Cumulative Probability Density Research Articles

An Improved Adaptive Subfield Coding Method for Driving AC PDPs

An improved adaptive subfield coding driving method was proposed to reduce the static false contours when the simple-accumulation lighting mode is applied to alternating current plasma display panels (ac PDPs). In the proposed method, when the weighted ratio of the subgrayscale interval to the main grayscale interval is smaller, the gray cumulative probability densities in the subgrayscale interval are sampled in order to locate the sampling gray levels at which the gray probability densities are larger. When the weighted ratio of the subgrayscale interval to the main grayscale interval is larger, the gray levels in the subgrayscale interval are sampled directly so as not to generate larger quantization error brought by the excessive convergence of the sampling gray levels. The simulation results show that the proposed method can eliminate the dynamic false contours in the AC PDPs and has better grayscale expression capability than the existing similar method appearing in the literature. The method proposed in this paper can reproduce the original image information more faithfully.

Distributions of Ratios of Two Correlated Skew-Normal Variables and of Ratios of Two Linear Functions of Order Statistics from Bivariate Normal Distribution

In this article, we first derive the distribution of the ratio of two correlated skew-normal variables. Then, with , where |ρ|< 1, and (X 1:2, X 2:2) T denoting the corresponding order statistics, we consider two linear functions of these order statistics, viz., a 1 X 1:2 + a 2 X 2:2 and b 1 X 1:2 + b 2 X 2:2, and derive explicit expressions for the cumulative distribution function (cdf) and probability density function (pdf) of the ratios and .

MIMO rayleigh-product channels with co-channel interference

This paper presents an analytical performance investigation of an interference-limited double scattering multiple-input multiple-output (MIMO) channel employing optimum combining. Our main contribution is the derivation of the closed-form expressions for the cumulative distribution function (c.d.f.) and probability density function (p.d.f.) of the maximum eigenvalue of the resultant channel matrix after optimal combining when the transmit, receive and scattering correlation matrices are identities (hence, the channel is referred to as a Rayleigh-product channel). These results allow us to obtain the outage probability of the optimal combining system in a Rayleigh-product channel with co-channel interferences. Furthermore, we investigate, in depth, an important special case of double scattering channel, the keyhole channel, where based on various closed-form expressions for exact and asymptotic measures derived, we examine three key performance metrics, namely, the ergodic capacity, the outage performance and the symbol-error-rate (SER). The analytical results derived are validated by Monte-Carlo simulations.

In Silico Analysis of Phosphoproteome Data Suggests a Rich-get-richer Process of Phosphosite Accumulation over Evolution

Recent phosphoproteome analyses using mass spectrometry-based technologies have provided new insights into the extensive presence of protein phosphorylation in various species and have raised the interesting question of how this protein modification was gained evolutionarily on such a large scale. We investigated this issue by using human and mouse phosphoproteome data. We initially found that phosphoproteins followed a power-law distribution with regard to their number of phosphosites: most of the proteins included only a few phosphosites, but some included dozens of phosphosites. The power-law distribution, unlike more commonly observed distributions such as normal and log-normal distributions, is considered by the field of complex systems science to be produced by a specific rich-get-richer process called preferential attachment growth. Therefore, we explored the factors that may have promoted the rich-get-richer process during phosphosite evolution. We conducted a bioinformatics analysis to evaluate the relationship of amino acid sequences of phosphoproteins with the positions of phosphosites and found an overconcentration of phosphosites in specific regions of protein surfaces and implications that in many phosphoproteins these clusters of phosphosites are activated simultaneously. Multiple phosphosites concentrated in limited spaces on phosphoprotein surfaces may therefore function biologically as cooperative modules that are resistant to selective pressures during phosphoprotein evolution. We therefore proposed a hypothetical model by which the modularization of multiple phosphosites has been resistant to natural selection and has driven the rich-get-richer process of the evolutionary growth of phosphosite numbers.

Transient calculations on process algebra derived Markov chains

The process of obtaining transient measures from a Markov chain as implemented in the software, ipclib is described. The software accepts models written in PEPA, Bio-PEPA or as a Petri net. In the case of the process algebras, a rich query specification language particularly well suited for the derivation of passage-time quantiles is provided. Such measurements are obtained from the derived Markov chain through a process known as uniformisation. The authors detail how the process algebra and query specification language allow one to ensure that the passage-time calculation is valid and then the entire process through to the final calculation of the cumulative distribution and probability density functions of the passage in question. The authors also show a more generic transient measure for which the full probability distributions at specific times are required.

Spectral efficiency evaluation for selection combining diversity (SCD) scheme over slow fading

In this paper we derive closed-form expressions for the single-user capacity of selection combining diversity (SCD) system, taking into account the effect of imperfect channel estimation at the receiver. The channel considered is a slowly varying spatially independent flat Rayleigh fading channel. The complex channel estimate and the actual channel are modelled as jointly Gaussian random variables with a correlation that depends on the estimation quality. Three adaptive transmission schemes are analysed: 1) optimal power and rate adaptation opra; 2) constant power with optimal rate adaptation ora; and 3) channel inversion with fixed rate cifr. Furthermore, we derive in this paper analytical results for capacity statistics including moment generating function (MGF), complementary cumulative distribution function (CDF) and probability density function (PDF). These statistics are valid for arbitrary number of receive antennas. Our numerical results show the effect of Gaussian channel estimation error on the achievable spectral efficiency.

Study of scalar macro- and microstructures in a confined jet

The scalar structures in a confined jet are studied at high Reynolds and Schmidt numbers. Both flow modes without the recirculation zone (jet mode) and with the massive separation and creation of the recirculation zone (r-mode) are considered. Despite of the big difference in the flow modes, the fine scale scalar structures gained from highly resolved PLIF measurements possess similar statistical properties such as the normalized cumulative distributions and probability densities of the dissipation rate. The fine scalar structures are distributed nearly uniformly in space with the scalar gradient vector having a slight preference to align with the most compressive mean strain axis. The scalar field exhibits small-scale intermittency which is strongly dependent on the flow mode. The intermittency is most pronounced in the front of the recirculation zone and becomes weaker on the centerline and downstream. The most contribution to the scalar variance is made by large scale motions whereas the contribution of fine scales smaller than typical inertial range scales is negligible. Examination of the multiplier distributions has not supported the concept of the multifractal nature of the scalar dissipation field.

Late Holocene environmental change in the Howgill Fells, Northwest England

New data from Chapel Beck in the southwest Howgill Fells combined with existing data support the identification of three phases of extensive hillslope gullying after 2200, between 1250–700 and after 500 cal. BP. Examination of cumulative probability density function (CPDF) plots of the distribution of calibrated radiocarbon dates confirms the identification of these phases. There are differences in the spatial distribution of geomorphic activity between these phases; with the c. 2200–1800 cal. BP episode limited to the western Howgill Fells. In comparison, the 1250–700 and post-500 cal. BP episodes are more widespread cross-region phenomena, and affected the more remote central fells. Pollen and geochemical data reveal several phases of increased human activity in these uplands, with small-scale temporary clearances during the late Bronze Age / early Iron Age and more substantial clearances during the late Iron Age and Romano-British times (2300–1500 cal. BP), and these were followed by woodland expansion and decline in human activity during both the mid- to late Iron Age and the period after the Roman withdrawal from Britain (after 1500 cal. BP). The final substantial woodland clearances occurred from c. 1100–900 cal. BP, after which there has been little woodland recovery. A range of pollen sites across the Howgill Fells indicate that there is spatial variability in the level of human activity and impact. Iron Age / Romano-British woodland clearances appear to have affected the west of the region more than the remote central valleys, whereas the later 1100–900 cal. BP woodland reduction affected the entire region. This pattern is similar to that identified from the geomorphology, and demonstrates the importance of pollen sites that record local palaeo-vegetation information and the significance of using a series of sites to explore intra-regional variability in the vegetation history. We suggest that human activity is a critical factor in mediating the late Holocene geomorphic record, but climate and particularly individual storms are the trigger mechanism responsible for erosion and incision on hillslopes and within the wider fluvial system. Palaeoclimate data (humification and plant macrofossil) from peat deposits at Archer Moss identify shifts to wetter conditions: c. 3100–2700; 2400–1700; 1300–1100; and after 650 cal. BP, and probably reflect increases in summer wetness. Of these, the 2400–1700, 1300–1100 and post-650 cal. BP wetter phases coincide with increased geomorphic activity, and perhaps encouraged incision on hillslopes rendered more susceptible to erosion by the activities of people.

The texture of natural sounds

The texture, a spectro-temporal pattern, of many sound sources is a robust and characteristic perceptual property that listeners use for sound source recognition. The robustness of the texture ensures that we can recognize sound sources like a helicopter, flowing water, or a surf breaking on pebbles in a wide variety of acoustic environments. This robustness suggests that textures can be used for automatic source identification or environment classification. We introduce a method to determine the presence of sound textures associated with, for example, flat noise, pulsed noises (helicopter), sweep based textures (running water), and tonal noises (babble). The cumulative probability density of time-frequency fluctuations are matched with prototypical cumulative probability density functions (cpdf) with a running variant of the Kolmogorov-Smirnov test. Textures with a similar distribution as the target distribution, contribute approximately equally to all values of the cpdf. The flatness of this distribution is used as a distance measure. When the pdf's of the target textures do not overlap strongly, the method can determine the texture of time-frequency-regions as small as 100 ms by 6 semi-tones. This method can therefore also be used to determine the texture of the background.

Signal detectability in extreme precipitation changes assessed from twentieth century climate simulations

This study assesses the detectability of external influences in changes of precipitation extremes in the twentieth century, which is explored through a perfect model analysis with an ensemble of coupled global climate model (GCM) simulations. Three indices of precipitation extremes are defined from the generalized extreme value (GEV) distribution: the 20-year return value (P 20), the median (P m), and the cumulative probability density as a probability-based index (PI). Time variations of area-averages of these three extreme indices are analyzed over different spatial domains from the globe to continental regions. Treating all forcing simulations (ALL; natural plus anthropogenic) of the twentieth century as observations and using a preindustrial control run (CTL) to estimate the internal variability, the amplitudes of response patterns to anthropogenic (ANT), natural (NAT), greenhouse-gases (GHG), and sulfate aerosols (SUL) forcings are estimated using a Bayesian decision method. Results show that there are decisively detectable ANT signals in global, hemispheric, and zonal band areas. When only land is considered, the global and hemispheric detection results are unchanged, but detectable ANT signals in the zonal bands are limited to low latitudes. The ANT signals are also detectable in the P m and PI but not in P 20 at continental scales over Asia, South America, Africa, and Australia. This indicates that indices located near the center of the GEV distribution (P m and PI) may give better signal-to-noise ratio than indices representing the tail of the distribution (P 20). GHG and NAT signals are also detectable, but less robustly for more limited extreme indices and regions. These results are largely insensitive when model data are masked to mimic the availability of the observed data. An imperfect model analysis in which fingerprints are obtained from simulations with a different GCM suggests that ANT is robustly detectable only at global and hemispheric scales, with high uncertainty in the zonal and continental results.

Mid- and Late Holocene fluvial chronology of Tunisia

Regarding fluvial response to recent climate change, it is important to identify and understand previous changes of fluvial dynamics related to past climatic shifts. In this paper, periods of increased flood activity in Central Tunisian river systems are presented. Changes in Holocene flood dynamics are reconstructed through a comprehensive analysis of 195 radiocarbon dates from alluvial archives. Holocene floodplain deposits in Central Tunisia normally consists of cohesive overbank fines, which exhibit excellent preservation conditions against lateral erosion and, therefore, permit chronostratigraphic records of the entire Holocene at most. Based on published radiocarbon dates, two 14C cumulative probability density plots are created for Central Tunisia: the former represents ‘activity dates’ indicating phases of increased fluvial dynamics, the latter documents ‘stability dates’ showing periods of soil formation and enhanced landscape stability within the floodplain and the catchment. Due to geomorphological considerations, ‘activity dates’ and ‘stability dates’ should be mutually exclusive. There is a good match for the Mid-Holocene with increased periods of flooding from 6.2 to 6.0, 4.8 to 4.5, 4.1 to 3.7, and 3.3 to 3.0 ka. These flood periods coincide with low soil formation signals. On the other hand, periods of increased alluvial soil formation from 6.8 to 6.6, 5.9 to 4.8, 4.5 to 4.1, 3.7 to 3.3, 3.0 to 2.8, and 1.8 to 1.6 ka coincide with periods of low flood plain aggradation. The data reveal a coupling with North Atlantic cooling. Short-term periods of enhanced fluvial dynamics in Central Tunisia match well with North Atlantic cooling. The findings indicate a strong climatic link from 4.7 ka until today. Compared to the Holocene floodplain dynamics in Tunisian drylands, the temperate mid-latitudes show Mid-Holocene switches in fluvial dynamics with opposite signs. Especially after 5 ka North Atlantic driven flooding in the temperate Central European river systems contrast sharply to flood dynamics in arid to semiarid Mediterranean Tunisia. While under temperate climate conditions floodplain sedimentation decreases, it increases under more arid conditions. This may indicate that fluvial archives of dissimilar climatic zones reveal different threshold values and sedimentation patterns, and, therefore, different responses to climatic shifts.

Inequality indicators and distinguishability in economics

Money has a material counterpart, such as banknotes or coins, and an ideal expression, monetary units. In the latter case, it is boson-like: individual incomes have no a priori limit, and their units are not distinguishable from each other in economic processes. Individuals, on the other hand, usually occupy one job at a time which makes them akin to fermions. We apply to individual incomes down-to-earth statistical calculations, similar to those for quantum particles, and obtain expressions for the cumulative distribution function, probability density and Lorenz function resulting from the simultaneous use of both statistics. They provide extremely good fits to corresponding data on French income distributions. On this basis, we propose a new entropic inequality indicator.

A Probabilistic Characterization of the Relationship between Fine Particulate Matter and Mortality: Elicitation of European Experts

In support of an assessment of the mortality impacts of the Kuwait Oil Fires we interviewed six European experts in epidemiology and toxicology using formal procedures for elicitation of expert judgment. While the primary focus of the elicitations was to characterize the public health impacts of the fires, the experts provided quantitative estimates of the mortality impacts of hypothetical changes in the levels of ambient fine particulate matter (PM2.5) in both the United States and Europe. Uncertainty was assessed by asking each expert to provide the 5th, 25th, 50th, 75th, and 90th percentiles of their subjective cumulative probability density function for each quantity of interest. The results suggest that many regulatory risk assessments underestimate the impacts of PM2.5 mortality; confirm that only a small fraction of the mortality impact occurs within the first few months after exposure; and indicate that it may be important to better address the differential toxicities of particles from various source classes. By providing quantitative estimates of the uncertainty in current estimates of PM2.5 mortality risks, the study facilitates structured analysis of the value of further research on PM2.5 and its impacts.

Eigenvalue Statistics of the Real Ginibre Ensemble

The real Ginibre ensemble consists of random N x N matrices formed from independent and identically distributed standard Gaussian entries. By using the method of skew orthogonal polynomials, the general n-point correlations for the real eigenvalues, and for the complex eigenvalues, are given as n x n Pfaffians with explicit entries. A computationally tractable formula for the cumulative probability density of the largest real eigenvalue is presented. This is relevant to May's stability analysis of biological webs.

Effect of alloying elements on the isothermal solidification during TLP bonding of SS 410 and SS 321 using a BNi-2 interlayer

The random diffusion of solute atoms during transient liquid phase (TLP) bonding of SS 410 and 321 with nickel-based brazing filler alloy BNi-2 have been modeled using Random Walk Modeling technique. Cumulative probability distributions and probability density functions of isothermal solidification times have been calculated for different process conditions and verified with experimental data. The solubility limit of boron has been found to have decreased from 0.3 at.% at higher temperature bonding operations (1358–1394 K) because of substantial iron-rich base metal dissolution when SS 410 was used as base metals; whereas it remained unchanged for SS 321/BNi-2 combination because of high concentrations of nickel and chromium in the base metal. Silicon diffusion model, based on the EDS analysis, also predicted the isothermal solidification times reasonably well.

A Note on the Coefficient of Determination in Models with Infinite Variance Variables

Since the seminal work of Mandelbrot (1963), alpha-stable distributions with infinite variance have been regarded as a more realistic distributional assumption than the normal distribution for some economic variables, especially financial data. After providing a brief survey of theoretical results on estimation and hypothesis testing in regression models with infinite-variance variables, we examine the statistical properties of the coefficient of determination in models with alpha-stable variables. If the regressor and error term share the same index of stability alpha&amp;amp;amp;lt;2, the coefficient of determination has a nondegenerate asymptotic distribution on the entire [0, 1] interval, and the density of this distribution is unbounded at 0 and 1. We provide closed-form expressions for the cumulative distribution function and probability density function of this limit random variable. In contrast, if the indices of stability of the regressor and error term are unequal, the coefficient of determination converges in probability to either 0 or 1, depending on which variable has the smaller index of stability. In an empirical application, we revisit the Fama-MacBeth two-stage regression and show that in the infinite-variance case the coefficient of determination of the second-stage regression converges to zero in probability even if the slope coefficient is nonzero.

Multivariate wavelet-based shape-preserving estimation for dependent observations

We introduce a new approach to shape-preserving estimation of cumulative distribution functions and probability density functions using the wavelet methodology for multivariate dependent data. Our estimators preserve shape constraints such as monotonicity, positivity and integration to one, and allow for low spatial regularity of the underlying functions. We discuss conditional quantile estimation for financial time series data as an application. Our methodology can be implemented with B-splines. We show by means of Monte Carlo simulations that it performs well in finite samples and for a data-driven choice of the resolution level.

Segmentation of diesel spray images with log-likelihood ratio test algorithm for non-Gaussian distributions

A methodology for processing images of diesel sprays under different experimental situations is presented. The new approach has been developed for cases where the background does not follow a Gaussian distribution but a positive bias appears. In such cases, the lognormal and the gamma probability density functions have been considered for the background digital level distributions. Two different algorithms have been compared with the standard log-likelihood ratio test (LRT): a threshold defined from the cumulative probability density function of the background shows a sensitive improvement, but the best results are obtained with modified versions of the LRT algorithm adapted to non-Gaussian cases.

Correlated multivariate Weibull fading channels with selection diversity

The dependent multivariate Weibull distribution is modelled for correlated fading channels, where the probability density function of a Weibull fading factor is defined with two parameters (ω, β), and the case of equal β is considered. The joint cumulative distribution function and probability density function of the Weibull distribution are derived, and the outage probability of selection diversity is evaluated.

A Note on the Coefficient of Determination in Regression Models with Infinite-Variance Variables

Since Mandelbrot's seminal work (1963), alpha-stable distributions with infinite variance have been regarded as a more realistic distributional assumption than the normal distribution for some economic variables, especially financial data. After providing a brief survey of theoretical results on estimation and hypothesis testing in regression models with infinite-variance variables, we examine the statistical properties of the coefficient of determination in regression models with infinite-variance variables. These properties differ in several important aspects from those in the well-known finite variance case. In the infinite-variance case when the regressor and error term share the same index of stability, the coefficient of determination has a nondegenerate asymptotic distribution on the entire [0,1] interval, and the probability density function of this distribution is unbounded at 0 and 1. We provide closedform expressions for the cumulative distribution function and probability density function of this limit random variable. In an empirical application, we revisit the Fama-MacBeth two-stage regression and show that in the infinite variance case the coefficient of determination of the second-stage regression converges to zero asymptotically.