Characterization of an Instrument Model for Exoplanet Transit Spectrum Estimation through Wide-scale Analysis on HST Data

Instrument models (IMs) enable the reduction of systematic error in transit spectroscopy light-curve data, but, since the model formulation can influence the estimation of science model parameters, characterization of the instrument model effects is crucial to the interpretation of the reduced data. We analyze a simple instrument model and assess its validity and performance across Hubble WFC3 and STIS instruments. Over a large, n = 63, sample of observed targets, a Markov chain Monte Carlo sampler computes the parent distribution of each instrument model parameter. Possible parent distribution functions are then fit and tested against the empirical IM distribution. Correlation and other analyses are then performed to find IM relationships. The model is shown to perform well across the two instruments and three filters analyzed and, further, the Student’s t distribution is shown to closely fit the empirical parent distribution of IM parameters and the Gaussian distribution is shown to poorly model the observed distribution. This parent distribution can be used in the MCMC prior fitting and demonstrates IM consistency for wide-scale atmospheric analysis using this model. Finally, we propose a simple metric based on light-curve residuals to determine model performance, and we demonstrate its ability to determine whether a derived spectrum under this IM is high quality and robust.

Properties and Applications of a New Family of Skew Distributions

We introduce two families of continuous distribution functions with not-necessarily symmetric densities, which contain a parent distribution as a special case. The two families proposed depend on two parameters and are presented as an alternative to the skew normal distribution and other proposals in the statistical literature. The density functions of these new families are given by a closed expression which allows us to easily compute probabilities, moments and related quantities. The second family can exhibit bimodality and its standardized fourth central moment (kurtosis) can be lower than that of the Azzalini skew normal distribution. Since the second proposed family can be bimodal we fit two well-known data set with this feature as applications. We concentrate attention on the case in which the normal distribution is the parent distribution but some consideration is given to other parent distributions, such as the logistic distribution.

Weighted Cumulative Residual (Past) Inaccuracy For Minimum (Maximum) of Order Statistics

In this paper, we propose a measure of weighted cumulative residual inaccuracy between survival function of the first-order statistic and parent survival function $\bar{F}$. We also consider weighted cumulative inaccuracy measure between distribution of the last- order statistic and parent distribution $F$. For these concepts, we obtain some reliability properties and characterization results such as relationships with other functions, bounds, stochastic ordering and effect of linear transformation. Dynamic versions of these weighted measures are considered.

Modelling counts with state-dependent zero inflation

We introduce a state-dependent zero-inflation mechanism for count distributions with unbounded or bounded support. Instead of uniformly downweighting the parent distribution, this flexible approach allows us to generate most of the zeros from either low or high counts. We derive the stochastic properties of the inflated distributions and discuss special instances designed for zero inflation caused by, for example, excessive demand or underreporting. Furthermore, we apply the state-dependent zero-inflation mechanism to generalize existing models for count time series with bounded support.

Threshold selection for extreme value estimation of vehicle load effect on bridges

In the design and condition assessment of bridges, the extreme vehicle load effects are necessary to be taken into consideration, which may occur during the service period of bridges. In order to obtain an accurate extrapolation of the extreme value based on limited duration, threshold selection is a critical step in the peak-over-threshold method. Overly high threshold results in little information to be used and excessively low threshold leads to large bias in parameters estimation of generalized Pareto distribution. To investigate this issue, 417 days of strain data acquired from the long-term structural health monitoring system of Taiping Lake Bridge in China are employed in this article. According to the tail distribution of the strain data induced by vehicle loads, four homothetic distributions are chosen as its parent distribution, from which lots of random samples are generated by the Monte Carlo method. For each parent distribution, the 100-yearly extreme values at different thresholds are estimated and compared with the theoretical value based on those samples. Then a simple and empirical threshold selection method is proposed and applied to estimate the weekly extreme strain due to vehicle loads on the Taiping Lake Bridge. Results show that the estimate on the basis of the threshold obtained by the proposed method is closer to the measured result than the commonly used methods. The proposed method can be an effective threshold selection tool for the extreme value estimation of vehicle load effect in future engineering practice.

Transmuted Singh-Maddala Distribution: A new Flexible and Upside-Down Bathtub Shaped Hazard Function Distribution

The Singh-Maddala distribution is very popular to analyze the data on income, expenditure, actuarial, environmental, and reliability related studies. To enhance its scope and application, we propose four parameters transmutedSingh-Maddala distribution, in this study. The proposed distribution is relatively more flexible than the parent distribution to model a variety of data sets. Its basic statistical properties, reliability function, and behaviors of the hazard function are derived. The hazard function showed the decreasing and an upside-down bathtub shape that is required in various survival analysis. The order statistics and generalized TL-moments with their special cases such as L-, TL-, LL-, and LH-moments are also explored. Furthermore, the maximum likelihood estimation is used to estimate the unknown parameters of the transmuted Singh-Maddala distribution. The real data sets are considered to illustrate the utility and potential of the proposed model. The results indicate that the transmuted Singh-Maddala distribution models the datasets better than its parent distribution.

The core dominance parameter for gamma-ray loud blazars

In this work, we compiled 604 blazars with available core-dominance parameter, out of which 149 blazars are known to have γ-ray emissions. We compared the logR between the 149 Fermi-detected blazars (FDB) and the rest non-Fermi-detected blazars (non-FDB), and found that the average values are < logR > = 1.12 ± 0.88 for FDBs and < logR > = 0.05 ± 0.94 for non-FDBs. A K-S test shows that the probability for the distributions of FDB and non-FDB to come from the same parent distribution is P = 2.38 × 10−7. We also investigated the correlation between the core-dominance parameters and the γ-ray emission variability index (VI) for 125 FDBs (45 BLs and 79 FSRQs), and found that there is a tendency for VI to increase with the core-dominance parameter for 79 FSRQs, but there is no such tendency for 46 BLs.

Probabilistic Methodology for Design of Arctic Ships

With the increased demand for hydrocarbon and mineral resources, as well as tourism, marine transportation in the arctic continues to increase. The region is harsh and fragile, making safety and environmental protection paramount. A key concern is how to estimate extreme design events that first and foremost satisfy safety and then economy. A rational approach to design of arctic ships based on probabilistic methods is detailed in this paper, including global impact forces and local panel design. Using a probabilistic approach, extreme design events can be identified by combining annual, seasonal and regional variability in environmental conditions with model uncertainty, and integrating these directly in the design methodology. Extreme design loads are estimated based on the annual number of interaction events, and the design strategy - target exceedence criteria established based on general public safety. The approach also provides a comprehensive basis for the selection of an appropriate ice class given certain operational requirements (e.g. an icebreaker for facility protection, or suitability of a cruise liner, having minimal ice class, to operate through a particular season). Otherwise, design for extremes is largely based on observational experience and judgment from one or more experts and such experience only reflects a relatively short span of natural occurrence. Neither is it appropriate to arbitrarily establish the most extreme condition imaginable. For extremal analysis, a parent distribution of global impact forces is first developed either through numerical ship-ice simulations or directly from measured full scale ship ram trial data. Using the parent distribution, and the expected annual number of ram events, a new design distribution representing the maximum of n annual force events is developed. Based on the global analysis, mean penetration and duration can be estimated which, when combined with number of interactions per year, provides a measure of exposure, a key input for local design analysis. A rational local pressure design model is presented that is derived based on measured ship ram data. Peak pressures through the full ram duration are considered and not just realizations at some arbitrary point of maximum force. A local scale effect is measured where pressures on smaller areas (i.e. <10m2) increase considerably above the global scale effect. A design pressure area curve based on a design strategy (e.g. 100 yr return period) is produced. A hypothetical design illustration is provided for a ship along a particular route including estimates of global forces and local design pressures. A linear trend in forces based on logarithmic trend in number of ramming events is observed. This illustrates that linking the design forces and pressures directly with expected number of interaction events is most reasonable and appropriate. Vertical impact forces estimated using the Polar Class rules are compared with estimates using the rational probabilistic approach and measured full scale MV Arctic data. The analysis illustrates how measured forces and expected exposure can be used for design and classification, as well as calibration. Preliminary results indicate that the higher PC1 and PC2 class forces seem rather conservative and a large gap exists between PC2 and PC3. Further calibration is needed. Introducing different design strategies (e.g. elastic-plastic and fully plastic) for corresponding load levels (e.g. 10−2extreme and 10−4abnormal) should be considered, allowing the designer to better understand the performance of his design.