Quantile Plots Research Articles

Effective sampling for drift mitigation in machine learning using scenario selection: A microgrid case study

Predictive modeling is pervasive across a variety of industries (e.g., driving patterns in insurance, fraud detection in finance, and forecasting in energy). However, the deterioration of prediction accuracy for most machine learning (ML) models due to the drift is inevitable despite having acceptable performance in a test setting. Drift is a natural occurrence as cumulative information changes over time but should be regulated to ensure an ML model’s prediction remains relevant in real-time when decisions are being made. This study proposes a drift mitigation framework (DMF) to obtain an effective sample size in a scalable and unbiased manner for sustainable predictive performance from ML models using microgrids (MGs) as a testbed. Scenario selection was used as an alternative sampling technique to obtain an effective sample from historical data contributing to probability theory. These scenarios were evaluated using a quantile-quantile (Q-Q) plot, Welch’s T-test, and relative entropy measures to ensure the obtained sample effectively captures the general population behavior. The results showed two of the three climate factors used in our experiment formed a nearly straight line on their Q-Q plots, suggesting the effective sample retained comparable statistical properties to theoretical distributions fitted to the original population and complete training data. At an alpha equal to 0.05, a hypothesis test was conducted with the null hypothesis claiming the means of reduced and complete data were statistically equivalent for ambient temperature, solar irradiance, and wind speed. The p-values obtained for each stochastic climate factor were 1.01, 0.296, and 4.13 suggesting insufficient evidence to reject the null hypothesis. Similarly, the resulting population stability index (PSI) values for each stochastic climate factor were 0.175, 0.352, and 0.023 respectively. Hence, there was no significant shift between the population data and the effective sample across each factor.

ARMA model development and analysis for global temperature uncertainty

Temperature uncertainty models for land and sea surfaces can be developed based on statistical methods. In this paper, we developed a novel time-series temperature uncertainty model, which is the autoregressive moving average (ARMA) (1,1) model. The model was developed for an observed annual mean temperature anomaly X(t), which is a combination of a true (latent) global anomaly Y(t) for a year (t) and normal variable w(t). The uncertainty is taken as the variance of w(t), which was divided into land surface temperature (LST) uncertainty, sea surface temperature (SST) uncertainty, and the corresponding source of uncertainty. The ARMA model was analyzed and compared with autoregressive (AR) and autoregressive integrated moving average (ARIMA) for the data obtained from the NASA Goddard Institute for Space Studies Surface Temperature (GISTEMP) Analysis. The statistical analysis of the autocorrelation function (ACF), partial autocorrelation function (PACF), normal quantile–quantile (normal Q-Q) plot, density of the residuals, and variance of normal variable w(t) shows that ARMA (1,1) fits better than AR (1) and ARIMA (1, d, 1) for d = 1, 2.

Investigation of tongue hardness using ultrasound elastography in children during growth period

ABSTRACT Purpose Previous studies, the changes in tongue hardness with growth were scarcely ever described, but tongue pressure and morphology were the focus of them. Given that, we decided to use ultrasound to examine the changes in tongue hardness during growth. Materials and methods 60 paediatric patients (30 boys and 30 girls) aged 6 to 11 years (mean age, 8.5 ± 1.7 years) who visited the Department of Orthodontics, Showa University Dental Hospital were selected for the study. Tongue hardness was measured using real-time ultrasound tissue elastography. The measured values of tongue elasticity were subjected to the Shapiro – Wilk test, and QQ plot for checking the normality. Pearson’s correlation coefficient was used to confirm the significance of the relationship among the three measurements of tongue elasticity, age, sex, height, weight, BMI, body fat, tongue pressure, and hand strength. Results We confirmed that the use of ultrasound SWE and SE are valuable for the measurement of tongue elasticity. A negative correlation between age and tongue elasticity SE (extraoral) (r = −0.26, P < 0.05), body weight and tongue elasticity SE (extraoral) (r = −0.30, P =＜0.05). Conclusion It was suggested that tongue hardness changes with changes with age. The balance between the tongue and perioral muscles is affected with the position of the teeth. Perioral muscle function is closely associated with malocclusion onset, particularly during childhood when maxillofacial growth and development are rapid. Therefore, the use of ultrasonography device can aid in the evaluation of treatments to improve perioral muscle function.

Traffic Characterization Based Stochastic Modelling of Network-on-Chip

The trend towards multi-core and many-core processors has changed the landscape of computers and servers. Now the performance of a microprocessor heavily depends not only on the data path but also on the memory technology and communication technology. On-chip communication networks or Network-on-Chip is a component which facilitates communication between the cores of a microprocessor. In this manuscript we propose an analytical model for the analysis of Network-on-Chip performance based on Jackson queuing networks for applications that exhibit Poisson injection process. The injection process statistics and the traffic profile of PARSEC benchmarks have been characterized. We have shown that injection process of PARSEC benchmarks does not match with the well known probability distributions using Quantile-Quantile plot and Kolmogorov-Smirnov test. For realistic benchmarks that does not follow Poisson injection process we propose <inline-formula><tex-math notation="LaTeX">$G/D/1$</tex-math></inline-formula> queuing model for the NoC router. We have carried out performance analysis using the traffic characterization in conjunction with our analytical model for prediction of performance metrics. The analytical model offers a speed up of around 13 times in comparison with the simulation based performance evaluation. The percentage of error between the analytical model and simulation is less than 6% for most of the benchmarks except Canneal and Ferret. We have also compared our analytical model results with the results of SNIPER simulator.

Standardization and quality control of Doppler and fetal biometric ultrasound measurements in low-income setting.

The aim of this study was to determine the quality of fetal biometry and pulsed-wave Doppler ultrasound measurements in a prospective cohort study in Uganda. This was an ancillary study of the Ending Preventable Stillbirths by Improving Diagnosis of Babies at Risk (EPID) project, in which women enroled in early pregnancy underwent Doppler and fetal biometric assessment at 32-40 weeks of gestation. Sonographers undertook 6 weeks of training followed by onsite refresher training and audit exercises. A total of 125 images for each of the umbilical artery (UA), fetal middle cerebral artery (MCA), left and right uterine arteries (UtA), head circumference (HC), abdominal circumference (AC) and femur length (FL) were selected randomly from the EPID study database and evaluated independently by two experts in a blinded fashion using objective scoring criteria. Inter-rater agreement was assessed using modified Fleiss' kappa for nominal variables and systematic errors were explored using quantile-quantile (Q-Q) plots. For Doppler measurements, 96.8% of the UA images, 84.8% of the MCA images and 93.6% of the right UtA images were classified as of acceptable quality by both reviewers. For fetal biometry, 96.0% of the HC images, 96.0% of the AC images and 88.0% of the FL images were considered acceptable by both reviewers. The kappa values for inter-rater reliability of quality assessment were 0.94 (95% CI, 0.87-0.99) for the UA, 0.71 (95% CI, 0.58-0.82) for the MCA, 0.87 (95% CI, 0.78-0.95) for the right UtA, 0.94 (95% CI, 0.87-0.98) for the HC, 0.93 (95% CI, 0.87-0.98) for the AC and 0.78 (95% CI, 0.66-0.88) for the FL measurements. The Q-Q plots indicated no influence of systematic bias in the measurements. Training local healthcare providers to perform Doppler ultrasound, and implementing quality control systems and audits using objective scoring tools in clinical and research settings, is feasible in low- and middle-income countries. Although we did not assess the impact of in-service retraining offered to practitioners deviating from prescribed standards, such interventions should enhance the quality of ultrasound measurements and should be investigated in future studies. © 2022 The Authors. Ultrasound in Obstetrics & Gynecology published by John Wiley & Sons Ltd on behalf of International Society of Ultrasound in Obstetrics and Gynecology.

The normality assumption on between-study random effects was questionable in a considerable number of Cochrane meta-analyses

BackgroundStudies included in a meta-analysis are often heterogeneous. The traditional random-effects models assume their true effects to follow a normal distribution, while it is unclear if this critical assumption is practical. Violations of this between-study normality assumption could lead to problematic meta-analytical conclusions. We aimed to empirically examine if this assumption is valid in published meta-analyses.MethodsIn this cross-sectional study, we collected meta-analyses available in the Cochrane Library with at least 10 studies and with between-study variance estimates > 0. For each extracted meta-analysis, we performed the Shapiro–Wilk (SW) test to quantitatively assess the between-study normality assumption. For binary outcomes, we assessed between-study normality for odds ratios (ORs), relative risks (RRs), and risk differences (RDs). Subgroup analyses based on sample sizes and event rates were used to rule out the potential confounders. In addition, we obtained the quantile–quantile (Q–Q) plot of study-specific standardized residuals for visually assessing between-study normality.ResultsBased on 4234 eligible meta-analyses with binary outcomes and 3433 with non-binary outcomes, the proportion of meta-analyses that had statistically significant non-normality varied from 15.1 to 26.2%. RDs and non-binary outcomes led to more frequent non-normality issues than ORs and RRs. For binary outcomes, the between-study non-normality was more frequently found in meta-analyses with larger sample sizes and event rates away from 0 and 100%. The agreements of assessing the normality between two independent researchers based on Q–Q plots were fair or moderate.ConclusionsThe between-study normality assumption is commonly violated in Cochrane meta-analyses. This assumption should be routinely assessed when performing a meta-analysis. When it may not hold, alternative meta-analysis methods that do not make this assumption should be considered.

Multivariate GWAS analysis reveals loci associated with liver functions in continental African populations.

Liver disease is any condition that causes liver damage and inflammation and may likely affect the function of the liver. Vital biochemical screening tools that can be used to evaluate the health of the liver and help diagnose, prevent, monitor, and control the development of liver disease are known as liver function tests (LFT). LFTs are performed to estimate the level of liver biomarkers in the blood. Several factors are associated with differences in concentration levels of LFTs in individuals, such as genetic and environmental factors. The aim of our study was to identify genetic loci associated with liver biomarker levels with a shared genetic basis in continental Africans, using a multivariate genome-wide association study (GWAS) approach. We used two distinct African populations, the Ugandan Genome Resource (UGR = 6,407) and South African Zulu cohort (SZC = 2,598). The six LFTs used in our analysis were: aspartate transaminase (AST), alanine transaminase (ALT), alkaline phosphatase (ALP), gamma-glutamyl transferase (GGT), total bilirubin, and albumin. A multivariate GWAS of LFTs was conducted using the exact linear mixed model (mvLMM) approach implemented in GEMMA and the resulting P-values were presented in Manhattan and quantile-quantile (QQ) plots. First, we attempted to replicate the findings of the UGR cohort in SZC. Secondly, given that the genetic architecture of UGR is different from that of SZC, we further undertook similar analysis in the SZC and discussed the results separately. A total of 59 SNPs reached genome-wide significance (P = 5x10-8) in the UGR cohort and with 13 SNPs successfully replicated in SZC. These included a novel lead SNP near the RHPN1 locus (lead SNP rs374279268, P-value = 4.79x10-9, Effect Allele Frequency (EAF) = 0.989) and a lead SNP at the RGS11 locus (lead SNP rs148110594, P-value = 2.34x10-8, EAF = 0.928). 17 SNPs were significant in the SZC, while all the SNPs fall within a signal on chromosome 2, rs1976391 mapped to UGT1A was identified as the lead SNP within this region. Using multivariate GWAS method improves the power to detect novel genotype-phenotype associations for liver functions not found with the standard univariate GWAS in the same dataset.

Linear regression models with autoregressive integrated moving average errors for measurements from real time kinematics-global navigation satellite system during dynamic test

&lt;span lang="EN-US"&gt;The autoregressive integrated moving average (ARIMA) method has been used to model global navigation satellite systems (GNSS) measurement errors. Most ARIMA error models describe time series data of static GNSS receivers. Its application for modeling of GNSS under dynamic tests is not evident. In this paper, we aim to describe real time kinematic-GNSS (RTK-GNSS) errors during dynamic tests using linear regression with ARIMA errors to establish a proof of concept via simulation that measurement errors along a trajectory logged by the RTK-GNSS can be “filtered”, which will result in improved positioning accuracy. Three sets of trajectory data of an RTK-GNSS logged in a multipath location were collected. Preliminary analysis on the data reveals the inability of the RTK-GNSS to achieve fixed integer solution most of the time, along with the presence of correlated noise in the error residuals. The best linear regression models with ARIMA errors for each data set were identified using the Akaike information criterion (AIC). The models were implemented via simulations to predict improved coordinate points. Evaluation on model residuals using autocorrelation, partial correlation, scatter plot, quantile-quantile (QQ) plot and histogram indicated that the models fitted the data well. Mean absolute errors were improved by up to 57.35% using the developed models.&lt;/span&gt;

Visualizing Uncertainty to Promote Clinicians' Understanding of Measurement Error.

Measurement error is an inherent part of any test score. This uncertainty is generally communicated in ways that can be difficult to understand for clinical practitioners. In this empirical study, we evaluate the impact of several communication formats on the interpretation of measurement accuracy and its influence on the decision-making process in clinical practice. We provided 230 clinical practitioners with score reports in five formats: textual, error bar, violin plot, diamond plot, and quantile dot plot. We found that quantile dot plots significantly increased accuracy in the assessment of measurement uncertainty compared with other formats. However, a direct relation between visualization format and decision quality could not be found. Although traditional confidence intervals and error bars were favored by many participants due to their familiarity, responses revealed several misconceptions that make the suitability of these formats for communicating uncertainty questionable. Our results indicate that new visualization formats can successfully reduce errors in interpretation.

Evaluating Sediment Yield Response to Watershed Management Practices (WMP) by Employing the Concept of Sediment Connectivity

Watershed management practices (WMP) are widely used in catchments as a measure to reduce soil erosion and sediment-related problems. We used a paired catchment in the Gonbad region of Hamadan province, Iran, to evaluate sediment yield response to watershed management practices (WMP) by employing the concept of sediment connectivity (SC). To do this, the SC index as a representation of sediment yield was firstly simulated for the control catchment that there is no WMP. In the next step, the SC index was simulated for impacted catchment, including some WMP, i.e., seeding, pit-seeding, and exclosure. After assessing the accuracy of the produced SC maps using filed observations and erosion plots, the SC maps using quantile-quantile plot (Q-Q plot) were compared to achieve the role of WMP in reducing the rate of sediment yield. The Q-Q plot showed that there is a strong similarity between the SC of catchments, it can be concluded that the WMP has no significant impact on the reducing rate of the sediment yield in this study.

Merging dual-polarization X-band radar network intelligence for improved microscale observation of summer rainfall in south Sweden

Compact dual-polarization doppler X-band weather radars (X-WRs) have recently gained attention in Scandinavia for sub-km and minute scale rainfall observations. This study develops a method for merging data from two X-WRs in Dalby and Helsingborg, southern Sweden (operated at five and one elevation angle levels, respectively) to improve the accuracy of rainfall observations. In total, 87 rainfall events from May-September 2021, observed by 38 tipping bucket gauges in the overlapping coverage of the X-WRs, were used for ground truth. The gauges were classified into four zones. An artificial neural network using doppler and dual-polarization variables (ANN) and a regression-based hybrid of RATEs (single-level rainfall products built-in to the X-WRs) based on the Marshall-Palmer equation (RMP) were calibrated for each zone. The calibrated models at 5-min scale significantly outperformed RATEs for all zones verified by Gilbert skill score (GSS), relative bias (rBIAS), mean absolute error (MAE), and Nash-Sutcliffe efficiency (NSE) not using the calibration data. Quantile-quantile plots confirmed a considerable improvement of the statistical distribution of the merged rainfall estimates for Zone I (closest to Dalby), II (mid-way between Dalby and Helsingborg), and IV (similar range as II for Dalby but farthest to Helsingborg) especially using ANN. Zone III (farthest to Dalby and closest to Helsingborg) was problematic for all RATEs, ANN, and RMP. The lowest-level elevation angle for both X-WRs showed the most erroneous RATEs. Consequently, the problems with Zone III can be solved if multiple levels of Helsingborg X-WR at higher levels are available.

Evolution of Statistical Strength during the Contact of Amorphous Polymer Specimens below the Glass Transition Temperature: Influence of Chain Length.

A comprehensive study of the statistical distribution of the auto-adhesion lap-shear strength (σ) of amorphous polymer-polymer interfaces using various types of statistical tests and models is a useful approach aimed at a better understanding of the mechanisms of the self-healing interface. In the present work, this approach has been applied, for the first time, to a temperature (T) range below the bulk glass transition temperature (Tgbulk). The interest of this T range consists in a very limited or even frozen translational segmental motion giving little or no chance for adhesion to occur. To clarify this issue, the two identical samples of entangled amorphous polystyrene (PS) with a molecular weight (M) of 105 g/mol or 106 g/mol were kept in contact at T = Tgbulk - 33 °C for one day. The as-self-bonded PS-PS auto-adhesive joints (AJ) of PSs differing in M by an order of magnitude were fractured at ambient temperature, and their σ distributions were analyzed using the Weibull model, the quantile-quantile plots, the normality tests, and the Gaussian distribution. It has been shown that the Weibull model most correctly describes the σ statistical distributions of the two self-bonded PS-PS AJs with different M due to the joints' brittleness. The values of the Weibull modulus (a statistical parameter) m = 2.40 and 1.89 calculated for PSs with M = 105 and 106 g/mol, respectively, were rather close, indicating that the chain length has a minor effect on the σ data scatter. The Gaussian distribution has been found to be less appropriate for this purpose, though all the normality tests performed have predicted the correctness of the normal distribution for these PS-PS interfaces.

Machine foundation response subjected to vertical vibration: experimental and analytical using cone model

The fundamental aim in the proper design of machine foundations is to limit the response amplitude by preventing resonance in all vibration modes. The effects of static and dynamic forces and embedment depths for foundation-induced vertical vibration have been examined, experimentally and analytically using the Cone model. Therefore, various vibration indicators such as displacement amplitude, resonance frequency and complex dynamic stiffness were evaluated. Finally, the statistical properties, Quantile-Quantile plots, and Root-Mean-Square Error values were used to gain confidence in applying the Cone model for predicting the soil bed dynamic behaviour. Per the results, it was observed that embedment increases resonance frequency, natural frequency ratio and damping ratio while the maximum resonant amplitude reduces as the embedment depth increases. Given the findings, due to the increasing dynamic force, a drop in resonance frequency and a rise in peak displacement amplitude of the foundation bed were observed. On the other hand, resonance frequency and amplitude are attenuated with an increase in static force level. Further, the complex dynamic stiffnesses predicted by the Cone model shows good agreement with that obtained experimentally. Thus, whenever feasible, the convenient and relatively accurate Cone model can be performed for assessing foundation vibration in practical engineering projects.

Fast and accurate centerline extraction algorithm for a laser stripe applied for shoe outsole inspection.

Line laser 3D reconstruction technology is widely used in industrial applications. As a key step of this technology, line laser midline extraction directly affects the accuracy of the 3D reconstructed model. In reconstructing the shoe outsole, the traditional algorithm based on the threshold method to determine the laser position may result in a large amount of information loss and miscellaneous point misjudgment owing to the irregularity of the shoe outsole surface, which critically affects the laser imaging quality. To address this problem, an algorithm based on the QQ plot inspection of the laser has been proposed. The QQ plot is a scatter plot, the abscissa is usually the quantile of the standard normal distribution, and the ordinate is the quantile of the data to be tested. If the points on the scatter plot tend to be straight lines, the data to be tested is in a normal distribution. Based on this property, the proposed algorithm aims to check whether the pixels of the image column tend to be normally distributed, rather than using traditional thresholding methods to locate the laser. The objective is to examine whether the image column pixel distribution is normal, instead of using the traditional threshold method to locate the laser. However, the calculation speed of this method is extremely low. To enhance the efficiency of testing the normality of the QQ plot, a quantile-repetition (Q-R) test method is proposed. In this approach, the degree of repetition of quantiles and the position of Q-R values are used to replace the QQ plot based evaluation of the points being on a straight line, and the exact center position is determined by the GGM. The experimental results show that the proposed algorithm can extract more effective points and fewer invalid points of the laser compared to those obtained using the traditional approach, in a rapid, stable, and accurate manner.

Exploring extreme value analysis of rainfall for some nuclear power plant sites in India

Extreme rainfall is an important consideration for safety of nuclear installations. Literature reported estimation of the same for Indian nuclear power plant sites using Gumbel and Frechet distributions, fitted by least square (graphical) method (LSM). In these reports, the goodness-of-fit was examined graphically by plots on probability papers. In this study, the data for six nuclear sites collected from literature were analysed. For this purpose, in addition to Gumbel and Frechet, other distributions were included and the parameters of the distributions were evaluated using Lieblein technique and maximum likelihood estimation, as well as LSM. The goodness-of-fit was evaluated using the quantitative tool: Anderson-Darling test; and qualitative tools: probability plot and quantile plot – which are suitable for evaluating goodness-of-fit of extreme value distributions. Maximum daily rainfall for return periods of 50, 100 and 1000 years were reported from the fitted distributions. Comparison with the respective values (50 and 100 year return period) from literature demonstrated that the extreme rainfall reported for these sites were quite accurate with maximum variation within ten per cent.

POWER SNIFFER PERFORMANCE DEGRADATION AND WAYS TO SUPPRESS THE DEVIATION OF THE WORKING PARAMETERS DUE TO RANDOM TECHNOLOGICAL VARIATIONS

One of the most important challenges of modern ICs is power dissipation, particula-rly the static power dissipation. To be able to reduce static power consumption of an IC, it is separated into different power domains so that the supply power can be turned off for certain domain when not in use. Separate power domains lead to several peculiarities, one of them is the powering up and down the power supply. To represent the supply voltage state by another domain supply, circuits like power sniffers are used. With the evolution of the technologies, the role of random technological variations in the circuits becomes substantial. The paper presents ways to reduce the performance degradation caused by random variations in the 16nm technological process node. HSpice tool is used for circuit simulations. Target sigma representing random variations is 5. For every PVT 300 iterations with random variations are run. The results are presented by QQ plots and measurement table. By applying the proposed modifications performance degradation is reduced by around 40% (average for all measured parameters). By implementing the proposed circuit changes the area of the circuit is increasing by around 35%, no power consumption increase is observed.

EWF: simulating exact paths of the Wright–Fisher diffusion

The Wright-Fisher diffusion is important in population genetics in modelling the evolution of allele frequencies over time subject to the influence of biological phenomena such as selection, mutation and genetic drift. Simulating the paths of the process is challenging due to the form of the transition density. We present EWF, a robust and efficient sampler which returns exact draws for the diffusion and diffusion bridge processes, accounting for general models of selection including those with frequency dependence. Given a configuration of selection, mutation and endpoints, EWF returns draws at the requested sampling times from the law of the corresponding Wright-Fisher process. Output was validated by comparison to approximations of the transition density via the Kolmogorov-Smirnov test and QQ plots. All softwares are available at https://github.com/JaroSant/EWF. Supplementary data are available at Bioinformatics online.

Probability Distribution of Soil Suction of Engineered Turf Cover and Compacted Clay Cover

It is unlikely to predict the distribution of soil suction in the field deterministically. It is well established that there are various sources of uncertainty in the measurement of matric suction, and the suction measurements in the field are even more critical because of the heterogeneities in the field conditions. Hence it becomes necessary to probabilistically characterize the suction in the field for enhanced reliability. The objective of this study was to conduct a probabilistic analysis of measured soil suction of two different test landfill covers, compacted clay cover (CC) and engineered turf cover (ETC), under similar meteorological events. The size of the two test landfill covers was 3 m × 3 m (10 ft. × 10 ft.) and 1.2 m (4ft.) in depth. The covers were constructed by excavating the existing subgrade, placing 6-mil plastic sheets, and backfilling the excavated soil, followed by layered compaction. Then the covers were instrumented identically with soil water potential sensors up to specified depths. One of the covers acted as the CC, and the other cover was ETC. In ETC, engineered turf was laid over the compacted soil. The engineered turf consisted of a structured LLDPE geomembrane overlain by synthetic turf (polyethylene fibers tufted through a double layer of woven polypropylene geotextiles). The sensors were connected to an automated data logging system and the collected data were probabilistically analyzed using the R program. There were significant inconsistencies in the descriptive statistical parameters of the measured soil suction at both covers under the same climatic conditions. Soil suction measured in the field ranged between almost 12 to 44 kPa in ETC, while it was in the range of almost 1 to 2020 kPa in the CC. The histogram and quantile-quantile (Q-Q) plot showed the data to be non-normally distributed in the field. A heavy-tailed leptokurtic (Kurtosis=13) distribution of suction was observed in the ETC with substantial outliers. In contrast, the suction distribution in CC was observed skewed to the right containing a thinner tail indicating an almost platykurtic distribution. The distribution of suction in the field under engineered turf was observed to be reasonably consistent with time compared to bare soil under the same meteorological events. The results obtained from this study revealed the engineered turf system to be an effective barrier to inducing changes in soil suction against climatic events.

Optimized Photometric Redshifts for the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS)

We present the first comprehensive release of photometric redshifts (photo- z's) from the Cosmic Assembly Near-Infrared Deep Extragalactic Legacy Survey (CANDELS) team. We use statistics based upon the Quantile–Quantile (Q–Q) plot to identify biases and signatures of underestimated or overestimated errors in photo- z probability density functions (PDFs) produced by six groups in the collaboration; correcting for these effects makes the resulting PDFs better match the statistical definition of a PDF. After correcting each group’s PDF, we explore three methods of combining the different groups’ PDFs for a given object into a consensus curve. Two of these methods are based on identifying the minimum f-divergence curve, i.e., the PDF that is closest in aggregate to the other PDFs in a set (analogous to the median of an array of numbers). We demonstrate that these techniques yield improved results using sets of spectroscopic redshifts independent of those used to optimize PDF modifications. The best photo- z PDFs and point estimates are achieved with the minimum f-divergence using the best four PDFs for each object (mFDa4) and the hierarchical Bayesian (HB4) methods, respectively. The HB4 photo- z point estimates produced σ NMAD = 0.0227/0.0189 and ∣Δz/(1 + z)∣ > 0.15 outlier fraction = 0.067/0.019 for spectroscopic and 3D Hubble Space Telescope redshifts, respectively. Finally, we describe the structure and provide guidance for the use of the CANDELS photo- z catalogs, which are available at https://archive.stsci.edu/prepds/candels/.

Distribution Nature of Trade Volume and Number of Trades at NEPSE Floor

Investors are concerned with market fluctuation. At NEPSE, market fluctuation is linked to the trade volume and number of shares traded during a specific day. A change in the benchmark index, NEPSE, in the Nepalese stock market depends on the market capitalization. Hence, to estimate the market pattern, a better understanding of the distribution nature of the trade volume and number of trades is beneficial to Nepalese investors. This ultimately helps an investor understand the market mechanism. The paper has followed basic descriptive statistics and a graphical presentation of the PP Plot, QQ Plot, and PDF Plot to test the normality and distribution nature of the NEPSE yearly trade volume and number of trades. Finally, the Sharpio-Wilk test, Jarque-Bera test, Kolmogorov-Smirnov test, and Anderson-Darling (A2) test are applied to test the goodness of fit for the observed and the respective NEPSE yearly trade volume and number of trades. The paper found that the NEPSE's yearly trade volume and number of trades from the year of its establishment to the fiscal year 2021–22 have a leptokurtic distribution. Similarly, the paper shows the distribution of trade volume and the number of trades toward non-normality. The probability distribution function reflects the log-normal (3P) distribution, also known as Galton’s distribution, for both sets of data. The distribution of the NEPSE's yearly trade volume and number of trades is best fitted by Galton’s distribution. The fitting of this specific distribution reflects a compounding effect on the transactions taped during the last two decades and more . Hence, an investor who enters in a NEPSE floor with a small numbers of scrips would multiply the numbers in a period of times.