On preserving statistical characteristics of accelerometry data using their empirical cumulative distribution

2013 ◽  
Author(s):  
Nils Y. Hammerla ◽  
Reuben Kirkham ◽  
Peter Andras ◽  
Thomas Ploetz
Keyword(s):  
Cumulative Distribution ◽  
Statistical Characteristics

scholarly journals Statistical Properties of SNR for Compressed Measurements

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Yulong Gao ◽  
Yanping Chen ◽  
Linxiao Su
Keyword(s):  
Numerical Simulation ◽  
Signal Processing ◽  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Statistical Properties ◽  
Cumulative Distribution ◽  
Statistical Characteristics ◽  
Communication Signal ◽  
The Mean ◽  
Simulation Results

Some basic statistical properties of the compressed measurements are investigated. It is well known that the statistical properties are a foundation for analyzing the performance of signal detection and the applications of compressed sensing in communication signal processing. Firstly, we discuss the statistical properties of the compressed signal, the compressed noise, and their corresponding energy. And then, the statistical characteristics of SNR of the compressed measurements are calculated, including the mean and the variance. Finally, probability density function and cumulative distribution function of SNR are derived for the cases of the Gamma distribution and the Gaussian distribution. Numerical simulation results demonstrate the correctness of the theoretical analysis.

Statistical Characteristics of Fatigue Failure of Copper Thin Films

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Jae-Won Jang ◽  
Yun Hwangbo ◽  
Jae-Hyun Kim ◽  
Hak-Joo Lee ◽  
Alexander E. Mag-isa ◽  
...  
Keyword(s):  
Fatigue Life ◽  
Probability Distribution ◽  
Probability Distributions ◽  
Copper Film ◽  
Deformation Mode ◽  
Cumulative Distribution ◽  
Statistical Prediction ◽  
Statistical Characteristics ◽  
Estimation Methods ◽  
Four Levels

Tension–tension fatigue tests were conducted on an electrodeposited copper film with a thickness of 12 μm under four levels of maximum stress and two levels of mean stress. Statistical characteristics of the measured fatigue lives were analyzed using three estimation methods for cumulative distribution function and five probability distributions in order to identify the dominant probability distribution for the fatigue life of copper film. It was found that while the 3-parameter Weibull distribution provided the best fit for the measured data in most cases, the other distributions also provide a similar coefficient of correlation for the fit. The absence of the dominant probability distribution was discussed with considerations of the deformation mode and the scanning electron microscope (SEM) measurements of fatigue-fractured surfaces. Based on the statistical analysis, the probabilistic stress-life (PSN) curves were obtained for statistical prediction of fatigue life of the copper film in the intermediate life regime.

scholarly journals Vulnerability Analysis to Drought Based on Remote Sensing Indexes

2020 ◽  
Vol 17 (20) ◽  
pp. 7660
Author(s):  
Huicong Jia ◽  
Fang Chen ◽  
Jing Zhang ◽  
Enyu Du
Keyword(s):  
Growth Rate ◽  
Vegetation Index ◽  
Estimation Method ◽  
Cumulative Distribution ◽  
Statistical Characteristics ◽  
Cumulative Probability ◽  
Drought Risk ◽  
Variance Ratio ◽  
Vulnerability Curve ◽  
Disaster Losses

A vulnerability curve is an important tool for the rapid assessment of drought losses, and it can provide a scientific basis for drought risk prevention and post-disaster relief. Those populations with difficulty in accessing drinking water because of drought (hereon “drought at risk populations”, abbreviated as DRP) were selected as the target of the analysis, which examined factors contributing to their risk status. Here, after the standardization of disaster data from the middle and lower reaches of the Yangtze River in 2013, the parameter estimation method was used to determine the probability distribution of drought perturbations data. The results showed that, at the significant level of α = 0.05, the DRP followed the Weibull distribution, whose parameters were optimal. According to the statistical characteristics of the probability density function and cumulative distribution function, the bulk of the standardized DRP is concentrated in the range of 0 to 0.2, with a cumulative probability of about 75%, of which 17% is the cumulative probability from 0.2 to 0.4, and that greater than 0.4 amounts to only 8%. From the perspective of the vulnerability curve, when the variance ratio of the normalized vegetation index (NDVI) is between 0.65 and 0.85, the DRP will increase at a faster rate; when it is greater than 0.85, the growth rate of DRP will be relatively slow, and the disaster losses will stabilize. When the variance ratio of the enhanced vegetation index (EVI) is between 0.5 and 0.85, the growth rate of DRP accelerates, but when it is greater than 0.85, the disaster losses tend to stabilize. By comparing the coefficient of determination (R2) values fitted for the vulnerability curve, in the same situation, EVI is more suitable to indicate drought vulnerability than NDVI for estimating the DRP.

scholarly journals An Extended Pranav Distribution

2019 ◽  
pp. 1-15
Author(s):  
O. R. Uwaeme ◽  
N. P. Akpan ◽  
U. C. Orumie
Keyword(s):  
Goodness Of Fit ◽  
Real Life ◽  
Reliability Function ◽  
Moment Generating Function ◽  
Cumulative Distribution ◽  
Maximum Likelihood Estimates ◽  
Statistical Characteristics ◽  
Data Sets ◽  
Rate Functions ◽  
New Distribution

In this study, we proposed a generalization of the Pranav distribution by Shukla (2018). This new distribution called an extended Pranav distribution is obtained using the exponentiation method. The statistical characteristics of this new distribution such as the moments, moment generating function, reliability function, hazard function, Rényi entropy and order statistics are derived. The graphical illustrations of the shapes of the probability density function, the cumulative distribution function, and hazard rate functions are provided. The maximum likelihood estimates of the parameters were obtained and finally, we examine the performance of this new distribution using some real-life data sets to show its flexibility and better goodness of fit as compared with other distributions.

scholarly journals A modified truncated distribution for modeling the heavy tail, engineering and environmental sciences data

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0249001
Author(s):  
Ahtasham Gul ◽  
Muhammad Mohsin ◽  
Muhammad Adil ◽  
Mansoor Ali
Keyword(s):  
Hazard Function ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Cumulative Distribution ◽  
Statistical Characteristics ◽  
Model Parameters ◽  
Truncated Distribution ◽  
Unknown Parameters ◽  
Proposed Model

Truncated models are imperative to efficiently analyze the finite data that we observe in almost all the real life situations. In this paper, a new truncated distribution having four parameters named Weibull-Truncated Exponential Distribution (W-TEXPD) is developed. The proposed model can be used as an alternative to the Exponential, standard Weibull and shifted Gamma-Weibull and three parameter Weibull distributions. The statistical characteristics including cumulative distribution function, hazard function, cumulative hazard function, central moments, skewness, kurtosis, percentile and entropy of the proposed model are derived. The maximum likelihood estimation method is employed to evaluate the unknown parameters of the W-TEXPD. A simulation study is also carried out to assess the performance of the model parameters. The proposed probability distribution is fitted on five data sets from different fields to demonstrate its vast application. A comparison of the proposed model with some extant models is given to justify the performance of the W-TEXPD.

Exploring the uncertainty of Weather Generators’ extreme estimates associated with the length of the input data series

2021 ◽  
Author(s):  
Carles Beneyto ◽  
José Ángel Aranda ◽  
Félix Francés
Keyword(s):  
Distribution Function ◽  
Input Data ◽  
Climate Scenario ◽  
Cumulative Distribution ◽  
Statistical Characteristics ◽  
Weather Data ◽  
Data Series ◽  
Sample Length ◽  
Weather Generators ◽  
Quantile Estimates

<p>Stochastic Weather Generators (WG) have been extensively used in recent years for hydrologic modeling, among others. Compared to traditional approaches, the main advantage of using WGs is that they can produce synthetic continuous time series of weather data of unlimited length preserving their spatiotemporal distribution. Synthetic simulations are based on the statistical characteristics of the observed weather, thus, relying upon the length and spatial distribution of the input data series. In most cases, and especially in arid/semiarid regions, these are scarce, which makes it difficult for WGs to obtain reliable quantile estimates, particularly those associated with low-frequency events. The present study aims to explore the importance of the input weather data length in the performance of WGs, focusing on the adequate estimation of the higher quantiles, and quantifying their uncertainty.</p><p>An experimental case study consisting of nine rain gauges from the Spain02-v5 network in a 0.11º resolution covering an approximate area of 180 km<sup>2</sup> was implemented. The WG used for the experiment was GWEX, which includes a three-parameter (σ, κ, and ξ) cumulative distribution function (E-GPD) to model de precipitation amounts, being the shape parameter ξ the one directly governing the upper tail of the distribution function. A fictitious climate scenario of 15,000 was simulated fixing the ξ value to 0.11.  From this scenario, 50 realizations of 5,000 years with a different sample length (i.e. 30, 60, 90, 120, 150, 200, 300 years) were simulated for four different particular cases: (1) leaving the ξ value as default (i.e. 0.05); (2) estimating the ξ value from the observations; (3) calibrating the ξ value with the T = 100 years quantile from the 15,000 years; and (4) fixing the ξ value to the fictitious scenario value. Relative root mean square error (RRMSE) and coefficient of variation (CV) were calculated for each set of realizations and compared with the obtained from the fictitious climate scenario.</p><p>Preliminary results showed a clear reduction in the value of both the CV and the RRMSE with the increase of the sample length for the four particular cases, being this reduction more evident for the higher order quantiles and as we move from particular case (1) to (4). Furthermore, it was observed that there was not any significant improvement in the higher quantile estimates between the 200-yrs and the 300-yrs samples, concluding that there is a sample length threshold from which the estimates do not improve. Finally, even observing a clear improvement in all estimates when increasing the sample length, a systematic underestimation of the higher quantiles in all cases was still observed, which remarks the importance of seeking extra sources of information (e.g. regional max. Pd. studies) for a better parameterization of the WG, especially for arid/semiarid climates.</p>

Influence of Yield Strength Variability over Cross-Section to Steel Beam Load-Carrying Capacity

2005 ◽  
Vol 10 (2) ◽  
pp. 151-160 ◽  
Author(s):  
J. Kala ◽  
Z. Kala
Keyword(s):  
Yield Strength ◽  
Cross Section ◽  
Carrying Capacity ◽  
Bending Moment ◽  
Statistical Characteristics ◽  
Load Carrying Capacity ◽  
Load Carrying ◽  
Strength Variability ◽  
Hot Rolled ◽  
Hot Rolled Steel

Authors of article analysed influence of variability of yield strength over cross-section of hot rolled steel member to its load-carrying capacity. In calculation models, the yield strength is usually taken as constant. But yield strength of a steel hot-rolled beam is generally a random quantity. Not only the whole beam but also its parts have slightly different material characteristics. According to the results of more accurate measurements, the statistical characteristics of the material taken from various cross-section points (e.g. from a web and a flange) are, however, more or less different. This variation is described by one dimensional random field. The load-carrying capacity of the beam IPE300 under bending moment at its ends with the lateral buckling influence included is analysed, nondimensional slenderness according to EC3 is λ¯ = 0.6. For this relatively low slender beam the influence of the yield strength on the load-carrying capacity is large. Also the influence of all the other imperfections as accurately as possible, the load-carrying capacity was determined by geometrically and materially nonlinear solution of very accurate FEM model by the ANSYS programme.

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