Kolmogorov-Smirnov Statistical Test Research Articles

Fluid–Structure Interaction study of carotid blood flow: Comparison between viscosity models

Blood is a complex biological fluid and has elements in its composition, such as erythrocytes, which give it a non-Newtonian behavior. Typically, when carotid blood flow is studied, this aspect is frequently ignored and blood is modeled as a Newtonian fluid, with constant viscosity. This work demonstrates a Fluid–Structure Interaction study of carotid blood flow, with the comparison of two distinct viscosity models (Newtonian and Carreau). The results of the Independent Samples Kolmogorov–Smirnov statistical test show that the velocity in the center of geometry of the is similar for both viscosity models (p = 1.00; p = 0.71; p = 1.00) in the three vessels of the bifurcation Wall Shear Stress is dependent on the blood viscosity (p = 0.027), and is considerably higher for the Carreau model. The displacement of the arterial wall is reliant on the fluid pressure, and it is not influenced by the blood viscosity.

A Bayes factor approach with informative prior for rare genetic variant analysis from next generation sequencing data.

The discovery of rare genetic variants through next generation sequencing is a very challenging issue in the field of human genetics. We propose a novel region-based statistical approach based on a Bayes Factor (BF) to assess evidence of association between a set of rare variants (RVs) located on the same genomic region and a disease outcome in the context of case-control design. Marginal likelihoods are computed under the null and alternative hypotheses assuming a binomial distribution for the RV count in the region and a beta or mixture of Dirac and beta prior distribution for the probability of RV. We derive the theoretical null distribution of the BF under our prior setting and show that a Bayesian control of the false Discovery Rate can be obtained for genome-wide inference. Informative priors are introduced using prior evidence of association from a Kolmogorov-Smirnov test statistic. We use our simulation program, sim1000G, to generate RV data similar to the 1000 genomes sequencing project. Our simulation studies showed that the new BF statistic outperforms standard methods (SKAT, SKAT-O, Burden test) in case-control studies with moderate sample sizes and is equivalent to them under large sample size scenarios. Our real data application to a lung cancer case-control study found enrichment for RVs in known and novel cancer genes. It also suggests that using the BF with informative prior improves the overall gene discovery compared to the BF with noninformativeprior.

Fracture Load of Veneered Telescopic Secondary Crowns Made of High-Performance Polymer on Zirconia Primary Crowns: Impact of Veneering Technique.

To analyze the impact of different veneering techniques on the fracture load of telescopic secondary crowns made of a high-performance polymer (Ultaire aryl ketone polymer [UAKP]). Zirconia primary crown models (taper of 0 degrees) were prepared (N = 48), polished, scanned, and divided into four veneering groups (n = 12 each): premanufactured, digital, full anatomical, and vestibular. For all groups except vestibular, a standardized telescopic secondary crown (thickness: 0.6 mm, circular margin: 1 mm) was constructed, adapted to the corresponding primary crown, milled from UAKP, and veneered. The veneered master crown was developed based on the premanufactured group. After surface polishing, all specimens were artificially aged in a chewing simulator (1.2 million cycles, 50 N, 1.1 Hz, between 5°C and 55°C). Fracture load was tested in a universal testing machine with a piston (Ø = 6 mm, 1 mm/minute). Fracture patterns were analyzed. For statistical analysis, Kolmogorov-Smirnov test and descriptive statistics followed by one-way ANOVA with post hoc Scheffé test were conducted (P < .05). Significant differences in fracture load were found between different veneering techniques (P < .001), with the highest values for the vestibular and digital groups, followed by the premanufactured group. Full anatomical veneering showed the significantly lowest fracture load (1,885 ± 397 N). For all specimens, cohesive brittle fractures with similar fracture patterns occurred, irrespective of the veneering technique. The veneering technique of telescopic secondary crowns made of high-performance polymer affects overall stability. All veneering techniques provided sufficient fracture load values for telescopic secondary crowns made of UAKP. Digital veneers seem the most recommendable.

The statistical behavior of PM10 events over guadeloupean archipelago: Stationarity, modelling and extreme events

Environmental pollution management is one of the most important features in pollution risk assessment. Several studies have shown that exposure to particulate matter with an aerodynamic diameter of 10 μm or less, i.e. PM10, were associated to adverse health effects. To our knowledge, no study has yet investigated the modelling of PM10 frequency distribution and extreme events in the Caribbean basin. Here, the descriptive statistics and four theoretical distributions (lognormal, Weibull, Burr and stable) were used to fit the parent distribution of PM10 daily average concentrations in Guadeloupe archipelago with a database of 11 years. In order to determine the best distribution, the Kolmogorov–Smirnov statistic test (KS test) was computed as performance indicator value. With an annual average of 26.4 ± 16.1 μg/m3, the descriptive statistics highlighted that PM10 concentrations in Guadeloupe are lower than those measured in cities of Europe, Asia or Africa. Contrary to other megacities, we found that high PM10 levels in Guadeloupe are mainly due to natural large-scale sources, i.e. African dust. From May to September, i.e. high dust season, PM10 concentrations are 1.5 times larger since dust outbreaks are more frequent. A statistical stationarity threshold of 66 months is estimated using the distribution analysis. This underlines the cycle stability of African dust over this last decade. Concerning the statistical modelling, our results showed that Burr & Weibull mixture model is the best distribution to represent PM10 daily average concentrations with a first statistical behavior corresponding to the low dust season and an another to the high dust season. By analysing the extreme events statistic with the classical power-law distribution, we observed that Burr & Weibull mixture model could also improve the modelling of these events. In summary, the Burr & Weibull mixture model is suitable to model both classical and extreme events.

Multi-model synthesis of future extreme temperature indices over Zambia

Although temperature is one of the most important climate variables to be considered in adapting systems to climate change, its study over Zambia has until recently been largely ignored. A dearth of the literature on future temperature extremes is especially apparent. For the first time, future extreme temperature variability is analysed in Zambia for the period 1961–2100. The nonparametric Mann–Kendall test statistic is used at 5% significant level to compute trends. Sen’s slope estimator is used to give the magnitude of the observed trends. A two-tailed Kolmogorov–Smirnov statistical test is used to calculate the significance of the observed changes. What stands out from the findings is that warm days and nights become warmer while cool days and nights are projected to become non-existent by 2100. Additionally, an increase in radiative forcing and time is seen to intensify extreme temperature events. Notably, much of southern Zambia is projected to experience ~ 30% increment in TX90p while the northern half will experience ~ 40% under RCP4.5 by the middle of the century (2021–2050). If the business-as-usual trajectory (RCP8.5) is followed, an intensification of TX90p is observed with ~ 40% in the southern half of the country and ~ 50% in the northern half. These projections are observed to almost double towards the end of the century (2071–2100). The projected increase in warm nights (TN90p) is more over Luapula and Northwestern province while the lowest is observed over the Livingstone/Magoye region. These results provide a foundation for strategic planning purposes to avert losses related to extreme temperature.

A Myth of Preferred Days of Strong Earthquakes?

AbstractExisting evidence on the origin times of magnitude M≥7.5 earthquakes worldwide, based on authoritative earthquake catalogs, does not permit rejection of the null hypotheses of random coincidental occurrence at any time during the Earth or the Moon cycles. Specifically, the nonparametric Kuiper test statistics for cyclic variations applied to seismic evidence resulting from the empirical distributions of the M≥7.5 earthquake origin time Julian day (JD) and the Moon phase (MP) do not allow the rejection of the null hypotheses of uniform distributions within the corresponding cycles. On the other hand, the same Kuiper test permits the rejection of the null hypotheses of the same chance of occurrence on any JD or MP for strong magnitude M≥6.0 earthquakes, at least for the past four decades of presumably the best-earthquake determinations and, in particular, for earthquakes in the Northern Hemisphere (with an evident seasonal pattern). The nonparametric two-sample Kolmogorov–Smirnov test statistics suggest no preferred distances to the Moon at the occurrence of large earthquakes. All of this contributes, to the results of solid statistical testing of hypotheses, for a better understanding of the complex seismic response of the Earth’s lithosphere to periodic gravitational loading.

Goodness-of-fit tests for the beta Gompertz distribution

This article studied the goodness-of-fit tests for the beta Gompertz distribution with four parameters based on a complete sample. The parameters were estimated by the maximum likelihood method. Critical values were found by Monte Carlo simulation for the modified Kolmogorov-Smirnov, Anderson-Darling, Cramer-von Mises, and Lilliefors test statistics. The power of these test statistics founded the optimal alternative distribution. Real data applications were used as examples for the goodness of fit tests.

Computing the Kolmogorov-Smirnov Distribution When the Underlying CDF is Purely Discrete, Mixed, or Continuous

The distribution of the Kolmogorov-Smirnov (KS) test statistic has been widely studied under the assumption that the underlying theoretical cumulative distribution function (CDF), F (x), is continuous. However, there are many real-life applications in which fitting discrete or mixed distributions is required. Nevertheless, due to inherent difficulties, the distribution of the KS statistic when F (x) has jump discontinuities has been studied to a much lesser extent and no exact and efficient computational methods have been proposed in the literature. In this paper, we provide a fast and accurate method to compute the (complementary) CDF of the KS statistic when F (x) is discontinuous, and thus obtain exact p values of the KS test. Our approach is to express the complementary CDF through the rectangle probability for uniform order statistics, and to compute it using fast Fourier transform (FFT). Secondly, we provide a C++ and an R implementation of the proposed method, which fills the existing gap in statistical software. We give also a useful extension of the Schmid's asymptotic formula for the distribution of the KS statistic, relaxing his requirement for F (x) to be increasing between jumps and thus allowing for any general mixed or purely discrete F (x). The numerical performance of the proposed FFT-based method, implemented both in C++ and in the R package KSgeneral, available from https://CRAN.R-project.org/package=KSgeneral, is illustrated when F (x) is mixed, purely discrete, and continuous. The performance of the general asymptotic formula is also studied.

Goodness-of-fit tests for the beta Gompertz distribution

This article studied the goodness-of-fit tests for the beta Gompertz distribution with four parameters based on a complete sample. The parameters were estimated by the maximum likelihood method. Critical values were found by Monte Carlo simulation for the modified Kolmogorov-Smirnov, Anderson-Darling, Cramer-von Mises, and Lilliefors test statistics. The power of these test statistics founded the optimal alternative distribution. Real data applications were used as examples for the goodness of fit tests.

Back-tracing space debris using proper elements

AbstractNormal form methods allow one to compute quasi-invariants of a Hamiltonian system, which are referred to as proper elements. The computation of the proper elements turns out to be useful to associate dynamical properties that lead to identify families of space debris, as it was done in the past for families of asteroids. In particular, through proper elements we are able to group fragments generated by the same break-up event and we possibly associate them to a parent body. A qualitative analysis of the results is given by the computation of the Pearson correlation coefficient and the probability of the Kolmogorov-Smirnov statistical test.

Determining the Most Sensitive Socioeconomic Parameters for Quantitative Risk Assessment

Risk assessment of climatic events and climate change is a globally challenging issue. For risk as well as vulnerability assessment, there can be a large number of socioeconomic indicators, from which it is difficult to identify the most sensitive ones. Many researchers have studied risk and vulnerability assessment through specific set of indicators. The set of selected indicators varies from expert to expert, which inherently results in a biased output. To avoid biased results in this study, the most sensitive indicators are selected through sensitivity analysis performed by applying a non-linear programming system, which is solved by Karush-Kuhn-Tucker conditions. Here, risk is assessed as a function of exposure, hazard, and vulnerability, which is defined in the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report (AR5), where, exposure and vulnerability are described via socioeconomic indicators. The Kolmogorov-Smirnov statistical test is applied to select the set of indicators that are the most sensitive for the system to assess risk. The method is applied to the Bangladesh coast to determine the most sensitive socioeconomic indicators in addition to assessing different climatic and climate change hazard risks. The methodology developed in this study can be a useful tool for risk-based planning.

Sandia Fracture Challenge 3: detailing the Sandia Team Q failure prediction strategy

The third Sandia Fracture Challenge highlighted the geometric and material uncertainties introduced by modern additive manufacturing techniques. Tasked with the challenge of predicting failure of a complex additively-manufactured geometry made of 316L stainless steel, we combined a rigorous material calibration scheme with a number of statistical assessments of problem uncertainties. Specifically, we used optimization techniques to calibrate a rate-dependent and anisotropic Hill plasticity model to represent material deformation coupled with a damage model driven by void growth and nucleation. Through targeted simulation studies we assessed the influence of internal voids and surface flaws on the specimens of interest in the challenge which guided our material modeling choices. Employing the Kolmogorov–Smirnov test statistic, we developed a representative suite of simulations to account for the geometric variability of test specimens and the variability introduced by material parameter uncertainty. This approach allowed the team to successfully predict the failure mode of the experimental test population as well as the global response with a high degree of accuracy.

Physicochemical and mineralogical characterization datasets from oil drill cuttings in comparison with other cement types for cement partial-replacement in concrete

Abstract This article presents data on the physical/chemical and mineralogical characterizations of treated oil drill cuttings (ODC) in comparisons with other cement types, for suitability insight for partial-replacement of cement in concrete. The physical properties were compared for cement/cement fillers including Portland Cement (PC), Pulverized Fuel Ash (PFA), and Ground Granulated Blast-furnace Slag (GGBS). The particle size distribution of the ODC and the other cement/cementitious materials were also rendered to the extreme-value probability density models, with the Normal distribution employed as a reference, while the goodness-of-fit data-distribution compatibility was ascertained using Kolmogorov-Smirnov test-statistics. Characterized properties indicated treated ODC physicochemical and mineralogical properties compared well to the ranges exhibited by the other cement types, and requisite standards. The presented comparative results from the measured/analyzed physicochemical and mineralogical data are useful information for furthering research on the suitability of ODC, wastes from oil and gas explorations, as partial-replacement of cement in concrete.

Development of a first order integrated moving average model corrupted with a Markov modulated convex combination of autoregressive moving average errors

ABSTRACTWith a view to providing a tool to accurately model time series processes which may be corrupted with errors such as measurement, round-off and data aggregation, this study developed an integrated moving average (IMA) model with a transition matrix for the errors resulting in a convex combination of two ARMA errors. Datasets on interest rates in the United States and Nigeria were used to demonstrate the application of the formulated model. Basic tools such as the autocovariance function, maximum likelihood method, Newton–Raphson iterative method and Kolmogorov–Smirnov test statistic were employed to examine and fit the formulated specification to data. Test results showed that the proposed model provided a generalisation and a more flexible specification than the existing models of AR error and ARMA error in fitting time series processes in the presence of errors.

Cyclic heat release variability in a spark ignition engine under exhaust gas recirculation

We have studied cyclic heat release variability in a spark-ignition engine under exhaust gas recirculation (EGR), using nitrogen to simulate EGR. Five EGR levels are examined. We used wavelet analysis to identify the dominant modes of fluctuation and how these modes vary in time. It is found that at a low EGR level, the heat release variations exhibit high-frequency intermittent oscillations. As the EGR level increases, the high-frequency oscillations tend to become more persistent, occurring continuously over many cycles. When the EGR level is sufficiently high, intermittent oscillations are observed at both high and low frequencies. In addition, persistent low-frequency fluctuations are present at the high EGR level. We have fitted theoretical probability models to the empirical heat release distributions. Depending on the EGR level, a three-parameter probability density function such as the generalized logistic distribution, a four-parameter distribution such as Johnson SB, or the five-parameter Wakeby distribution is found to provide a good fit. The goodness of fit of the theoretical distributions is assessed by the Kolmogorov-Smirnov (KS) test statistics. A good understanding of cyclic variability is essential to develop effective control strategies for efficient combustion.

Inferring distributions from observed mRNA and protein copy counts in genetic circuits

Defining distributions of molecule counts produced in the cell can elucidate stochastic dynamics of the underlying biological circuits. For genetic circuits, only a few distributions of messenger RNA and protein counts were reported in literature, so the task is to decide which of these candidate distributions best fit the observed data. In this paper, we present a statistical method to infer distributions of mRNA and protein counts from observed data. The main advantage of this method is that it does not require any prior assumptions or knowledge about underlying chemical reactions. In particular, a given distribution is fitted to the observed copy counts using a histogram with optimized bin sizes in order to reduce the fitting error. The goodness of fit is evaluated by Kolmogorov-Smirnov and chi-square statistical tests to accept or reject the hypothesis that observed molecule counts were generated from given distribution. The distribution fitting also yields the values of distribution parameters, or they can be estimated using the Bayes theorem. These parameters appear to be themselves random processes. The presented statistical framework for analyzing the observed mRNA and protein copy counts is illustrated for a simulated model of lac genetic circuit in Escherichia coli. For reaction rates assumed in the model, the results in literature predict that mRNA and protein counts at steady-state are gamma distributed. Our analysis shows that both mRNA and protein in the lac circuit model can be considered gamma distributed in at least 70% of times from the initial state until steady-state. The shape and scale parameters of observed gamma distributions are also gamma distributed, giving rise to double stochastic processes. More importantly, as shown previously, the distribution parameters are functions of transcription and translation rates, so presented statistical framework can be used to estimate or optimize reaction rates in biochemical systems.

Non-destructive testing of industrial equipment using muon radiography.

A new application of muon radiography (MR) is presented in the context of non-destructive testing of industrial equipment. The long-term operation of industrial facilities frequently involves the deterioration of critical components such as pipes and cauldrons due to corrosion and other processes. The precise determination of the inner state of this equipment is needed to ensure the integrity of the facility. MR can be used to infer the thickness of these components through the comparison and further classification of muon observables with respect to well-known templates. A simulation example is presented where the thickness of a pipe made of steel is studied using the Point of Closest Approach method and simple Kolmogorov-Smirnov statistical tests. A precision of about 2-4 mm is obtained using a simple detector with a spatial resolution of 4 mm and exposure times of about 2 h.This article is part of the Theo Murphy meeting issue 'Cosmic-ray muography'.

Quantification of source specific black carbon scavenging using an aethalometer and a disdrometer

Aerosol black carbon (BC) is the second strongest contributor to global warming, after CO2, and it is linked to many adverse health effects. A sampling campaign of 15 months was carried out in León (Spain) in order to evaluate the scavenging of BC with an ensemble aethalometer-disdrometer. The aethalometer provides the concentration of equivalent black carbon (eBC), and the disdrometer, the raindrop size distribution. A total of seventy-five rain events were studied and in 73% of them there was an effective (eBCinitial > eBCfinal) scavenging, with a mean decrease of 48 ± 37% in long rain events (>8 h) and 39 ± 38% in short rain events. The scavenging of BC is strongly related to its source. Thus, the scavenging coefficient (SC) mean value of the BC from fossil fuel (eBCff) for short and long rain events was 5.1 10−5 and 1.3 10−5 s−1, respectively. For the BC from biomass burning (eBCbb), the SC values were 1.6 10−4 and 2.8 10−5 s−1 in short and long events, respectively. There was a significant positive correlation between the SC and the number of drops with diameters between 0.375 and 2.5 mm. Rain scavenging of eBC was analyzed depending on the air mass origin obtaining an effective scavenging for air masses from Atlantic, Arctic and Africa. A linear model (R2 = 0.72) was built to estimate the ΔeBC values with variables from an aethalometer, a disdrometer and a weather station: eBC concentration before rain, swept volume and precipitation accumulated. A Kolmogorov-Smirnov statistical test confirmed the goodness of fit of the model to the measured data.

Kolmogorov–Smirnov Test for Statistical Characterization of Photopyroelectric Signals Obtained from Maize Seeds

Photothermal techniques are useful experimental methodologies for characterization of the optical and thermal parameters of different materials like maize seeds due to its advantages such as non-invasive and non-destructive nature. Among these techniques, the photopyroelectric microscopy was applied in the present research to obtain thermal images where each of their coordinates represents amplitude values of the photopyroelectric signal, indicating differences in the structural components of both genotypes of maize seeds. The random variations of the amplitude of the photopyroelectric signal caused by the heterogeneous nature of the thermal properties of the samples, were represented by histograms to identify the probability density function underlying the data sample, observing that in the case of the maize seed with floury structure, the amplitude variations could be described statistically by the transformed Moyal distribution when a linear transformation with censored data was applied to the data set obtained from the thermal image with a significance level of 0.001, according to the Kolmogorov–Smirnov statistical test for goodness-of-fit. In the case of the photopyroelectric signal obtained from a maize seed with crystalline structure, it was not possible to describe statistically the amplitude variations of the signal by means of the transformed Moyal distribution because it did not pass the Kolmogorov–Smirnov test, so the same statistical test for goodness of fit was applied to both genotypes of maize seeds for analyzing the populations of the data sample, in order to find the distributions that best fit each population with a significance level of at least 0.05 increasing in this way the power of the test. The distributions with the best fit were logistic, log-logistic, uniform, least extreme value and normal.

Methods of Estimating the Parameters of the Quasi Lindley Distribution

In this paper, we review the quasi Lindley distribution and established its quantile function. A simulation study is conducted to examine the bias and mean square error of the parameter estimates of the distribution through the method of moment estimation and the maximum likelihood estimation. Result obtained shows that the method of maximum likelihood is a better choice of estimation method for the parameters of the quasi Lindley distribution. Finally, an applicability of the quasi Lindley disttribution to a waiting time data set suggests that the distribution demonstrates superiority over the power Lindley distribution, Sushila distribution and the classical oneparameter Lindley distribution in terms of the maximized loglikelihood, the Akaike information criterion, the Kolmogorov-Smirnov and Cramer von Mises test statistic.