Cumulative Distribution Function Values Research Articles

Spatial pilot reassignment algorithm for channel estimation stage of cell-free multi-ARS communication systems

In this paper, we investigate the user throughputs of a Cell-Free (CF) system with multiple aerial relay stations (ARSs), where each ARS is defined as an unmanned aerial vehicle (UAV)-mounted relay station. The system operates under a decode-and-forward (DF) protocol and facilitates connectivity between a terrestrial base station (TBS) and terrestrial users. ARSs are equipped with multiple antennas and simultaneously serve users that are outfitted with single antennas and distributed in a specific area. Additionally, a small-cell (SC) system based on the CF structure, where each ARS serves one user with the best channel conditions, is also considered. We analyze system communication in two stages, including user-ARS links and ARS-TBS links, and then we derive expressions for the data rate of users and ARSs. Moreover, we propose the spatial pilot reassignment (SPR) algorithm to optimize pilot assignment, enhancing channel estimation over random pilot assignment methods. The user throughput is evaluated by altering several system parameters, including the with/without data power control, the number of users, the number of ARSs, and the time interval allocated for channel estimation. The results show that the SPR algorithm improves throughput by about 10% compared to the random pilot assignment method at a 90%-likely user throughput, which is equal to a cumulative distribution function value of 0.1.

A vine-copulas based multi-sensor fusion structural damage monitoring method and its application in dam engineering

As a civil engineer that is susceptible to the mechanism of slow and continuous deterioration, the dam must detect damage according to the static data of the arranged sensors, which is an important issue in structural health monitoring. Due to the characteristics of huge solid structures, damage with a slight degree and small range usually does not cause significant changes in the monitoring data of a single sensor. Therefore, it is difficult to effectively detect local damage by traditional monitoring methods that establish operating warning values for a single sensor. Currently, there have been some approaches to fuse sensor information that consider correlations between multiple sensors as well as the overall operational behavior of the dam. However, their objectives are focused on improving the accuracy of response variable prediction models without addressing the local damage identification aspect. In this study, we apply the Vine-Copula model for the first time in a multi-sensor information fusion dam damage detection method based on static monitoring data. In this way, it improves the sensitivity of local damage identification for huge solid structures. A prediction model is fitted with the measuring data of each sensor to obtain the residual series. Then the joint probability distribution of the multidimensional residuals is acquired by constructing the Vine-Copula model. Finally, the joint cumulative distribution function value is used as an alarm limit to determine whether the structure has an abnormal damage condition. The effectiveness and accuracy of the proposed method were demonstrated in both a numerical arch dam simulating local damage and an actual rockfill dam engineering with cracks at the crest.

Dispersion network-transition entropy: A metric for characterizing the complexity of nonlinear signals.

Extracting meaningful information from signals has always been a challenge. Due to the influence of environmental noise, collected signals often exhibit nonlinear characteristics, rendering traditional metrics inadequate in capturing the dynamic properties and complex structures of signals. To address this challenge, this study proposes an innovative metric for quantifying signal complexity-dispersion network-transition entropy (DNTE), which integrates the concepts of complex networks and information entropy. Specifically, we assign single cumulative distribution function values to network nodes and utilize Markov chains to represent links, transforming nonlinear signals into weighted directed complex networks. Subsequently, we assess the importance of network nodes and links, and employ the mathematical expression of information entropy to calculate the DNTE value, quantifying the complexity of the original signal. Next, through extensive experiments on simulated chaotic models and real underwater acoustic signals, we confirm the outstanding performance of DNTE. The results indicate that, compared to Lempel-Ziv complexity, permutation entropy, and dispersion entropy, DNTE not only more accurately reflects changes in signal complexity but also exhibits higher computational efficiency. Importantly, DNTE demonstrates optimal performance in distinguishing different categories of chaotic models, ships, and modulation signals, showcasing its significant potential in extracting effective information from signals.

Estimating the proportions and latencies of reaction time outliers: A pooling method and case study of lexical decision tasks

A methodological problem in most reaction time (RT) studies is that some measured RTs may be outliers—that is, they may be very fast or very slow for reasons unconnected to the task-related processing of interest. Numerous ad hoc methods have been suggested to discriminate between such outliers and the valid RTs of interest, but it is extremely difficult to determine how well these methods work in practice because virtually nothing is known about the actual characteristics of outliers in real RT datasets. This article proposes a new method of pooling cumulative distribution function values for examining empirical RT distributions to assess both the proportions of outliers and their latencies relative to those of the valid RTs. As the method is developed, its strengths and weaknesses are examined using simulations based on previously suggested ad hoc models for RT outliers with particular assumed proportions and distributions of valid RTs and outliers. The method is then applied to several large RT datasets from lexical decision tasks, and the results provide the first empirically based description of outlier RTs. For these datasets, fewer than 1% of the RTs seem to be outliers, and the median outlier latency appears to be approximately 4–6 standard deviations of RT above the mean of the valid RT distribution.

Using Simpson’s Rule to Evaluate the Normal Cumulative Distribution Function in an Algorithmic Option Pricing Problem

Algorithmic problems are frequently used to help ensure academic honesty during assessments in quantitative courses, asthey allow instructors to easily generate multiple versions of a test, quiz, or assignment with questions that are similar but whoseinput variables and correct answers differ. In general, instructors who create an algorithmic problem must program its solutionby entering an algebraic expression using the input variables. While this is usually straightforward enough, it can be problematicwhen the solution requires a more advanced function that has no algebraic representation. One such challenge occurs withfinancial option pricing problems based on the Black-Scholes model, which relies on the normal cumulative distribution function(CDF). Although students can easily obtain normal CDF values from a calculator or spreadsheet function, no such function isavailable within testing software, presenting an obstacle for instructors attempting to author algorithmic problems on optionpricing. I demonstrate how to overcome this difficulty by using Simpson’s Rule to numerically integrate the underlying normalprobability density function, thereby generating a highly accurate approximation of the CDF that can be programmed into thesoftware and used in the Black-Scholes formula.

Estimating flood catastrophe bond prices using approximation method of the loss aggregate distribution: Evidence from Indonesia

Losses experienced by the Indonesian government due to floods are predicted. It is because of the significance of population growth, closure of water catchment areas, and climate change in many regions in Indonesia. The government has tried to reduce the risk but faces insufficient funds. Therefore, new innovative funding sources are essential to overcome these limitations. One way to obtain it is through issuing Flood Catastrophe Bonds (FCB). Unfortunately, Indonesia has had no FCB price estimate until now. On the basis of this problem, this study aims to estimate the FCB price in Indonesia. The primary method used is the approximation method of the aggregate loss distribution. This method can compute the aggregate flood loss cumulative distribution function value faster. The FCB fair price estimation results are cheap because the risk of the instrument is significant. This significant risk is also proportional to the large return. Finally, further analysis shows that in Indonesia, the attachment point of the FCB has a relationship that is in line with the price, while the term of FCB does not. This research is expected to assist the Indonesian government in determining the fair price of FCB in Indonesia. This research can assist the investors in choosing FCB based on expected return, attachment point, and the term they want.

Very Short-Term Photoplethysmography-Based Heart Rate Variability for Continuous Autoregulation Assessment

Background: Heart rate variability (HRV) has been widely applied for disease diagnosis. However, the 5 min signal length for HRV analysis is needed. Method: A signal processing procedure for very short-term photoplethysmography (PPG) signal for fever detection and autoregulation assessment was proposed. The Time-Shift Multiscale Entropy Analysis (TSME) was applied to instantaneous pulse rate time series (iPR) and normalized by the cumulative distribution function (CDF) of all scales to calculate novel indices. A total of 33 subjects were recruited for the study. Fifteen participants whose body temperatures were higher than 37.9 °C were served as the fever group. Others were served as the non-fever group. The total 15 s PPG signal with 200 sampling rates was used for iPR calculation. Result: The CDF value of entropy on the scale k = 19 (CDF(E(k = 19))) of iPR had the lowest p-value calculated by the Weltch t-test between two groups (p < 0.001). The Spearman correlation r between CDF(E(k = 19)) and body temperature is −0.757, 0.287, and −0.830 in all subjects, the non-fever group and the Fever group, respectively. The area under the curve, calculated from the receiver operating characteristic of CDF(E(k = 19)) of iPR is 0.915. Conclusion: The entropy of iPR is useful for detecting fever. Moreover, a short-term PPG signal is suitable to develop real-time applications, and multiscale entropy provides different scales of information for daily healthcare.

A new early warning method for dam displacement behavior based on non-normal distribution function

Traditional methods for early warning of dam displacements usually assume that residual displacements follow a normal distribution. This assumption deviates from the reality, thereby affecting the reliability of early warning results and leading to misjudgments of dam displacement behavior. To solve this problem, this study proposed an early warning method using a non-normal distribution function. A new early warning index was developed using cumulative distribution function (CDF) values. The method of kernel density estimation was used to calculate the CDF values of residual displacements at a single point. The copula function was used to compute the CDF values of residual displacements at multiple points. Numerical results showed that, with residual displacements in a non-normal distribution, the early warning method proposed in this study accurately reflected the dam displacement behavior and effectively reduced the frequency of false alarms. This method is expected to aid in the safe operation of dams.

PAPR-Degraded Secure OFDM-WDM-PON Based on Chaotic Set-Partitioned SLM

This letter proposes and experimentally demonstrates an orthogonal frequency division multiplexing wavelength division multiplexing passive optical network (OFDM-WDM-PON) system based on novel chaotic set-partitioned selective mapping (SP-SLM) scheme. With the implementation of a three-dimensional chaotic system, peak-to-average power ratio (PAPR) reduction and chaotic encryption are simultaneously realized on the process of OFDM signal modulation, so as to enhance the system performance in the presence of PAPR, bit error rate (BER), fiber nonlinear tolerance and security. The experimental results show that, when compared with original OFDM signal, the OFDM signal with SP-SLM can achieve 4 dB PAPR reduction at the complementary cumulative distribution function value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{-4}$ </tex-math></inline-formula> , as well as a 1.1 dB gain in receiver sensitivity at a BER of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{-3}$ </tex-math></inline-formula> . For fiber nonlinear tolerance, the optimal launch fiber power of OFDM signal with SP-SLM is 10 dBm, which is better than 9 dBm of original OFDM signal under the same received optical power of −16 dBm. Furthermore, the key space of the proposed scheme can reach up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{98}$ </tex-math></inline-formula> , which is large enough to effectively protect against illegal attackers.

A scaling approach to size effect modeling of Jc CDF for 20MnMoNi55 reactor steel in transition temperature region

Ever since the 1980s there is a sustained interest in the size effect, as one of the most pronounced consequences of fracture mechanics. In the present study, the investigation of the size effect is focused on estimation of the Weibull cumulative distribution function (CDF) of the critical value of the J-integral (Jc) in the transition temperature region under constraint of a small statistical sample size. Specifically, the Jc experimental data correspond to the C(T) specimen testing of the reactor pressure-vessel steel 20MnMoNi55 at only two geometrically-similar sizes. Thus, a simple approximate scaling algorithm has been developed to tackle the effect of the C(T) specimen size on the Jc CDF under these circumstances. Due to the specific form of the two-parameter Weibull CDF, F(Jc|β,η), the scaling procedure is applied according to a two-step scheme. First, the Jc-scaling is performed to ensure the approximate overlap of the points that correspond to the CDF value F(Jc = η) = 1 − 1/e ≈ 0.632 for different C(T) specimen widths (W), which assumes η·Wκ = const. Second, the F-scaling is performed to ensure the equality of the slopes of the CDF in the scaled (F·Wξ vs. Jc·Wκ) space. The objective of the sketched approach is to obtain a size-dependent Jc CDF that encapsulates a reasonably conservative data extrapolation.

Character of images development on Gaussian copula model using distribution of cumulative distribution function

This paper is a preliminary study that aims to build the character of color image object through the Gaussian copula model. The development of the Gaussian copula model is carried out with the distribution of Cumulative Distribution Function (CDF) of the pixels as input. In contrast to other studies that use image pixel values. The random variables used are the CDF value at the point of differentiation determined by the Kulback-Leibler Divergence (KLD). The case discussed in this paper is the image modeling of red apples and green apples. The model is built on each Red, Green, and Blue (RGB) image with three distinguishing points. The result obtained is a Gaussian copula model with different parameters for red apples and green apples. The character of joint distribution is also different. The joint distribution value of green apples is greater than that of red apples in R and G images. The difference in the models obtained shows that the character of this image is different. Future research will use the acquired models to identify new images, whether they are recognized as red and green apples or not. Further development in the field of healthy vision. This model can be used to identify fruit images in an application.

Degradation assessment of in‐service aerial bundled cables in coastal areas leading to prognosis using infrared thermography

Of late, cross-linked polyethylene insulated aerial bundled cables have replaced conventional copper conductors being resistant to electricity pilferage, offer lower maintenance costs and reduced power losses. However, in coastal areas, aerial bundled cables experience frequent insulation breakdown causing sudden cable failures leading to unexpected power shutdowns. Condition monitoring, employing sophisticated diagnostic techniques, has thus become a major requirement of the energy sector. The reported research work utilizes infrared thermography as one such candidate NDT technique. A novel framework is proposed to investigate the progressive shift in the statistical parameters of the temperature distribution in aerial bundled cables’ insulation, as it degrades over time. The cumulative distribution function of pixel intensity data from a healthy/ operational aerial bundled cable is first compared with a reported failed aerial bundled cable. A prominent difference in 0.9 cumulative distribution function values is observed in the temperature distributions. Therefore, 0.9 cumulative distribution function values are used for degradation quantification with respect to ageing. Degradation rates are then computed using periodically acquired thermographic data from operational aerial bundled cables, installed at two different locations in a coastal region, each subjected to different marine climate. The proposed technique proved effective in degradation rate assessment of insulation of operational aerial bundled cables. Consequently, the results achieved can also be utilized for remaining useful life prediction of these cables.

CD-vine model for capturing complex dependence

ABSTRACT Copula based finite mixture models allow us to capture the dependence between random variables more flexibly. Although bivariate case of finite mixture models has been commonly studied, limited efforts have been spent on finite mixture of vines. Instead of using classical mixture models, it is possible to incorporate C-vines into the D-vine model (CD-vine) to understand both the dependence among the variables over different time points. The aim of this study is to create a CD-vine mixture model expressing the dependencies between variables in temporal order. To achieve this, cumulative distribution function values generated within the time components are tied together with D-vine probabilistically. With this approach, dependence structure between variables at each time point is explained by C-vine and the dependence among the time points is captured by the D-vine model. The performance of the proposed CD-vine model is validated using simulated data and applied on four stock market indices.

A Bayesian machine learning approach for online detection of railway wheel defects using track-side monitoring

Wheel condition assessment is of great significance to ensure the operation safety of trains and metro systems. This study is intended to develop a Bayesian probabilistic method for online and quantitative assessment of railway wheel conditions using track-side strain-monitoring data. The proposed method is a fully data-driven, nonparametric approach without the need of a physical model. To enable defect identification using only response measurement, the measured dynamic strain responses of rail tracks during the passage of trains are processed to elicit the normalized cumulative distribution function values representative of the effect of individual wheels, which in conjunction with the frequency points are used to formulate a probabilistic reference model in terms of sparse Bayesian learning. Through cleverly realizing sparsity by introducing hyper-parameters and their priors, the sparse Bayesian learning makes the resulting model to exempt from overfitting and generalize well on unseen data. Only the monitoring data in healthy state are needed in formulating the reference model. A novel Bayesian null hypothesis significance testing in terms of scale-invariant intrinsic Bayes factor, which does not suffer from the Jeffreys–Lindley paradox, is then pursued in the presence of new monitoring data collected from possibly defective wheel(s) to detect wheel defects and quantitatively assess wheel condition. The proposed method in fully Bayesian inference framework is verified by utilizing the real-world monitoring data acquired by a distributed fiber Bragg grating–based track-side monitoring system and comparing with the offline inspection results.

A probability density function generator based on neural networks

In order to generate a probability density function (PDF) for fitting the probability distributions of practical data, this study proposes a deep learning method which consists of two stages: (1) a training stage for estimating the cumulative distribution function (CDF) and (2) a performing stage for predicting the corresponding PDF. The CDFs of common probability distributions can be utilised as activation functions in the hidden layers of the proposed deep learning model for learning actual cumulative probabilities, and the differential equation of the trained deep learning model can be used to estimate the PDF. Numerical experiments with single and mixed distributions are conducted to evaluate the performance of the proposed method. The experimental results show that the values of both CDF and PDF can be precisely estimated by the proposed method.

Sub-Band Pre-Distortion for PAPR Reduction in Spectral Efficient 5G Mobile Fronthaul

We propose a pre-distortion scheme in transmitter DSP to reduce the peak-to-average power ratio (PAPR) in multi-intermediate-frequency (IF)-over-fiber mobile fronthaul (MFH). In optical spectral efficient MFH, multiple modulated sub-bands are transmitted with different IFs serving multi-in multi-out and carrier aggregation in 5G. By applying phase pre-distortion on sub-bands in the transmitter DSP, we reduce the PAPR by more than 2.2 dB with 1% complementary cumulative distribution function value in MFH for 5G mobile networks and significantly increase the transmitted signal power and quality without modifying the system linearity and resolution. The proposed scheme generates small latency. It is DSP efficient and compatible with current mobile devices, without additional noise. With 32 sub-bands served, we demonstrated a 2-dB sensitivity improvement experimentally by applying the proposed scheme.

Cooperative Diversity Selection Protocol Using Pareto Method with Multi Objective Criterion in Wireless Ad Hoc Networks

In cooperative diversity of ad hoc networks, the selection of the path pair becomes very important to achieve optimum performance. In this paper, it was created the cooperative diversity protocol by using Pareto method for multi objective criteria problems namely the signal to noise ratio (SNR) and load variance. Pareto method was used to find a nondominated solution by way of Continuously Updated. The non-dominated solution was chosen based on the smallest euclidean distance. The advantage of this protocol is to provide fair and the best path pairs of cooperative diversity. From the simulation results, it was obtained the path pairs for cooperative diversity is path S-11-D and S-28-D selected by the smallest value of euclidean distance that is 0.108 and 0.379. Furthermore, the reliability of protocol with Pareto method was compared with the scalarization method in the form of value of cumulative distribution function (CDF).

Fast Local Histogram Specification

Local histogram specification (LHS) is a useful technique for image processing. However, LHS faces a critical computational challenge when it is applied to high-resolution high-precision images. The calculation of the values in the cumulative distribution function (CDF) and the mapped value for the central pixel in each sliding window is time consuming with the computational complexity $O(s+L)$ of the state-of-the-art techniques, where $s$ is the side length of the square window and $L$ is the number of gray levels. In this paper, we propose a fast algorithm for LHS, called fast local histogram specification (FLHS). FLHS reduces the complexity of calculating the CDF value for the central pixel in each sliding window to $O(s+\sqrt {L})$ , and the time complexity for the mapping procedure in each window to $O(\log L)$ . This results in the overall time complexity of LHS reduced from $O(s+L)$ to $O(s+\sqrt {L})$ in each sliding window. Theoretical analysis shows that the newly developed algorithm is efficient. Experimental results on the 8-bit and high-resolution high-precision (16-bit) images demonstrate the efficiency of our proposed algorithm.

Compounding: an R package for computing continuous distributions obtained by compounding a continuous and a discrete distribution

In this manuscript we introduce R package Compounding for dealing with continuous distributions obtained by compounding continuous distributions with discrete distributions. We demonstrate its use by computing values of cumulative distribution function, probability density function, quantile function and hazard rate function, generating random samples from a population with compounding distribution, and computing mean, variance, skewness and kurtosis of a random variable with a compounding distribution. We consider 24 discrete distributions which can be compounded with any continuous distribution implemented in R.

Subset simulation-based method for cumulative distribution function sensitivity of output response in random environment

To measure effects of the distribution parameters of input variables on the output response of engineering structures, the analysis methods are investigated to solve the sensitivity of the cumulative distribution function of the output response with respect to the input parameters. For a linear input–output response model with independently normal input variables, the properties of the cumulative distribution function sensitivity are analytically derived. For a complicated input–output response model, a novel subset simulation-based method is presented to solve the response cumulative distribution function sensitivity. By using the stratified subset Markov Chain simulation in the subset simulation-based method, the response cumulative distribution function sensitivity can be adaptively obtained at the threshold of each subset. The sensitivity with larger cumulative distribution function value can be treated as the byproduct of those with the smaller ones in the presented subset simulation-based method, thus greatly reducing the computational cost. Several engineering examples are analyzed by the subset simulation-based method to get the response cumulative distribution function sensitivities, and the comparisons in the example results show that the presented subset simulation-based method is more efficient than Monte Carlo simulation with acceptable precision.