A Stochastic Condensation Mechanism for Inducing Underdispersion in Count Models

It is quite easy to stochastically distort an original count variable to obtain a new count variable with relatively more variability than in the original variable. Many popular overdispersion models (variance greater than mean) can indeed be obtained by mixtures, compounding or randomlystopped sums. There is no analogous stochastic mechanism for the construction of underdispersed count variables (variance less than mean), starting from an original count distribution of interest. This work proposes a generic method to stochastically distort an original count variable to obtain a new count variable with relatively less variability than in the original variable. The proposed mechanism, termed condensation, attracts probability masses from the quantiles in the tails of the original distribution and redirect them toward quantiles around the expected value. If the original distribution can be simulated, then the simulation of variates from a condensed distribution is straightforward. Moreover, condensed distributions have a simple mean-parametrization, a characteristic useful in a count regression context. An application to the negative binomial distribution resulted in a distribution allowing under, equi and overdispersion. In addition to graphical insights, fields of applications of special cases of condensed Poisson and condensed negative binomial distributions were pointed out as an indication of the potential of condensation for a flexible analysis of count data

Design and Preliminary Analysis of the Variable Axisymmetric Divergent Bypass Dual Throat Nozzle

Turbofan engines with afterburners usually have variable nozzle throat area, and the nozzle throat area may increase by 50–100% during afterburning. An axisymmetric divergent bypass dual throat nozzle (ADBDTN) can offer high thrust vectoring efficiency without requiring additional secondary flow in the pitch and yaw directions. In this study, a variable ADBDTN configuration with flow adaptive capability, wide nozzle throat area adjustment range, and excellent overall performance was designed and investigated numerically. The nozzle throat and exit area can be controlled mechanically, while thrust vectoring is achieved via fluidic methods. Both the original variable geometry schemes and their corresponding improved schemes, namely, “slider-rocker mechanism & rotation” (SRM-R) and “slider-rocker mechanism & slide” (SRM-S) schemes, along with their improved schemes, were proposed and investigated. Results indicated that compared to the original variable geometry schemes, the nozzle configurations with improved variable geometry schemes not only achieve 50% increase in the nozzle throat area but also acquire flow adaptive capability and excellent overall performance by appropriately adjusting the nozzle exit area. At a nozzle pressure ratio (NPR) of 4.47, the highest thrust coefficient reaches 0.940; the largest pitch thrust-vector angle is 19.52 deg; and the discharge coefficients are 0.968 and 0.970 under the nonafterburning and afterburning states, respectively. In addition, compared to the improved SRM-R scheme, the nozzle configuration with improved SRM-S scheme possesses better overall performance.

Geostatistical interpolation by quantile kriging

The widely applied geostatistical interpolation methods of ordinary kriging (OK) or external drift kriging (EDK) interpolate the variable of interest to the unknown location, providing a linear estimator and an estimation variance as measure of uncertainty. The methods implicitly pose the assumption of Gaussianity on the observations, which is not given for many variables. The resulting “best linear and unbiased estimator” from the subsequent interpolation optimizes the mean error over many realizations for the entire spatial domain and, therefore, allows a systematic under-(over-)estimation of the variable in regions of relatively high (low) observations. In case of a variable with observed time series, the spatial marginal distributions are estimated separately for one time step after the other, and the errors from the interpolations might accumulate over time in regions of relatively extreme observations. Therefore, we propose the interpolation method of quantile kriging (QK) with a two-step procedure prior to interpolation: we firstly estimate distributions of the variable over time at the observation locations and then estimate the marginal distributions over space for every given time step. For this purpose, a distribution function is selected and fitted to the observed time series at every observation location, thus converting the variable into quantiles and defining parameters. At a given time step, the quantiles from all observation locations are then transformed into a Gaussian-distributed variable by a 2-fold quantile–quantile transformation with the beta- and normal-distribution function. The spatio-temporal description of the proposed method accommodates skewed marginal distributions and resolves the spatial non-stationarity of the original variable. The Gaussian-distributed variable and the distribution parameters are now interpolated by OK and EDK. At the unknown location, the resulting outcomes are reconverted back into the estimator and the estimation variance of the original variable. As a summary, QK newly incorporates information from the temporal axis for its spatial marginal distribution and subsequent interpolation and, therefore, could be interpreted as a space–time version of probability kriging. In this study, QK is applied for the variable of observed monthly precipitation from raingauges in South Africa. The estimators and estimation variances from the interpolation are compared to the respective outcomes from OK and EDK. The cross-validations show that QK improves the estimator and the estimation variance for most of the selected objective functions. QK further enables the reduction of the temporal bias at locations of extreme observations. The performance of QK, however, declines when many zero-value observations are present in the input data. It is further revealed that QK relates the magnitude of its estimator with the magnitude of the respective estimation variance as opposed to the traditional methods of OK and EDK, whose estimation variances do only depend on the spatial configuration of the observation locations and the model settings.

Geostatistical interpolation by Quantile Kriging

The widely applied geostatistical interpolation methods of Ordinary Kriging (OK) or External Drift Kriging (EDK) interpolate the variable of interest to the unknown location, providing a linear estimator and an estimation variance as measure of uncertainty. The methods implicitly pose the assumption of Gaussianity on the observations, which is not given for many variables. The resulting best linear and unbiased estimator from the subsequent interpolation optimizes the mean error over many realizations for the entire spatial domain and, therefore, allows a systematic under- (over-) estimation of the variable in regions of relatively high (low) observations. In case of a variable with observed time-series, the spatial marginal distributions are estimated separately for one time step after the other, and the errors from the interpolations might accumulate over time in regions of relatively extreme observations. Therefore, we propose the interpolation method of Quantile Kriging (QK) with a two step procedure prior to interpolation: we firstly estimate distributions of the variable over time at the observation locations and then estimate the marginal distributions over space for every given time step. For this purpose, a distribution function is selected and fitted to the observed time-series at every observation location, thus converting the variable into quantiles and defining parameters. At a given time step, the quantiles from all observation locations are then transformed into a Gaussian-distributed variable by a twofold quantile-quantile transformation with the Beta- and the Normal-distribution function. The spatio-temporal description of the proposed method accommodates skewed marginal distributions and resolves the spatial non-stationarity of the original variable. The Gaussian-distributed variable and the distribution parameters are now interpolated by OK and EDK. At the unknown location, the resulting outcomes are reconverted back into the estimator and the estimation variance of the original variable. As a summary, QK newly incorporates information from the temporal axis for its spatial marginal distribution and subsequent interpolation and, therefore, could be interpreted as a space-time version of Probability Kriging. In this study, QK is applied for the variable of observed monthly precipitation from raingauges in South Africa. The estimators and estimation variances from the interpolation are compared to the respective outcomes from OK and EDK. The cross-validations shows that QK improves the estimator and the estimation variance for most of the selected objective functions. QK further enables the reduction of the temporal bias at locations of extreme observations. The performance of QK, however, declines when many zero-value observations are present in the input data. It is further revealed that QK relates the magnitude of its estimator with the magnitude of the respective estimation variance as opposed to the traditional methods of OK and EDK, whose estimation variances do only depend on the spatial configuration of the observation locations and the model settings.

Entropie analysis of floating car data systems

The knowledge of the actual traffic state is a basic prerequisite of modern traffic telematic systems. Floating Car Data (FCD) systems are becoming more and more important for the provision of actual and reliable traffic data. In these systems the vehicle velocity is the original variable for the evaluation of the current traffic condition. As real FCDsystems are operating under conditions of limited transmission and processing capacity the analysis of the original variable vehicle speed is of special interest. Entropy considerations are especially useful for the deduction of fundamental restrictions and limitations. The paper analyses velocity-time profiles by means of information entropy. It emphasises in quantification of the information content of velocity-time profiles and the discussion of entropy dynamic in velocity-time profiles. Investigations are based on empirical data derived during field trials. The analysis of entropy dynamic is carried out in two different ways. On one hand velocity differences within a certain interval of time are used, on the other hand the transinformation between velocities in certain time distances was evaluated. One important result is an optimal sample-rate for the detection of velocity data in FCD-systems. The influence of spatial segmentation and of different states of traffic was discussed.

The variance of a truncated mixed exponential process

Mullooly (1988) provides sufficient conditions under which the variance of a left-truncated, non-negative random variable will be greater than the variance of the original variable. We consider this problem for the class of exponential mixtures, and provide an explicit expression for the inflation in variance in terms of the mixing density.

The variance of a truncated mixed exponential process

Mullooly (1988) provides sufficient conditions under which the variance of a left-truncated, non-negative random variable will be greater than the variance of the original variable. We consider this problem for the class of exponential mixtures, and provide an explicit expression for the inflation in variance in terms of the mixing density.