  
Cumulative Distribution ◽  
Distribution Model ◽  
Emission Characteristics ◽  
Goodness Of Fit Test ◽  
Empirical Cumulative Distribution Function

Abstract The paper presents the results of research aimed at verifying the hypothesis that the Weibull distribution is an appropriate statistical distribution model of microseismicity emission characteristics, namely: energy of phenomena and inter-event time. It is understood that the emission under consideration is induced by the natural rock mass fracturing. Because the recorded emission contain noise, therefore, it is subjected to an appropriate filtering. The study has been conducted using the method of statistical verification of null hypothesis that the Weibull distribution fits the empirical cumulative distribution function. As the model describing the cumulative distribution function is given in an analytical form, its verification may be performed using the Kolmogorov-Smirnov goodness-of-fit test. Interpretations by means of probabilistic methods require specifying the correct model describing the statistical distribution of data. Because in these methods measurement data are not used directly, but their statistical distributions, e.g., in the method based on the hazard analysis, or in that that uses maximum value statistics.

scholarly journals A Simple Method to Retrieve Cloud Properties from Atmospheric Transmittance and Liquid Water Column Measurements

2011 ◽  
Vol 50 (2) ◽  
pp. 283-295 ◽  
Author(s):  
Salvador Matamoros ◽  
Josep-Abel González ◽  
Josep Calbó
Keyword(s):  
Standard Deviation ◽  
Optical Depth ◽  
Liquid Water ◽  
Surface Albedo ◽  
Effective Radius ◽  
Droplet Radius ◽  
Similar Data ◽  
Simple Method ◽  
The Mean ◽  
Atmospheric Transmittance

Abstract A deeper knowledge of the effects and interactions of clouds in the climatic system requires developing both satellite and ground-based methods to assess their optical properties. A simple method based on a parameterized inversion of a radiative transfer model is proposed to estimate the optical depth of thick liquid water clouds from the atmospheric transmittance at 415 nm, solar zenith angle, surface albedo, effective droplet radius, and aerosol load. When concurrent measurements of atmospheric transmittance and liquid water path are available, the effective radius of the droplet size distribution can also be retrieved. The method is compared with a reference algorithm from Min and Harrison, which uses similar data, except aerosol load. When applied to measurements performed at the Southern Great Plains site of the Atmospheric Radiation Measurement Program, the mean bias deviation between the proposed method and the reference method is only −0.08 in units of optical depth, whereas the standard deviation is only 0.46. For the effective droplet radius estimations, the mean bias deviation is −0.13 μm, and the standard deviation is 0.14 μm. Maximum relative deviations are lower than 5% and 8% for cloud optical depth and effective radius, respectively. The effects on these retrievals of the assumed aerosol optical depth and surface albedo are also analyzed.

Imprecise Adequacy Assessment of Generating System Incorporating Wind Power Based on Interval Probability

2013 ◽  
Vol 860-863 ◽  
pp. 2083-2087
Author(s):  
Xian Jun Qi ◽  
Jia Yi Shi ◽  
Xiang Tian Peng
Keyword(s):  
Wind Power ◽  
Output Power ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Empirical Cumulative Distribution Function ◽  
Interval Probability ◽  
Generating Capacity ◽  
Adequacy Assessment ◽  
Generating System

Probability box (P-box) and interval probability (IP) were used to express both variability and imprecision of wind speed and output power of WTGs. The p-box of WTG's output power was constructed by empirical cumulative distribution function and K.S. confidence limits. The discrete IP distribution of WTG's output power was elicited from the p-box. The optimization model of imprecise generating capacity adequacy assessment incorporating wind power was established and solved by genetic algorithm (GA). Case study on RBTSW system shows the rationality of presented method.

Sign in / Sign up

Export Citation Format

Share Document