Exponential Probability Research Articles

Статистический подход к управлению московскими многофункциональными центрами

The article presents a statistical approach to the service management. This approach is based on the use of the exponential probability distribution in service models and is demonstrated on the examples of multifunctional service centers. 
 The authors offer a method for setting the maximum limit for the waiting time in a queue to be served, which is interpreted in statistical terms as the failsafe (by level) quantile of waiting time. Given the average waiting time, a formula for specifying the maximum limit for the waiting time considering an allowable percentage of customers, who will have to wait longer than the maximum waiting time, is given. The formula reads as follows: the maximum limit for the waiting time is equal to the average waiting time multiplied by the modulus of natural logarithms of the failure level F, where F is equal to the anticipated share of customers who will have to wait longer than the time set by the manager as the maximum waiting time or, in other words, F⋅⋅ 100% is the percentage of failures. For advertising the efficiency, the manager is interested in setting the minimum allowable maximum waiting time; this time corresponds to a maximum allowable failure level F. Software for computing the maximum limit for the waiting time is offered. As a byproduct, an interesting result is obtained: In any queue, 37% of customers wait longer than the average waiting time to be served while 39% of customers wait shorter than half of the average waiting time.
 In summary, the main time-related quality indicator of service is the average waiting time in a queue. This indicator is equal to the ratio of two characteristics: the maximum limit for the waiting time / the absolute value of the natural logarithm of the share of failures in the total number of customers, that is, the proportion of customers who will have to wait longer than the time declared as the maximum waiting time.

Statistical Modelling and Characterization of Experimental mm-Wave Indoor Channels for Future 5G Wireless Communication Networks.

This paper presents an experimental characterization of millimeter-wave (mm-wave) channels in the 6.5 GHz, 10.5 GHz, 15 GHz, 19 GHz, 28 GHz and 38 GHz frequency bands in an indoor corridor environment. More than 4,000 power delay profiles were measured across the bands using an omnidirectional transmitter antenna and a highly directional horn receiver antenna for both co- and cross-polarized antenna configurations. This paper develops a new path-loss model to account for the frequency attenuation with distance, which we term the frequency attenuation (FA) path-loss model and introduce a frequency-dependent attenuation factor. The large-scale path loss was characterized based on both new and well-known path-loss models. A general and less complex method is also proposed to estimate the cross-polarization discrimination (XPD) factor of close-in reference distance with the XPD (CIX) and ABG with the XPD (ABGX) path-loss models to avoid the computational complexity of minimum mean square error (MMSE) approach. Moreover, small-scale parameters such as root mean square (RMS) delay spread, mean excess (MN-EX) delay, dispersion factors and maximum excess (MAX-EX) delay parameters were used to characterize the multipath channel dispersion. Multiple statistical distributions for RMS delay spread were also investigated. The results show that our proposed models are simpler and more physically-based than other well-known models. The path-loss exponents for all studied models are smaller than that of the free-space model by values in the range of 0.1 to 1.4 for all measured frequencies. The RMS delay spread values varied between 0.2 ns and 13.8 ns, and the dispersion factor values were less than 1 for all measured frequencies. The exponential and Weibull probability distribution models best fit the RMS delay spread empirical distribution for all of the measured frequencies in all scenarios.

FMEA에서 고장 심각도의 탐지시간에 따른 위험성 평가

The FMEA is a widely used technique to pre-evaluate and avoid risks due to potential failures for developing an improved design. The conventional FMEA does not consider the possible time gap between occurrence and detection of failure cause. When a failure cause is detected and corrected before the failure itself occurs, there will be no other effect except the correction cost. But, if its cause is detected after the failure actually occurs, its effects will become more severe depending on the duration of the uncorrected failure. Taking this situation into account, a risk metric is developed as an alternative to the RPN of the conventional FMEA. The severity of a failure effect is first modeled as linear and quadratic severity functions of undetected failure time duration. Assuming exponential probability distribution for occurrence and detection time of failures and causes, the expected severity is derived for each failure cause. A new risk metric REM is defined as the product of a failure cause occurrence rate and the expected severity of its corresponding failure. A numerical example and some discussions are provided for illustration.

Transient trapping of two microparticles interacting with optical tweezers and cavitation bubbles

In this work we show that two absorbing microbeads can briefly share the same optical trap while creating microscopic explosions. Optical forces pull the particles towards the waist of the trapping beam, once a particle reaches the vicinity of the waist, the surrounding liquid is superheated creating an explosion or cavitation bubble that pushes the particle away while lengthening or shortening the trajectories of the surrounding particles. Hence effectively coupling all the trajectories to each cavitation event. We find that when two microbeads reach the waist simultaneously within a distance of from the beam center in the transverse plane, a larger explosion might result in ejection from the trap. The measured maximum radial displacements due to cavitation are when the particles reach simultaneously with maximum bubble sizes , while for individual cases is and . We also measure the characteristic timescale of two particle coalescence which is a measure of the expected time that the particles can stay trapped near the waist. The measurements are fitted by a Poisson decaying exponential probability distribution. A simple one-dimensional model shows that the characteristic timescales for transient trapping of multiple absorbing particles decrease as more objects are added.

Some possible q-exponential type probability distribution in the non-extensive statistical physics

In this paper, we present two exponential type probability distributions which are different from Tsallis’s case which we call Type I: one given by [Formula: see text] (Type IIA) and another given by [Formula: see text] (Type IIIA). Starting with the Boltzman–Gibbs entropy, we obtain the different probability distribution by using the Kolmogorov–Nagumo average for the microstate energies. We present the first-order differential equations related to Types I, II and III. For three types of probability distributions, we discuss the quantum harmonic oscillator, two-level problem and the spin-[Formula: see text] paramagnet.

Evidence for Truncated Exponential Probability Distribution of Earthquake Slip

Earthquake ruptures comprise spatially varying slip on the fault surface, where slip represents the displacement discontinuity between the two sides of the rupture plane. In this study, we analyze the probability distribution of coseismic slip, which provides important information to better understand earthquake source physics. Although the probability distribution of slip is crucial for generating realistic rupture scenarios for simulation‐based seismic and tsunami‐hazard analysis, the statistical properties of earthquake slip have received limited attention so far. Here, we use the online database of earthquake source models (SRCMOD) to show that the probability distribution of slip follows the truncated exponential law. This law agrees with rupture‐specific physical constraints limiting the maximum possible slip on the fault, similar to physical constraints on maximum earthquake magnitudes. We show the parameters of the best‐fitting truncated exponential distribution scale with average coseismic slip. This scaling property reflects the control of the underlying stress distribution and fault strength on the rupture dimensions, which determines the average slip. Thus, the scale‐dependent behavior of slip heterogeneity is captured by the probability distribution of slip. We conclude that the truncated exponential law accurately quantifies coseismic slip distribution and therefore allows for more realistic modeling of rupture scenarios. Online Material: Figures showing scaling of slip area with seismic moment and Q – Q plots and tables listing earthquakes, rupture models, and fits of various distributions to the empirical probability distribution.

A direct analysis of flood interval probability using approximately 100-year streamflow datasets

ABSTRACTSeries of observed flood intervals, defined as the time intervals between successive flood peaks over a threshold, were extracted directly from 11 approximately 100-year streamflow datasets from Queensland, Australia. A range of discharge thresholds were analysed that correspond to return periods of approximately 3.7 months to 6.3 years. Flood interval histograms at South East Queensland gauges were consistently unimodal whereas those of the North and Central Queensland sites were often multimodal. The exponential probability distribution (pd) is often used to describe interval exceedence probabilities, but fitting utilizing the Anderson-Darling statistic found little evidence that it is the most suitable. The fatigue life pd dominated sub-year return periods (<1 year), often transitioning to a log Pearson 3 pd at above-year return periods. Fatigue life pd is used in analysis of the lifetime to structural failure when a threshold is exceeded, and this paper demonstrates its relevance also to the elapsed time between above-threshold floods. At most sites, the interval medians were substantially less than the means for sub-year return periods. Statistically the median is a better measure of the central tendency of skewed distributions but the mean is generally used in practice to describe the classical concept of flood return period.Editor Z.W. Kundzewicz; Associate editor I. Nalbantis

Evaluation of Millimeter-Wave Line-of-Sight Probability With Point Cloud Data

Line-of-sight (LOS) probability is an integral part of radio channel models for cellular network design and evaluation. The probability along with the pathloss models in LOS and non-LOS scenarios gives us an estimate of the cellular coverage. In this letter, we present a novel method to evaluate the LOS probability by using point cloud data obtained with laser scanning. The LOS probability is derived for two new scenarios, an urban open square and a shopping mall, along with an office environment, and a generic exponential LOS probability model, which shows excellent performance in the tested environments is proposed. Also the frequency dependency of LOS probability is investigated.

Using Geometric and Exponential Distributions for the Prediction of Drift Parameters in Technical Objects

We develop a technique for stochastic prediction of the drift duration of technical parameters of objects within tolerances, using geometric and exponential probability distribution laws. We consider the application of this methodology when estimating the duration of the calibration interval of platinum resistance thermometers.

A probability model for discretionary lane changes in highways

Lane changes are made frequently on the road and are therefore an important component in analyzing traffic situations. This behavior interferes with surrounding traffic, causes negative shockwaves, and may even lead to collisions. Lane changes can be categorized into mandatory lane changes and discretionary lane changes. There are various factors influencing the decision-making involved in discretionary lane changes, including relative velocity between target and original lane, and lead and lag gaps. The purpose of this paper is to present a stochastic approach for modeling discretionary lane changes with influential factors of velocity and spacing advantages. Using Next Generation Simulation (NGSIM) data, we proposed an exponential probability model with speed difference and lead gap difference between the target lane and the original lane. By transformed linear regression, these traffic variables have actual influences on the lane change probability of discretionary lane changes. The found results can be used for lane change models in microscopic traffic simulation.

Development of a Direct Geomorphologic IUH Model for Daily Runoff Estimation in Ungauged Watersheds

AbstractThe aim of this paper is to propose a new geomorphologic method for deriving the complete shape of instantaneous unit hydrograph (IUH) in ungauged watersheds by calculating the mean travel time of excess rainfall in overland and channel segments. All required parameters for the calculations of travel time of sheet and channel flows for different hydrologic orders are determined based on geomorphologic data of a watershed. In the proposed model, IUH is obtained using the exponential probability density function (PDF) of mean travel time of possible flow paths in a watershed. In this method, the excess rainfall is determined using the National Resources Conservation Service) NRCS curve number (CN) method (SCS-CN). To investigate the performance of the proposed IUH model, it is applied for daily rainfall-runoff simulation in two separate watersheds with different climate conditions (i.e., cool-humid and semiarid) in Iran. Also, other geomorphologic IUH (GIUH) models are utilized as benchmark models f...

Probing Non-Gaussianity in Confined Diffusion of Nanoparticles.

Confined diffusion is ubiquitous in nature. Ever since the "anomalous yet Brownian" motion was observed, the non-Gaussianity in confined diffusion has been unveiled as an important issue. In this Letter, we experimentally investigate the characteristics and source of non-Gaussian behavior in confined diffusion of nanoparticles suspended in polymer solutions. A time-varied and size-dependent non-Gaussianity is reported based on the non-Gaussian parameter and displacement probability distribution, especially when the nanoparticle's size is smaller than the typical polymer mesh size. This non-Gaussianity does not vanish even at the long-time Brownian stage. By inspecting the displacement autocorrelation, we observe that the nanoparticle-structure interaction, indicated by the anticorrelation, is limited in the short-time stage and makes little contribution to the non-Gaussianity in the long-time stage. The main source of the non-Gaussianity can therefore be attributed to hopping diffusion that results in an exponential probability distribution with the large displacements, which may also explain certain processes dominated by rare events in the biological environment.

Survival analysis approach to account for non-exponential decay rate effects in lifetime experiments

In experiments that measure the lifetime of trapped particles, in addition to loss mechanisms with exponential survival probability functions, particles can be lost by mechanisms with non-exponential survival probability functions. Failure to account for such loss mechanisms produces systematic measurement error and associated systematic uncertainties in these measurements. In this work, we develop a general competing risks survival analysis method to account for the joint effect of loss mechanisms with either exponential or non-exponential survival probability functions, and a method to quantify the size of systematic effects and associated uncertainties for lifetime estimates. As a case study, we apply our survival analysis formalism and method to the Ultra Cold Neutron lifetime experiment at NIST. In this experiment, neutrons can escape a magnetic trap before they decay due to a wall loss mechanism with an associated non-exponential survival probability function.

Performance bounds for parameter estimates of high-dimensional linear models with correlated errors

This paper develops a systematic theory for high-dimensional linear models with dependent errors and/or dependent covariates. To study properties of estimates of the regression parameters, we adopt the framework of functional dependence measures ([43]). For the covariates two schemes are addressed: the random design and the deterministic design. For the former we apply the constrained $\ell_{1}$ minimization approach, while for the latter the Lasso estimation procedure is used. We provide a detailed characterization on how the error rates of the estimates depend on the moment conditions that control the tail behaviors, the dependencies of the underlying processes that generate the errors and the covariates, the dimension and the sample size. Our theory substantially extends earlier ones by allowing dependent and/or heavy-tailed errors and the covariates. As our main tools, we derive exponential tail probability inequalities for dependent sub-Gaussian errors and Nagaev-type inequalities for dependent non-sub-Gaussian errors that arise from linear or non-linear processes.

Functions of probability for fitting monthly rainfall in sites of Mato Grosso do Sul state

The identification of the probability distribution function for the representation of the monthly rainfall is relevant in agricultural planning, mainly regard to the establishment of crops. The aim of this work was to verify the probability distribution (exponential, gamma or normal) which best fits to data monthly rainfall of 14 sites in the state of Mato Grosso do Sul. Rainfall data of 14 stations (sites) of the State of Mato Grosso do Sul it were obtained from the National Water Agency (ANA) database, collected in the period 1975 - 2013. At each of the 168 time series of monthly rainfall was applied the Kolmogorov-Smirnov test to assess the fit to probability distributions exponential, gamma and normal. The normal probability distribution presented the best fit to monthly rainfall series of Mato Grosso do Sul and it can be used for the estimation the monthly rainfall, especially in the rainy season months (October to March). The exponential probability distribution can be used for the estimation of monthly rainfall in the driest months of the year (May to September). Thus, we recommend that these distributions be used in future research, aimed to estimate the probable rainfall for the Mato Grosso do Sul State.

A statistical model for seismic hazard assessment of hydraulic‐fracturing‐induced seismicity

AbstractWe analyze the interevent time distribution of hydraulic‐fracturing‐induced seismicity collected during 18 stages at four different regions. We identify a universal statistical process describing the distribution of hydraulic‐fracturing‐induced events in time. The distribution of waiting times between subsequently occurring events is given by the exponential probability density function of the homogeneous Poisson process. Our findings suggest that hydraulic‐fracturing‐induced seismicity is directly triggered by the relaxation of stress and pore pressure perturbation initially created by the injection. Therefore, compared to this relaxation, the stress transfer caused by the occurrence of preceding seismic events is mainly insignificant for the seismogenesis of subsequently occurring events. We develop a statistical model to compute the occurrence probability of hydraulic‐fracturing‐induced seismicity. This model can be used to assess the seismic hazard associated with hydraulic fracturing operations. No aftershock triggering has to be included in the statistical model.

Modeling frequency distributions of tree height, diameter and crown area by six probability functions for open forests of Quercus persica in Iran

The prediction of the distribution of quantitative variables in a forest stand is of great interest to forest managers, for the evaluation of forest resources and scheduling of future silvicultural treatments. The aim of this research was to model the distribution of quantitative variables for Quercus persica in open forests in Iran. To investigate the probability distribution of trees in natural stands, 642 trees were selected for measurement using a systematic random sampling method. Selected trees were measured and data were analyzed. Gamma, beta, normal, lognormal, exponential and Weibull probability distributions were fitted to the height distribution of trees. Variables of distribution functions were estimated using the maximum likelihood estimation method. Actual probability and probability which derived from functions was compared using Kolmogorov–Smirnov and Anderson–Darling tests. Beta, Weibull and Weibull probability distributions explained the distributions of tree height, DBH and crown area.

Maximum Likelihood Estimation—A Reliable Statistical Method for Hydrate Nucleation Data Analysis

Analyses on hydrate nucleation and nucleation processes in general are assumed to require a large number of parallels due to the stochastic nature of the process. Stochastic processes are described by an exponential probability distribution. The present work adopts the Maximum Likelihood Estimation (MLE) with penalized estimators for data analysis in gas hydrate nucleation studies. Key parameters analyzed and discussed are nucleation rate and lag time during formation of critical size nuclei. The MLE technique is commonly used in analysis of other types of stochastic processes, but it has not, to our knowledge, previously been applied to hydrate nucleation. A total of six data sets, three on methane–propane hydrate nucleation from the present work, and three on general crystal nucleation extracted from the literature, were analyzed using the MLE. The MLE analysis was compared with a conventional method fitting the Experimental Probability Array to the exponential Probability Distribution Function (EPA-PDF...

이동 무선망의 경로 붕괴시간에 대한 통계적 분석

Mobile wireless networks have received a lot of attention as a future wireless network due to its rapid deployment without communication infrastructure. In these networks communication path between two arbitrary nodes break down because some links in the path are beyond transmission range() due to the mobility of the nodes. The set of total path break down time(), which is the union of path break down time of every node pair, can be a good measure of the connectivity of the dynamic mobile wireless network. In this paper we show that the distribution of the total path break down time can be approximated as a exponential probability density function and confirms it through experimental data. Statistical knowledge of break down time enables quantitative prediction of delay, packet loss between two nodes, thus provides confidence in the simulation results of mobile wireless networks.

Genomic inbreeding coefficients based on the distribution of the length of runs of homozygosity in a closed line of Iberian pigs.

BackgroundThe increasing availability of DNA markers provides new metrics of inbreeding based on single nucleotide polymorphisms (SNPs), i.e. molecular inbreeding or the proportion of runs of homozygosity (ROH), as alternatives to traditional pedigree-based inbreeding coefficients. However, none of these metrics incorporate the length of ROH as an indicator of recent inbreeding. Novel inbreeding coefficients that incorporate length of ROH as a random variable with an associated density are investigated.MethodsNew inbreeding metrics based on the distribution of the length of ROH are proposed: (1) the Kolmolgorov–Smirnov test, (2) a function of the quantiles of the cumulative distribution function of an individual versus the population, and (3) fitting of an exponential distribution to ROH lengths (mean, variance, and the probability of drawing at random a ROH larger than a given threshold). The new inbreeding and pedigree-based metrics were compared using 217 sows of an Iberian line that belong to three groups: C1 (conservation), C2 (conservation derived from C1), and S (selected and derived from C1), with complete pedigrees and genotyped for 35,023 SNPs.ResultsCorrelations between pedigree-based and the new genomic inbreeding coefficients ranged from 0.22 to 0.72 but most ranged from 0.60 to 0.70. The correlation between quantile chromosomal inbreeding coefficients (using molecular information of just one chromosome at the time) and chromosomal length was 0.84 (SE = 0.14), supporting the hypothesis that these coefficients incorporate information on ROH length as an indication of recent inbreeding. Kolmogorov–Smirnov and exponential chromosomal inbreeding coefficients were also correlated with chromosomal length (0.57). Chromosome 1 had the largest quantile ROH inbreeding coefficient (largest ROH sizes), whereas chromosome 10 had the lowest (shortest ROH sizes). Selection for lean growth increased ROH-based inbreeding coefficients for group S when compared to unselected groups C1 and C2. At the chromosomal level, this comparison showed that the level of autozygosity and the length of ROH for most of the autosomes increased in the selection line.ConclusionsQuantile and exponential probability inbreeding coefficients using ROH length as a random variable provide additional information about recent inbreeding compared to existing inbreeding coefficients such as molecular, pedigree-based or total ROH content inbreeding coefficients.Electronic supplementary materialThe online version of this article (doi:10.1186/s12711-015-0153-1) contains supplementary material, which is available to authorized users.