On a Skew t–discrete Gamma Alternative to the Normal-Poisson Model for Clustered Count Outcomes

The normal and Poisson distribution assumptions in the normal-Poisson mixed effects regression model are often too restrictive for many real count data. Several works have independently relaxed the Poisson conditional distribution assumption for counts or the normal distribution assumption for random effects. This work couples some recent advances in these two regards to develop a skew t–discrete gamma regression model in which the count outcomes have full dispersion flexibility and random effets can be skewed and heavy tailed. Inference in the model is achieved by maximum likelihood using pseudo-adaptive Gaussian quadature. The use of the proposal is demonstrated on a popular owl sibling negotiation data. It appears that, for this example, the proposed approach outperforms models based on normal random effects and the Poisson or negative binomial count distribution.

Optimal futures hedging strategies based on an improved kernel density estimation method

In this paper, we study the hedging effectiveness of crude oil futures on the basis of the lower partial moments (LPMs). An improved kernel density estimation method is proposed to estimate the optimal hedge ratio. We investigate crude oil price hedging by contributing to the literature in the following two-fold: first, unlike the existing studies which focus on univariate kernel density method, we use bivariate kernel density to calculate the estimated LPMs, wherein the two bandwidths of the bivariate kernel density are not limited to the same, which is our main innovation point. According to the criterion of minimizing the mean integrated square error, we derive the conditions that the optimal bandwidths satisfy. In the process of derivation, we make a distribution assumption “locally” in order to simplify calculation, but this type of “local” distribution assumption is far better than “global” distribution assumption used in parameter method theoretically and empirically. Second, in order to meet the requirement of bivariate kernel density for independent random variables, we adopt ARCH models to obtain the independent noises with related to the returns of crude oil spot and futures. Genetic algorithm is used to tune the parameters that maximize Quasi-likelihood. Empirical results reveal that, at first, the hedging strategy based on the improved kernel density estimation method is of highly efficiency, then it achieves better performance than the hedging strategy based on the traditional parametric method. We also compare the risk control effectiveness of static hedge ratio vs. time-varying hedge ratio, and find that static hedging has a better performance than time-varying hedging.

Relationship between noise-induced annoyance and age based on data of previous literatures

Many studies have investigated subjective responses to noise, but few concerned about the influence of age on the annoyance (discomfort) caused by noise. It is difficult to get a quantitative model featuring the relationship between noise-induced annoyance and age from one or several laboratory studies due to relatively small samples and limited age groups. This paper investigated recent studies (published after the year 2000) on noise-induced annoyance by the literature review method. We classified the studies according to their employed noise types and summarized the quantified subjective values and the ranges of age. The quantitative values of annoyance obtained from variable rating scales were transferred to a uniform scale and normalized. A probability density function then figured out the corresponding annoyance of a certain age under the small sample -distribution assumption. A predicting model of noise-induced annoyance from the age of 7-55 was proposed, which fitted previous data well.

In day 150 of COVID-19 disease, forecasting the number of cases and deaths in Turkey

Objective: This study aims to forecast the number of deaths and cases in Turkey 150 days after (6 August 2020) the first occurrence of COVID-19 in Turkey. The data used is from 10 March 2020 (the first day has seen of COVID-19 in Turkey) to 15 June 2020 and includes people of all ages from all provinces of Turkey. Material and Method: The relationship between cases, deaths, patients in intensive care units, intubated patients, and recovered patients, which are observations of COVID-19, was examined with a correlation matrix. Afterward, the ARIMA (0,2,4) model to forecast the number of COVID-19 cases in Turkey and the ARIMA(0,3,1) model to forecast the number of COVID-19 deaths in Turkey were established. Result: COVID-19 cases were forecasted that there may be 266.692 cases in Turkey on 6 August in the 1st model. Subsequently, a similar forecast has been made on COVID-19 deaths in Turkey on 6 August in the 2nd model. COVID-19 deaths were forecasted that there may be 5718. The p-values of these parameters of models were observed statistically significant (p<0.05). Later, the stationarity of ARIMA models related to these estimates was examined. According to the Augmented Dickey-Fuller (ADF) test results, ARIMA models were stationary and statistically convenient to use (p<0.05). Finally, the Jarque-Bera (JB) test examining the normal distribution assumption was applied and the models were found to be normally distributed. Conclusions: Consequently, there is an increase in both predicted cases and predicted deaths by the 150th day of COVID-19. These estimates show that the number of cases and deaths will not decrease to zero level until August 6. Factors such as the biological development of the COVID-19 virus, the rate of spread of COVID-19 disease, or the presence of COVID-19 therapy may not cause any increase in these observations. On the contrary, more than expected increase may occur in observed cases.

Position-Domain Non-Gaussian Error Overbounding for ARAIM

The non-Gaussian observation error is a threat for advanced receiver autonomous integrity monitoring (ARAIM), because the protection level of ARAIM based on the Gaussian distribution assumption is insufficient to envelope the positioning error (PE), and the probability of hazardously misleading information (PHMI) is difficult to be satisfied. The traditional non-Gaussian overbounding method is limited by the correlation among observation errors, and the deteriorated continuity risk resulting from the conservative inflation factor for overbounding, simultaneously. We propose an enhanced ARAIM method by position-domain non-Gaussian error overbounding. Furthermore, the upper bound of the inflation factor is imposed to release the conservativeness of overbounding. The simulation and the real-world data are utilized to test the proposed method. The simulation experiment has shown that the global worldwide availability level can be increased to 99.99% by using the proposed method. The real-word data experiment reveals that the proposed method can simultaneously satisfy the integrity risk and continuity risk with the boundary of the inflation factor.

Robust calibration of hierarchical population models for heterogeneous cell populations

Cellular heterogeneity is known to have important effects on signal processing and cellular decision making. To understand these processes, multiple classes of mathematical models have been introduced. The hierarchical population model builds a novel class which allows for the mechanistic description of heterogeneity and explicitly takes into account subpopulation structures. However, this model requires a parametric distribution assumption for the cell population and, so far, only the normal distribution has been employed. Here, we incorporate alternative distribution assumptions into the model, assess their robustness against outliers and evaluate their influence on the performance of model calibration in a simulation study and a real-world application example. We found that alternative distributions provide reliable parameter estimates even in the presence of outliers, and can in fact increase the convergence of model calibration.HighlightsGeneralizes hierarchical population model to various distribution assumptionsProvides framework for efficient calibration of the hierarchical population modelSimulation study and application to experimental data reveal improved robustness and optimization performance