Showing papers on "Cumulative distribution function published in 2014"

Statistical Characterization of $\kappa{ - }\mu$ Shadowed Fading

Abstract: This paper investigates a natural generalization of the κ - μ fading channel in which the line-of-sight (LOS) component is subject to shadowing. This fading distribution has a clear physical interpretation and good analytical properties and unifies the one-side Gaussian, Rayleigh, Nakagami- m, Rician, κ - μ, and Rician shadow fading distributions. The three basic statistical characterizations, i.e., probability density function (pdf), cumulative distribution function (cdf), and moment-generating function (mgf), of the κ - μ shadowed distribution are obtained in closed form. Then, it is also shown that the sum and maximum distributions of independent but arbitrarily distributed κ - μ shadowed variates can be expressed in closed form. This set of new statistical results is finally applied to modeling and analysis of several wireless communication systems, e.g., the proposed distribution has applications to land mobile satellite (LMS) communications and underwater acoustic communications (UAC).

On the Capacity of Decode-and-Forward Relaying over Rician Fading Channels

Abstract: In this letter, we derive the probability density function (PDF) and cumulative distribution function (CDF) of the minimum of two non-central Chi-square random variables with two degrees of freedom in terms of power series. With the help of the derived PDF and CDF, we obtain the exact ergodic capacity of the following adaptive protocols in a decode-and-forward (DF) cooperative system over dissimilar Rician fading channels: (i) constant power with optimal rate adaptation; (ii) optimal simultaneous power and rate adaptation; (iii) channel inversion with fixed rate. By using the analytical expressions of the capacity, it is observed that the optimal power and rate adaptation provides better capacity than the optimal rate adaptation with constant power from low to moderate signal-to-noise ratio values over dissimilar Rician fading channels. Despite low complexity, the channel inversion based adaptive transmission is shown to suffer from significant loss in capacity as compared to the other adaptive transmission based techniques over DF Rician channels.

Multihop Free-Space Optical Communications Over Turbulence Channels with Pointing Errors using Heterodyne Detection

Abstract: This paper proposes and analyzes the performance of the multihop free-space optical (FSO) communication links using a heterodyne differential phase-shift keying modulation scheme operating over a turbulence induced fading channel. A novel statistical fading channel model for multihop FSO systems using channel-state-information-assisted and fixed-gain relays is developed incorporating the atmospheric turbulence, pointing errors, and path-loss effects. The closed-form expressions for the moment generating function, probability density function, and cumulative distribution function of the multihop FSO channel are derived using Meijer's G-function. They are then used to derive the fundamental limits of the outage probability and average symbol error rate. Results confirm the performance loss as a function of the number of hops. Effects of the turbulence strength varying from weak-to-moderate and moderate-to-strong turbulence, geometric loss, and pointing errors are studied. The pointing errors can be mitigated by widening the beam at the expense of the received power level, whereas narrowing the beam can reduce the geometric loss at the cost of increased misalignment effects.

Solving Probabilistic Optimal Power Flow Problem Using Quasi Monte Carlo Method and Ninth-Order Polynomial Normal Transformation

Abstract: This paper aims at establishing the cumulative distribution function (CDF) of the output variable of the probabilistic optimal power flow. In the context of the probability weighted moment (PWM), the uncertainties in the power system are modelled by a ninth-order polynomial normal transformation (NPNT) technique, whereby the dependencies among the inputs are conveniently handled. The quasi-Monte Carlo simulation (MCS) is employed to get the statistical information of the outputs. Based on the PWMs of the output variable, the CDF is reconstructed by NPNT technique. Testing on a modified 118-bus system, results from the proposed method are compared against those from MCS. The proposed method demonstrates a high level of accuracy for the mean, standard deviation and CDF, while significantly reducing the computational burden.

Performance Analysis of Relay-Assisted All-Optical FSO Networks Over Strong Atmospheric Turbulence Channels With Pointing Errors

Abstract: In this study, we consider a relay-assisted free-space optical communication scheme over strong atmospheric turbulence channels with misalignment-induced pointing errors. The links from the source to the destination are assumed to be all-optical links. Assuming a variable gain relay with amplify-and-forward protocol, the electrical signal at the source is forwarded to the destination with the help of this relay through all-optical links. More specifically, we first present a cumulative density function (CDF) analysis for the end-to-end signal-to-noise ratio. Based on this CDF, the outage probability, bit-error rate, and average capacity of our proposed system are derived. Results show that the system diversity order is related to the minimum value of the channel parameters.

Outage Probability in Arbitrarily-Shaped Finite Wireless Networks

Abstract: This paper analyzes the outage performance in finite wireless networks. Unlike most prior works, which either assumed a specific network shape or considered a special location of the reference receiver, we propose two general frameworks for analytically computing the outage probability at any arbitrary location of an arbitrarily-shaped finite wireless network: (i) a moment generating function-based framework which is based on the numerical inversion of the Laplace transform of a cumulative distribution and (ii) a reference link power gain-based framework which exploits the distribution of the fading power gain between the reference transmitter and receiver. The outage probability is spatially averaged over both the fading distribution and the possible locations of the interferers. The boundary effects are accurately accounted for using the probability distribution function of the distance of a random node from the reference receiver. For the case of the node locations modeled by a Binomial point process and Nakagami-m fading channel, we demonstrate the use of the proposed frameworks to evaluate the outage probability at any location inside either a disk or polygon region. The analysis illustrates the location-dependent performance in finite wireless networks and highlights the importance of accurately modeling the boundary effects.

Drought characterization using a new copula-based trivariate approach

Abstract: Meteorological drought is a natural climatic phenomenon that occurs over various time scales and may cause significant economic, environmental and social damages. Three drought characteristics, namely duration, average severity and peak intensity, are important variables in water resources planning and decision making. This study presents a new method for construction of three-dimensional copulas to describe the joint distribution function of meteorological drought characteristics. Using the inference function for margins, the parameters for six types of copulas were tested to select the best-fitted copulas. According to the values of the log-likelihood function, Galambos, Frank and Clayton were the selected copula models to describe the dependence structure for pairs of duration–severity, severity–peak and duration–peak, respectively. Trivariate cumulative probability, conditional probability and drought return period were also investigated based on the derived copula-based joint distributions. The proposed model was evaluated over the observed data of a Qazvin synoptic station, and the results were compared with the empirical probabilities. For measuring the model accuracy, R 2, root mean square error (RMSE) and the Nash–Sutcliffe efficiency (NSE) criteria were used. Results indicated that R 2, RMSE and NSE were equal to 0.91, 0.098 and 0.668, respectively, which demonstrate sufficient accuracy of the proposed model. Drought probabilistic characteristics can provide useful information for water resource planning and management.

The Equivalent-in-Distribution (EiD)-Based Approach: On the Analysis of Cellular Networks Using Stochastic Geometry

Abstract: In this Letter, the Equivalent-in-Distribution (EiD)-based approach to the analysis of cellular networks is introduced It is based upon finding EiD representations of the aggregate other-cell interference of cellular networks, which lead to tractable and exact mathematical formulations of the Average Symbol Error Probability (ASEP) for arbitrary bi-dimensional modulations As a byproduct, a new lemma is introduced, which provides a single-integral expression of the ASEP in terms of the Complementary Cumulative Distribution Function (CCDF) of the Signal-to-Interference-plus-Noise-Ratio (SINR)

Input character estimation device and program

Abstract: PROBLEM TO BE SOLVED: To improve operability in inputting a sentence with flick input to a software keyboard.SOLUTION: An input character estimation device includes: a time-series input coordinate storage unit 3 for storing input coordinates when a user touches a touch panel display, in a time series; a character model storage unit 4 for defining character models for plural types of operation states for each character allocated to an operation button of a software keyboard, defining a probability density function for each state with two-dimensional coordinates being as a feature quantity, and storing the probability density function defined for each state for each character; a probability computation unit 5 for computing an occurrence probability of each character on the basis of the input coordinates and the character models; a cumulative probability memory unit 6 for storing a cumulative probability value obtained by cumulating probability values from the start of input by the user as a cumulative occurrence probability of each character; and an input candidate character selection unit 7 for selecting a character having the highest cumulative occurrence probability as an input candidate character.

System and Methods for Generating Price Sensitivity

Abstract: The present invention relates to systems and methods for calculating a segment's sensitivity to price changes. A histogram distribution is generated for transaction frequency by price as the initial part of the sensitivity analysis. The shape of this histogram may be used to extrapolate a sensitivity measure. This can be done in two distinct ways: statistical regression or slope approximation. For statistical regression, the inverse of the cumulative distribution function is first calculated. The slope of this function is determined to be the sensitivity; the steeper the curve the more sensitive the segment is to price changes. The second technique approximates the slope of the right hand side of the histogram in order to determine sensitivity.

The Beta-Gompertz Distribution

Abstract: In this paper, we introduce a new four-parameter generalized version of the Gompertz model which is called Beta-Gompertz (BG) distribution. It includes some well-known lifetime distributions such as beta-exponential and generalized Gompertz distributions as special sub-models. This new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a decreasing, increasing, and bathtub-shaped failure rate function depending on its parameters. Some mathematical properties of the new distribution, such as closed-form expressions for the density, cumulative distribution, hazard rate function, the $k$th order moment, moment generating function, Shannon entropy, and the quantile measure are provided. We discuss maximum likelihood estimation of the BG parameters from one observed sample and derive the observed Fisher's information matrix. A simulation study is performed in order to investigate this proposed estimator for parameters. At the end, in order to show the BG distribution flexibility, an application using a real data set is presented.

Random variables, monotone relations, and convex analysis

Abstract: Random variables can be described by their cumulative distribution functions, a class of nondecreasing functions on the real line. Those functions can in turn be identified, after the possible vertical gaps in their graphs are filled in, with maximal monotone relations. Such relations are known to be the subdifferentials of convex functions. Analysis of these connections yields new insights. The generalized inversion operation between distribution functions and quantile functions corresponds to graphical inversion of monotone relations. In subdifferential terms, it corresponds to passing to conjugate convex functions under the Legendre---Fenchel transform. Among other things, this shows that convergence in distribution for sequences of random variables is equivalent to graphical convergence of the monotone relations and epigraphical convergence of the associated convex functions. Measures of risk that employ quantiles (VaR) and superquantiles (CVaR), either individually or in mixtures, are illuminated in this way. Formulas for their calculation are seen from a perspective that reveals how they were discovered. The approach leads further to developments in which the superquantiles for a given distribution are interpreted as the quantiles for an overlying "superdistribution." In this way a generalization of Koenker---Basset error is derived which lays a foundation for superquantile regression as a higher-order extension of quantile regression.

Stable Distributions as Noise Models for Molecular Communication

Abstract: In this work, we consider diffusion-based molecular communication timing channels. Three different timing channels are presented based on three different modulation techniques, i.e., i) modulation of the release timing of the information particles, ii) modulation on the time between two consecutive information particles of the same type, and iii) modulation on the time between two consecutive information particles of different types. We show that each channel can be represented as an additive noise channel, where the noise follows one of the subclasses of stable distributions. We provide expressions for the probability density function of the noise terms, and numerical evaluations for the probability density function and cumulative density function. We also show that the tails are longer than Gaussian distribution, as expected.

On the Performance Analysis of Hybrid ARQ With Incremental Redundancy and With Code Combining Over Free-Space Optical Channels With Pointing Errors

Abstract: In this paper, we investigate the performance of hybrid automatic repeat request (HARQ) with incremental redundancy (IR) and with code combining (CC) from an information-theoretic perspective over a point-to-point free-space optical (FSO) system. First, we introduce new closed-form expressions for the probability density function, the cumulative distribution function, the moment generating function, and the moments of an FSO link modeled by the Gamma fading channel subject to pointing errors and using intensity modulation with direct detection technique at the receiver. Based on these formulas, we derive exact results for the average bit error rate and the capacity in terms of Meijer's G functions. Moreover, we present asymptotic expressions by utilizing the Meijer's G function expansion and using the moments method, too, for the ergodic capacity approximations. Then, we provide novel analytical expressions for the outage probability, the average number of transmissions, and the average transmission rate for HARQ with IR, assuming a maximum number of rounds for the HARQ protocol. Besides, we offer asymptotic expressions for these results in terms of simple elementary functions. Additionally, we compare the performance of HARQ with IR and HARQ with CC. Our analysis demonstrates that HARQ with IR outperforms HARQ with CC.

On the empirical multilinear copula process for count data

Abstract: Continuation refers to the operation by which the cumulative distribution function of a discontinuous random vector is made continuous through multilinear interpolation The copula that results from the application of this technique to the classical empirical copula is either called the multilinear or the checkerboard copula As shown by Genest and Neslehova (Astin Bull 37 (2007) 475-515) and Neslehova (J Multivariate Anal 98 (2007) 544-567), this copula plays a central role in characterizing dependence concepts in discrete random vectors In this paper, the authors establish the asymptotic behavior of the empirical process associated with the multilinear copula based on $d$-variate count data This empirical process does not generally converge in law on the space $\mathcal {C}([0,1]^d)$ of continuous functions on $[0,1]^d$, equipped with the uniform norm However, the authors show that the process converges in $\mathcal{C}(K)$ for any compact $K\subset\mathcal{O}$, where $\mathcal{O}$ is a dense open subset of $[0,1]^d$, whose complement is the Cartesian product of the ranges of the marginal distribution functions This result is sufficient to deduce the weak limit of many functionals of the process, including classical statistics for monotone trend It also leads to a powerful and consistent test of independence which is applicable even to sparse contingency tables whose dimension is sample size dependent

Blind Identification of Spatial Multiplexing and Alamouti Space-Time Block Code via Kolmogorov-Smirnov (K-S) Test

Abstract: A novel algorithm for blind identification of spatial multiplexing and Alamouti space-time block code is proposed in this paper. It relies on the Kolmogrov-Smirnov test, and employs the maximum distance between the empirical cumulative distribution functions of two statistics derived from the received signal. The proposed algorithm does not require estimation of the channel coefficients, noise statistics and modulation type, and is robust to the carrier frequency offset and impulsive noise. Additionally, it outperforms the algorithms in the literature under a variety of transmission impairments.

Modelling seed germination in response to continuous variables: use and limitations of probit analysis and alternative approaches

Abstract: Probit-based models relating a proportional response variable to a temporal explanatory variable, assuming that the times to response are normally distributed within the population, have been used in seed biology for describing the rate of loss of viability during seed ageing and the progress of germination over time in response to environmental signals (e.g. water, temperature). These models may be expressed as generalized linear models (GLMs) with a probit (cumulative normal distribution) link function, and, using GLM fitting procedures in current statistical software, parameters of these models are efficiently estimated while taking into account the binomial error distribution of the dependent variable. The fitted parameters can then be used to calculate the ‘traditional’ model parameters, such as the hydro- or hydrothermal time constant, the mean or median response of the seeds (e.g. mean time to death, median base water potential), and the standard deviation of the normal distribution of that response. Furthermore, through consideration of the deviance and residuals, performing model evaluation and modification can lead to improved understanding of the underlying physiological/ecological processes. However, fitting a binomial GLM is not appropriate for the cumulative count data often collected from germination studies, as successive observations are not independent, and time-to-event/survival analysis should be considered instead. This review discusses well-known probit-based models, providing advice on how to collect appropriate data and fit the models to those data, and gives an overview of alternative analysis approaches to improve understanding of the underlying mechanisms of seed dormancy and germination behaviour.

PLC Performance Analysis Assuming BPSK Modulation Over Nakagami- $m$ Additive Noise

Abstract: In this letter, we derive a maximum likelihood receiver of binary phase shift keying signals over Nakagami- $m$ distributed additive noise in power line communication system. The decision variable is characterized by using copula approach. The analytical average bit error rate of the considered scheme is numerically evaluated by using the cumulative distribution function of the decision variable. It is shown by simulations that the proposed receiver performs significantly better than an existing suboptimal receiver.

Outage Probability Analysis in Generalized Fading Channels with Co-Channel Interference and Background Noise: η-μ/η-μ, η-μ/κ-μ, and κ-μ/η-μ Scenarios

Abstract: In this paper, we present expressions for the cumulative distribution function (CDF) of a specially constructed random variable (RV) represented by the ratio of two generalized RVs. The obtained theoretical results are used to evaluate the outage probability in scenarios with η-μ-faded signals of interest (SoI), η-μ- or κ-μ-faded co-channel interference (CCI), and background white Gaussian noise. Our results are applicable also to scenarios where the SoI passes through the κ-μ fading channel, and the interfering signals are η-μ-faded. The derived results can be used if all parameters μi of the η-μ models representing the statistical distributions of either the SoI components or CCI components are integers. We prove, in particular, that in the former case, the CDF is expressed in terms of elementary functions.

Mean-value first-order saddlepoint approximation based collaborative optimization for multidisciplinary problems under aleatory uncertainty

Abstract: Reliability-based multidisciplinary design optimization (RBMDO) has received increasing attention in engineering design for achieving high reliability and safety in complex and coupling systems (e.g., multidisciplinary systems). Mean-value first-order saddlepoint approximation (MVFOSA) is introduced in this paper and is combined with the collaborative optimization (CO) method for reliability analysis under aleatory uncertainty in RBMDO. Similar to the mean-value first-order second moment (MVFOSM) method, MVFOSA approximated the performance function with the first-order Taylor expansion at the mean values of random variables. MVFOSA uses saddlepoint approximation rather than the first two moments of the random variables to estimate the probability density and cumulative distribution functions. MVFOSA-based CO (MVFOSA-CO) is also formulated and proposed. Two examples are provided to show the accuracy and efficiency of the MVFOSA-CO method.

An illustration of the effect of various sources of uncertainty on DNA likelihood ratio calculations

Abstract: A typical assessment of the strength of forensic DNA evidence is based on a population genetic model and estimated allele frequencies determined from a population database. Some experts provide a confidence or credible interval which takes into account the sampling variation inherent in deriving these estimates from only a sample of a total population. This interval is given in conjunction with the statistic of interest, be it a likelihood ratio (LR), match probability, or cumulative probability of inclusion. Bayesian methods of addressing database sampling variation produce a distribution for the statistic from which the bound(s) of the desired interval can be determined. Population database sampling uncertainty represents only one of the sources of uncertainty that affects estimation of the strength of DNA evidence. There are other uncertainties which can potentially have a much larger effect on the statistic such as, those inherent in the value of F st , the weights given to genotype combinations in a continuous interpretation model, and the composition of the relevant population. In this paper we model the effect of each of these sources of uncertainty on a likelihood ratio (LR) calculation and demonstrate how changes in the distribution of these parameters affect the reported value. In addition, we illustrate the impact the different approaches of accounting for sampling uncertainties has on the LR for a four person mixture.

Discrete Pareto Distributions

Abstract: We review several common discretization schemes and study a particular class of power-tail probability distributions on integers, obtained by discretizing continuous Pareto II (Lomax) distribution through one of them. Our results include expressions for the density and cumulative distribution functions, probability generating function, moments and related parameters, stability and divisibility properties, stochastic representations, and limiting distributions of random sums with discrete-Pareto number of terms. We also briefly discuss issues of simulation and estimation and extensions to multivariate setting.