Showing papers on "Cumulative distribution function published in 2015"
TL;DR: A novel GSA method, called PAWN, to efficiently compute density-based sensitivity indices, which is to characterise output distributions by their Cumulative Distribution Functions (CDF), which are easier to derive than PDFs.
Abstract: Variance-based approaches are widely used for Global Sensitivity Analysis (GSA) of environmental models. However, methods that consider the entire Probability Density Function (PDF) of the model output, rather than its variance only, are preferable in cases where variance is not an adequate proxy of uncertainty, e.g. when the output distribution is highly-skewed or when it is multi-modal. Still, the adoption of density-based methods has been limited so far, possibly because they are relatively more difficult to implement. Here we present a novel GSA method, called PAWN, to efficiently compute density-based sensitivity indices. The key idea is to characterise output distributions by their Cumulative Distribution Functions (CDF), which are easier to derive than PDFs. We discuss and demonstrate the advantages of PAWN through applications to numerical and environmental modelling examples. We expect PAWN to increase the application of density-based approaches and to be a complementary approach to variance-based GSA. We present a new density-based GSA method called PAWN to complement variance-based GSA.Differently from variance-based methods, PAWN can be applied to highly-skewed or multi-modal output distributions.Differently from other density-based methods, PAWN uses output CDFs, which simplifies numerical implementation.PAWN can be easily tailored to focus on output sub-ranges, for instance extreme values.Intermediate results generated in the application of PAWN can be visualized to gather insights about the model behaviour.
311 citations
TL;DR: A unified performance analysis of a dual-hop relay system over the asymmetric links composed of both radio-frequency and unified free-space optical links under the effect of pointing errors is carried out.
Abstract: In this paper, we carry out a unified performance analysis of a dual-hop relay system over the asymmetric links composed of both radio-frequency (RF) and unified free-space optical (FSO) links under the effect of pointing errors. Both fixed and variable gain relay systems are studied. The RF link is modeled by the Nakagami-m fading channel and the FSO link by the Gamma-Gamma fading channel subject to both types of detection techniques (i.e., heterodyne detection and intensity modulation with direct detection). In particular, we derive new unified closed-form expressions for the cumulative distribution function, the probability density function, the moment generating function (MGF), and the moments of the end-to-end signal-to-noise ratio (SNR) of these systems in terms of the Meijer's G function. Based on these formulas, we offer exact closed-form expressions for the outage probability (OP), the higher order amount of fading, and the average bit error rate (BER) of a variety of binary modulations in terms of the Meijer's G function. Furthermore, an exact closed-form expression of the end-to-end ergodic capacity is derived in terms of the bivariate G function. Additionally, by using the asymptotic expansion of the Meijer's G function at the high-SNR regime, we derive new asymptotic results for the OP, the MGF, and the average BER in terms of simple elementary functions.
253 citations
TL;DR: In this work, the performance and the capacity analysis of a fixed-gain amplify-and-forward (AF)-based dual-hop asymmetric radio frequency-free space optical (RF-FSO) communication system is performed and the effects of fading, turbulence, and pointing error are studied on the outage probability, average BER, and the channel capacity.
Abstract: In this work, the performance and the capacity analysis of a fixed-gain amplify-and-forward (AF)-based dual-hop asymmetric radio frequency–free space optical (RF–FSO) communication system is performed. The RF link experiences Nakagami-m fading and the FSO link experiences Gamma–Gamma turbulence. For this mixed RF–FSO cooperative system, novel and finite power series-based mathematical expressions for the cumulative distribution function, probability density function, and moment generating function of the end-to-end signal-to-noise ratio are derived. Using these channel statistics new finite power series-based analytical expressions are obtained for the outage probability, the average bit error rate (BER) for various binary and M-ary modulation techniques, and the average channel capacity of the considered system. The same analysis is also performed for the scenario when the FSO link undergoes significant pointing errors along with the Gamma–Gamma distributed turbulence. As a special case analytical expressions for the outage probability, BER, and channel capacity are also presented for a dual-hop asymmetric RF–FSO system where the RF link is Rayleigh distributed. Simulation results validate the proposed mathematical analysis. The effects of fading, turbulence, and pointing error are studied on the outage probability, average BER, and the channel capacity.
186 citations
TL;DR: A dual-hop amplify-and-forward (AF) relaying scheme over shadowed Rician fading channels is investigated, and some useful engineering insights are manifested, such as simplified asymptotic outage performance results, the diversity order, and the impact on the number of antennas at the source and the destination.
Abstract: A dual-hop amplify-and-forward (AF) relaying scheme over shadowed Rician fading channels is investigated. Specifically, the source and destination nodes are equipped with $N$ and $M$ antennas, respectively, whereas the relay is equipped with a single antenna. Communication via satellite relaying represents a direct application of the considered infrastructure. To this end, we study the scenario when the source and the destination are terrestrial nodes, whereas the end-to-end communication is established through an intermediate AF relay node, which is a satellite. To fully exploit the spatial diversity provided by multiple antennas, maximum ratio transmission and maximum ratio combining are implemented at the source and the destination, respectively. First, a new closed-form expression for the probability density function (pdf) of the sum of independent and identically distributed (i.i.d.) squared shadowed Rician random variables is derived by assuming integer distribution parameters. Capitalizing on the latter pdf, new closed-form results for the cumulative distribution function (cdf) and the moment function of the end-to-end signal-to-noise ratio (SNR) are obtained. Particularly, the proposed unified analysis includes the channel-state-information (CSI)-assisted and the fixed-gain AF relaying protocols. New expressions for important performance measures, namely, the outage probability, the average symbol error probability (ASEP), and the ergodic capacity of the end-to-end SNR, are presented for both AF schemes. Moreover, some useful engineering insights are manifested, such as simplified asymptotic outage performance results, the diversity order, and the impact on the number of antennas at the source and the destination.
157 citations
TL;DR: A unified performance analysis framework of a dual-hop relay system over asymmetric RF/FSO links is presented, which considers the RF link follows generalized κ-μ or η-μ distributions, while the FSO link experiences the gamma-gamma distribution, respectively.
Abstract: The mixed radio frequency (RF)/free-space optical (FSO) relaying is a promising technology for coverage improvement, while there lacks unified expressions to describe its performance. In this paper, a unified performance analysis framework of a dual-hop relay system over asymmetric RF/FSO links is presented. More specifically, we consider the RF link follows generalized $\kappa$ - $\mu$ or $\eta$ - $\mu$ distributions, while the FSO link experiences the gamma-gamma distribution, respectively. Novel analytical expressions of the probability density function and cumulative distribution function are derived. We then capitalize on these results to provide new exact analytical expressions of the outage probability and bit error rate (BER). Furthermore, the outage probability for high signal-to-noise ratios and the BER for different modulation schemes are deduced to provide useful insights into the impact of system and channel parameters of the overall system performance. These accurate expressions are general, since they correspond to generalized fading in the RF link and account for pointing errors, atmospheric turbulence, and different modulation schemes in the FSO link. The links between derived results and previous results are presented. Finally, numerical and Monte–Carlo simulation results are provided to demonstrate the validity of the proposed unified expressions.
127 citations
TL;DR: In this paper, the authors evaluated the seismic reliability of a base-isolated structure with friction pendulum isolators considering both isolator properties (i.e., coefficient of friction) and earthquake main characteristics as random variables.
125 citations
TL;DR: A new unified model is proposed that accounts for the impact of pointing errors and type of receiver detector in free-space optical systems and presents unified closed-form expressions for the cumulative distribution function, the probability density function, and the moment generating function of a single link FSO transmission system in terms of the Meijer's G-function.
Abstract: Starting with the double generalized Gamma (GG) model to describe turbulence-induced fading in free-space optical (FSO) systems, we propose a new unified model that accounts for the impact of pointing errors and type of receiver detector. More specifically, we present unified closed-form expressions for the cumulative distribution function, the probability density function, the moment generating function, and the moments of the end-to-end signal-to-noise ratio (SNR) of a single link FSO transmission system in terms of the Meijer's G-function. We then use these unified expressions to evaluate performance measures such as the bit error rate, the outage probability, and the ergodic capacity of: 1) a single FSO link operating over double GG fading model; and 2) asymmetric RF-FSO dual-hop relay transmission system with fixed gain relay. Using an asymptotic expansion of the Meijer's G-function at high SNR, we express all the expressions, derived earlier, in terms of elementary functions. All our analytical results are verified using computer based-Monte Carlo simulations.
110 citations
TL;DR: An analytical model for investigating the transient behavior of the RACHs with bursty arrivals generated in a specific time interval for orthogonal frequency-division multiple access (OFDMA) wireless networks is presented.
Abstract: Random access channels (RACHs) in cellular networks are normally designed for Poisson-distributed arrivals with a constant rate. Unexpected bursty arrivals may result in severe collisions in RACHs and thus degrade users' service qualities. This paper presents an analytical model for investigating the transient behavior of the RACHs with bursty arrivals generated in a specific time interval for orthogonal frequency-division multiple access (OFDMA) wireless networks. The proposed model has considered the implementation details of the OFDMA random access procedure (such as periodic access characteristic, uniform random backoff policy, and power-ramping effect) and the effect of new arrivals. The performance metrics of collision probability, success probability, and average access delay and the cumulative distribution function of the number of preamble transmissions and access delay for the successfully accessed mobile station are then derived based on the analytical model. The accuracy of the proposed analytical model was verified through computer simulations, and the results show the effectiveness of the proposed model.
103 citations
TL;DR: For this mixed RF-FSO cooperative system, novel closed-form mathematical expressions are derived for cumulative distribution function, probability density function and moment generating function of the equivalent signal-to-noise ratio in terms of Meijer-G function.
Abstract: In this study, the error performance and the capacity analysis is performed for the decode-and-forward based dual-hop asymmetric radio frequency-free space optical communication (RF-FSO) system. The RF link is characterised by Nakagami-
m
fading and the FSO link is characterised by path loss, Gamma-Gamma distributed turbulence and pointing error. For this mixed RF-FSO cooperative system, novel closed-form mathematical expressions are derived for cumulative distribution function, probability density function and moment generating function of the equivalent signal-to-noise ratio in terms of Meijer-G function. Using these channel statistics, new finite power series based analytical expressions are obtained for the outage probability, the average bit error rate for various binary and M
-ary modulation techniques and the average channel capacity of the considered system in terms of Meijer-G function. As a special case, the analytical framework can also be obtained for channel statistics and performance metrics of dual-hop mixed Rayleigh-Gamma-Gamma system. Simulation results validate the proposed mathematical analysis. The effects of fading, turbulence and pointing error are studied on the outage probability, average bit error rate and channel capacity of the asymmetric RF-FSO system.
95 citations
TL;DR: Using follow-up data from January 1975 to August 2009 collected in the Childhood Cancer Survivor Study, applications of mean cumulative count and cumulative incidence for the outcome of subsequent neoplasms are shown to demonstrate different but complementary information obtained from the 2 approaches and the specific utility of the former.
Abstract: Cumulative incidence has been widely used to estimate the cumulative probability of developing an event of interest by a given time, in the presence of competing risks. When it is of interest to measure the total burden of recurrent events in a population, however, the cumulative incidence method is not appropriate because it considers only the first occurrence of the event of interest for each individual in the analysis: Subsequent occurrences are not included. Here, we discuss a straightforward and intuitive method termed “mean cumulative count,” which reflects a summarization of all events that occur in the population by a given time, not just the first event for each subject. We explore the mathematical relationship between mean cumulative count and cumulative incidence. Detailed calculation of mean cumulative count is described by using a simple hypothetical example, and the computation code with an illustrative example is provided. Using follow-up data from January 1975 to August 2009 collected in the Childhood Cancer Survivor Study, we show applications of mean cumulative count and cumulative incidence for the outcome of subsequent neoplasms to demonstrate different but complementary information obtained from the 2 approaches and the specific utility of the former.
TL;DR: By deriving the asymptotic expressions for the outage probability and the symbol error rate, as well as the high SNR approximations of the ergodic capacity, new design insights are established under the two distinct constraint scenarios: 1) proportional interference power constraint, and 2) fixed interferencePower constraint.
Abstract: We consider transmit antenna selection with receive generalized selection combining (TAS/GSC) for cognitive decode-and-forward (DF) relaying in Nakagami- $m$ fading channels. In an effort to assess the performance, the probability density function and the cumulative distribution function of the end-to-end SNR are derived using the moment generating function, from which new exact closed-form expressions for the outage probability and the symbol error rate are derived. We then derive a new closed-form expression for the ergodic capacity. More important, by deriving the asymptotic expressions for the outage probability and the symbol error rate, as well as the high SNR approximations of the ergodic capacity, we establish new design insights under the two distinct constraint scenarios: 1) proportional interference power constraint, and 2) fixed interference power constraint. Several pivotal conclusions are reached. For the first scenario, the full diversity order of the outage probability and the symbol error rate is achieved, and the high SNR slope of the ergodic capacity is 1/2. For the second scenario, the diversity order of the outage probability and the symbol error rate is zero with error floors, and the high SNR slope of the ergodic capacity is zero with capacity ceiling.
01 Jan 2015
TL;DR: The probability of obtaining 0, 1, 2, 3, etc, events follows a simple mathematical formula developed by Poisson as mentioned in this paper, which describes methods for setting confidence limits, determining sample size, and comparing groups.
Abstract: Many rare events occur at random in time or space, for example, the number of radioactive disintegrations per minute or the number of bacteria per unit area of Petri dish The probability of obtaining 0, 1, 2, 3, etc, events follows a simple mathematical formula developed by Poisson After presenting the basic information, the chapter describes methods for setting confidence limits, determining sample size, and comparing groups Ways of determining cumulative probabilities are given, for example, how many nurses are needed to staff a delivery room that on average has 12 deliveries per day
TL;DR: A data-driven, nonparametric approach to reformulate (conditional) individual and joint chance constraints with right-hand side uncertainty into algebraic constraints by using kernel smoothing to approximate unknown true continuous probability density/distribution functions.
TL;DR: A heuristic load flow method considering the effects of intermittent behaviour of RERs and load is modelled in probabilistic load flow (PLF) algorithm, suitable for both radial and weakly meshed distribution networks with RER for operation and planning of microgrids.
Abstract: One of the basic components of future distribution networks is renewable energy resources (RER). The uncertainty in power production of renewable resources such as wind and solar as well as load is another characteristic of such networks. Conventional power flow methods may not be suitable for active distribution networks such as microgrids. In this study, a heuristic load flow method considering the effects of intermittent behaviour of RERs and load is modelled in probabilistic load flow (PLF) algorithm. The method is suitable for both radial and weakly meshed distribution networks with RER for operation and planning of microgrids. Imperialist competitive algorithm (ICA) as heuristic-based optimisation algorithm is applied to solve the PLF. Based on PLF technique, calculated parameters of the system such as bus voltages and feeders’ current are extracted as random variables. A modified version of IEEE 33-bus test system with RER is used to evaluate efficiency and capability of the algorithm. Results are compared with Monte Carlo simulation method. The probability density function and cumulative distribution function (CDF) of some network variable are compared. Based on the results, the presented approach can solve the PLF problem regardless of the type of distribution network.
TL;DR: This work investigates the performance of multi-antenna two-way relay networks, where both amplify-and-forward (AF) and decode- and- forward (DF) relaying strategies are considered and an antenna selection scheme among all nodes is proposed based on maximizing the worse received signal-to-noise ratio of two end users.
Abstract: We investigate the performance of multi-antenna two-way relay networks, where both amplify-and-forward (AF) and decode-and-forward (DF) relaying strategies are considered. First an antenna selection scheme among all nodes is proposed based on maximizing the worse received signal-to-noise ratio (SNR) of two end users. Then, we derive the probability density function (PDF) and cumulative distribution function (CDF) of the received SNRs of both users. We also obtain the closed-form expressions of average bit error rates (BER) and the outage probability of our system. Furthermore, we study the asymptotic behavior of our system when transmitting SNR or the number of antennas is large. The results show that the proposed antenna selection scheme achieves full diversity, and the simulation results closely match to our theoretical analysis. To further improve the spectrum efficiency of the system, a hybrid selection antenna scheme is proposed. Finally, the numerical results show that our scheme outperforms the state of art.
TL;DR: In this paper, the end-to-end performance of a multihop free-space optical system with amplify-and-forward channel-state-information-assisted or fixed-gain relays using intensity modulation with direct detection technique over Gamma-Gamma turbulence fading with pointing error impairments is studied.
Abstract: In this paper, the end-to-end performance of a multihop free-space optical system with amplify-and-forward channel-state-information-assisted or fixed-gain relays using intensity modulation with direct detection technique over Gamma–Gamma turbulence fading with pointing error impairments is studied. More specifically, novel closed-form results for the probability density function and the cumulative distribution function of the end-to-end signal-to-noise ratio (SNR) are derived in terms of the Fox's H function. Based on these formulas, closed form bounds for the outage probability, the average bit-error rate of on–off keying modulation scheme, the moments, and the ergodic capacity are presented. Furthermore, using the moments-based approach, tight asymptotic approximations at high- and low-average SNR regimes are derived for the ergodic capacity in terms of simple elementary functions. The obtained results indicate that the overall system performance degrades with an increase of the number of hops. The effects of the atmospheric turbulence conditions and the pointing error are also quantified. All the analytical results are verified via computer-based Monte-Carlo simulations.
TL;DR: In this paper, the authors used a log logistic probability density function (PDF) to best describe the behavior of cost overruns and used a cumulative distribution function to determine a realistic probability of a cost overrun being experienced from the point at which a contract is awarded.
Abstract: The determination of a project’s cost contingency is a pervasive problem as the amount that is incorporated into an estimate is invariably insufficient to accommodate a project’s actual cost overrun. The cost overruns experienced in 49 road construction projects procured using traditional lump contracts are analyzed. The theoretical probability distributions are fitted to cost overrun data derived from the sampled projects whose contract values ranged from AU $0.5 and AU $97 million. Goodness of fit tests are used in conjunction with probability-probability (P-P) plots to compare the sample distribution from the known theoretical distribution. A log logistic probability density function (PDF) was found to best describe the behavior of cost overruns. The cumulative distribution function is then used to determine a realistic probability of a cost overrun being experienced from the point at which a contract is awarded. This is required so that public sector clients can determine an appropriate contin...
TL;DR: A new command, kcdf, is presented, for bandwidth selection in kernel estimation of the cumulative distribution function, and its use with an application to artificial data is illustrated.
Abstract: I present a new command, kcdf, for bandwidth selection in kernel estimation of the cumulative distribution function. I briefly review plug-in and cross-validation bandwidth selectors, both of which are implemented in kcdf. I then describe the command syntax and illustrate its use with an application to artificial data.
21 Sep 2015
TL;DR: In this article, the arrival of molecules in molecular communication via diffusion (MCvD) is a counting process and exhibits binomial distribution by its nature, and both Poisson and Gaussian approximations of the binomial cumulative distribution function are used.
Abstract: The arrival of molecules in molecular communication via diffusion (MCvD) is a counting process and exhibits binomial distribution by its nature. Even if the arrival of molecules is described well by the binomial process, the binomial cumulative distribution function (CDF) is difficult to work with when considering consecutively sent symbols. Therefore, in the literature, Poisson and Gaussian approximations of the binomial distribution are used. In this paper, we analyze these two approximations of the binomial model of the arrival process in MCvD with drift. We investigate the regions in which either Poisson or Gaussian model is better in terms of root mean squared error (RMSE) of the CDFs with varying the distance, drift velocity, and the number of emitted molecules. Moreover, we confirm the boundaries of the region via numerical simulations and derive the error probabilities for continuous communication and analyze which model approximates it more accurately.
TL;DR: A general expression is derived for the complementary cumulative distribution function of a sum of K independent random variables, where each random variable is a product of an exponential and a Bernoulli random variable, and applied to find a simple closed-form expression that characterizes the system outage performance as a function of network parameters and node geometry.
Abstract: A cooperative wireless network, where a cluster of $K$ single-antenna transmitters jointly serve a single-antenna receiver, is considered. Each transmitter is connected to the control unit (CU) via independent but unreliable backhaul links. The CU sends a common message to each transmitter over backhaul links, which upon successful reception, jointly transmit this message to the intended receiver. To facilitate analysis, a general expression is derived for the complementary cumulative distribution function of a sum of $K$ independent random variables, where each random variable is a product of an exponential and a Bernoulli random variable. This result is applied to find a simple closed-form expression that characterizes the system outage performance as a function of network parameters and node geometry. The analytical model is validated using numerical simulations. As an application, the derived expression is also used for investigating the impact of backhaul assignment on the system performance.
09 Mar 2015
TL;DR: In this article, a dual-hop amplify-and-forward fixed gain relay system over asymmetric links composed of both radio-frequency (RF) and unified free-space optics (FSO) under the effect of pointing errors is analyzed.
Abstract: In this work, we carry out a unified performance analysis of a dual-hop amplify-and-forward fixed gain relay system over asymmetric links composed of both radio-frequency (RF) and unified free-space optics (FSO) under the effect of pointing errors. The RF link is modeled by the Nakagami-m fading channel and the FSO link by the Gamma-Gamma fading channel subject to both types of detection techniques (i.e. heterodyne detection and intensity modulation with direct detection (IM/DD)). In particular, we derive new unified closed-form expressions for the cumulative distribution function, the probability density function, the moment generating function, and the moments of the end-to-end signal-to-noise ratio of these systems in terms of the Meijer's G function. Based on these formulas, we offer exact closed-form expressions for the outage probability, the higher-order amount of fading, and the average bit-error rate of a variety of binary modulations in terms of the Meijer's G function. Further, an exact closed-form expression for the end-to-end ergodic capacity for the Nakagami-m-unified FSO relay links is derived in terms of the extended generalized bivariate Meijer's G function. All the given results are verified via computer-based Monte-Carlo simulations.
TL;DR: In this article, the authors studied one-dimensional exact scaling lognormal multiplicative chaos measures at criticality and determined the exact asymptotics of the right tail of the distribution of the total mass of the measure.
Abstract: We study one-dimensional exact scaling lognormal multiplicative chaos measures at criticality. Our main results are the determination of the exact asymptotics of the right tail of the distribution of the total mass of the measure, and an almost sure upper bound for the modulus of continuity of the cumulative distribution function of the measure. We also find an almost sure lower bound for the increments of the measure almost everywhere with respect to the measure itself, strong enough to show that the measure is supported on a set of Hausdorff dimension 0.
TL;DR: In this paper, the performance contrast of four statistical methods, i.e., energy pattern factor method, least squares regression method, method of moments and mean standard deviation method in estimating extensively used Weibull parameters for wind energy application at four selected locations of northern Ethiopia has been studied.
Abstract: Paramount two-parameter Weibull function has been extensively used to assess the wind energy potential. The performance contrast of four statistical methods, i.e., energy pattern factor method, least squares regression method, method of moments and mean standard deviation method in estimating extensively used Weibull parameters for wind energy application at four selected locations of northern Ethiopia has been studied. The contrast of statistical methods is compared through relative percentage error, root mean square error, mean percentage error, mean absolute percentage error, Chi-square error and analysis of variance (or) efficiency of the methods used. Test results evidently revealed that, least squares regression method presents better performance than other methods selected in the investigation. The least efficient methods to fit the Weibull distribution curves for the assessment of wind speed data especially for four selected locations are energy pattern factor method, method of moments and mean standard deviation. From the actual data analysis, it is found that if wind speed distribution matches well with the Weibull function, the above three methods are applicable, but if not, least squares regression method can be considered based
on the cross checks including energy potential and cumulative distribution function.
TL;DR: In this article, the authors studied the nature of exponential and Lindley distributions using different graphs of their probability density functions and cumulative distribution functions and obtained the expressions for the index of dispersion for both exponential distributions.
Abstract: In this paper, firstly the nature of exponential and Lindley distributions have been studied using different graphs of their probability density functions and cumulative distribution functions. The expressions for the index of dispersion for both exponential and Lindley distributions have been obtained and the conditions under which the exponential and Lindley distributions are over-dispersed, equidispersed, and under-dispersed has been given. Several real lifetimes data-sets has been fitted using exponential and Lindley distributions for comparative study and it has been shown that in some cases exponential distribution provides better fit than the Lindley distribution whereas in other cases Lindley distribution provides better fit than the exponential distribution.
TL;DR: In this paper, the authors studied the problem of maximizing a decision-maker's utility function when the utility function of the decisionmaker is bounded and the uncertainty set can only be specified by an uncertainty set and showed that a discretized version of the problem may be formulated as a linear program.
Abstract: In many situations, decision-makers need to exceed a random target or make decisions using expected utilities. These two situations are equivalent when a decision-maker’s utility function is increasing and bounded. This article focuses on the problem where the random target has a concave cumulative distribution function (cdf) or a risk-averse decision-maker’s utility is concave (alternatively, the probability density function (pdf) of the random target or the decision-maker’ marginal utility is decreasing) and the concave cdf or utility can only be specified by an uncertainty set. Specifically, a robust (maximin) framework is studied to facilitate decision making in such situations. Functional bounds on the random target’s cdf and pdf are used. Additional general auxiliary requirements may also be used to describe the uncertainty set. It is shown that a discretized version of the problem may be formulated as a linear program. A result showing the convergence of discretized models for uncertainty sets spec...
TL;DR: In this article, a parametric, bijective transformation to generate heavy tail versions of arbitrary random variables is presented, where the tail behavior of this heavy tail Lambert W × F X random variable depends on a tail parameter δ ≥ 0.
Abstract: I present a parametric, bijective transformation to generate heavy tail versions of arbitrary random variables. The tail behavior of this heavy tail Lambert W × F X random variable depends on a tail parameter δ ≥ 0: for δ = 0, Y ≡ X, for δ > 0 Y has heavier tails than X. For X being Gaussian it reduces to Tukey's h distribution. The Lambert W function provides an explicit inverse transformation, which can thus remove heavy tails from observed data. It also provides closed-form expressions for the cumulative distribution (cdf) and probability density function (pdf). As a special case, these yield analytic expression for Tukey's h pdf and cdf. Parameters can be estimated by maximum likelihood and applications to S&P 500 log-returns demonstrate the usefulness of the presented methodology. The R package Lambert W implements most of the introduced methodology and is publicly available on CRAN.
TL;DR: This work presents a generalized system model that can be used to analyze and design FSO communication systems and shows that the performances of both systems could be improved with large aperture diameters adopted for the structure parameters R and C selected.
Abstract: The performances of multihop parallel free-space optical (FSO) cooperative communication systems with decode-and-forward protocol under exponentiated Weibull (EW) fading channels have been investigated systematically. With the max-min criterion as the best path selection scheme, the probability density function and the cumulative distribution function of the max-min EW random variable are derived. The analytical expressions for the average bit error rate (ABER) and outage probability with identically and independently distributed (i.i.d.) links are then obtained, respectively. Based on it, the ABER for a non-identically and independently distributed (non-i.i.d.) FSO system is also deduced with the help of the Gauss-Laguerre quadrature rule. The ABER perfor- mance of the considered system are further analyzed, in detail, under different turbu- lence conditions, receiver aperture sizes, and structure parameters (R and C). The comparison between i.i.d. and non-i.i.d. FSO systems over EW fading channels shows that the performances of both systems could be improved with large aperture diameters adopted for the structure parameters R and C selected. Monte Carlo simulation is also provided to confirm the correctness of the analytical ABER expressions. This work pre- sents a generalized system model, and it can be used to analyze and design FSO com- munication systems.
TL;DR: In this paper, two model averaging methods are evaluated for merging forecasts for 12 locations, i.e., Bayesian model averaging (BMA) and Quantile Model Averaging (QMA), to optimize forecasting skill by weighting and merging statistical and dynamic forecasts.
Abstract: The Australian Bureau of Meteorology produces statistical and dynamic seasonal streamflow forecasts The statistical and dynamic forecasts are similarly reliable in ensemble spread; however, skill varies by catchment and season Therefore, it may be possible to optimize forecasting skill by weighting and merging statistical and dynamic forecasts Two model averaging methods are evaluated for merging forecasts for 12 locations The first method, Bayesian model averaging (BMA), applies averaging to forecast probability densities (and thus cumulative probabilities) for a given forecast variable value The second method, quantile model averaging (QMA), applies averaging to forecast variable values (quantiles) for a given cumulative probability (quantile fraction) BMA and QMA are found to perform similarly in terms of overall skill scores and reliability in ensemble spread Both methods improve forecast skill across catchments and seasons However, when both the statistical and dynamical forecasting approaches are skillful but produce, on special occasions, very different event forecasts, the BMA merged forecasts for these events can have unusually wide and bimodal distributions In contrast, the distributions of the QMA merged forecasts for these events are narrower, unimodal and generally more smoothly shaped, and are potentially more easily communicated to and interpreted by the forecast users Such special occasions are found to be rare However, every forecast counts in an operational service, and therefore the occasional contrast in merged forecasts between the two methods may be more significant than the indifference shown by the overall skill and reliability performance
TL;DR: In this article, a dynamic version of the cumulative Kullback-Leibler information has been proposed for past lifetimes, which is related to the concept of relative aging.
Abstract: The cumulative Kullback-Leibler information has been proposed recently as a suitable extension of Kullback-Leibler information to the cumulative distribution function. In this paper, we obtain various results on such a measure, with reference to its relation with other information measures and notions of reliability theory. We also provide some lower and upper bounds. A dynamic version of the cumulative Kullback-Leibler information is then proposed for past lifetimes. Furthermore, we investigate its monotonicity property, which is related to some new concepts of relative aging. Moreover, we propose an application to the failure of nanocomponents. Finally, in order to provide an application in image analysis, we introduce the empirical cumulative Kullback-Leibler information and prove an asymptotic result. Copyright © 2015John Wiley & Sons, Ltd.