On the simulated sampling distribution of RMAD2 for inverse Gaussian samples

Background: Remaining useful life (RUL) estimation is the central mission to the complex systems’ prognostics and health management. During last decades, numbers of developments and applications of the RUL estimation have proliferated. Objective: As one of the most popular approaches, stochastic process-based approach has been widely used for characterizing the degradation trajectories and estimating RULs. This paper aimed at reviewing the latest methods and patents on this topic. Methods: The review is concentrated on four common stochastic processes for degradation modelling and RUL estimation, i.e., Gamma process, Wiener process, inverse Gaussian process and Markov chain. Results: After a briefly review of these four models, we pointed out the pros and cons of them, as well as the improvement direction of each method. Conclusion: For better implementation, the applications of these four approaches on maintenance and decision-making are systematically introduced. Finally, the possible future trends are concluded tentatively.

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Asymptotic Inference for Optimal Rerandomization Designs

Open Statistics ◽

10.1515/stat-2020-0102 ◽

2021 ◽

Vol 1 (1) ◽

pp. 49-58

Author(s):

Mårten Schultzberg ◽

Per Johansson

Keyword(s):

Experimental Design ◽

Normal Distribution ◽

Mahalanobis Distance ◽

Design Strategy ◽

Sampling Distribution ◽

Optimal Designs ◽

Asymptotic Inference ◽

Optimal Allocations ◽

Asymptotic Sampling

AbstractRecently a computational-based experimental design strategy called rerandomization has been proposed as an alternative or complement to traditional blocked designs. The idea of rerandomization is to remove, from consideration, those allocations with large imbalances in observed covariates according to a balance criterion, and then randomize within the set of acceptable allocations. Based on the Mahalanobis distance criterion for balancing the covariates, we show that asymptotic inference to the population, from which the units in the sample are randomly drawn, is possible using only the set of best, or ‘optimal’, allocations. Finally, we show that for the optimal and near optimal designs, the quite complex asymptotic sampling distribution derived by Li et al. (2018), is well approximated by a normal distribution.

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Lidar-Based Morphometry of Conical Hills in Temperate Karst Areas in Slovenia

Remote Sensing ◽

10.3390/rs13142668 ◽

2021 ◽

Vol 13 (14) ◽

pp. 2668

Author(s):

Tamás Telbisz

Keyword(s):

Empirical Distribution ◽

Inverse Gaussian ◽

Digital Terrain ◽

Terrain Models ◽

Starting Point ◽

Significant Difference ◽

Karst Areas ◽

Hill Area ◽

The Hill ◽

Comprehensive Study

Conical hills, or residual hills, are frequently mentioned landforms in the context of humid tropical karsts as they are dominant surface elements there. Residual hills are also present in temperate karsts, but generally in a less remarkable way. These landforms have not been thoroughly addressed in the literature to date, therefore the present article is the first attempt to morphometrically characterize temperate zone residual karst hills. We use the methods already developed for doline morphometry, and we apply them to the “inverse” topography using LiDAR-based digital terrain models (DTMs) of three Slovenian sample areas. The characteristics of hills and depressions are analysed in parallel, taking into account the rank of the forms. A common feature of hills and dolines is that, for both types, the empirical distribution of planform areas has a strongly positive skew. After logarithmic transformation, these distributions can be approximated by Inverse Gaussian, Normal, and Weibull distributions. Along with the rank, the planform area and vertical extent of the hills and dolines increase similarly. High circularity is characteristic only of the first-rank forms for both dolines and hills. For the sample areas, the the hill area ratios and the doline area ratios have similar values, but the total extent of the hills is slightly larger in each case. A difference between dolines and hills is that the shapes of hills are more similar to one another than those of dolines. The reason for this is that the larger, closed depressions are created by lateral coalescence, while the hills are residual forms carved from large blocks. Another significant difference is that the density of dolines is much higher than that of hills. This article is intended as a methodological starting point for a new topic, aiming at the comprehensive study of residual karst hills across different climatic areas.

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A Bimodal Extension of the Exponential Distribution with Applications in Risk Theory

Symmetry ◽

10.3390/sym13040679 ◽

2021 ◽

Vol 13 (4) ◽

pp. 679

Author(s):

Jimmy Reyes ◽

Emilio Gómez-Déniz ◽

Héctor W. Gómez ◽

Enrique Calderín-Ojeda

Keyword(s):

Exponential Distribution ◽

Hazard Rate ◽

Rate Function ◽

Estimation Methods ◽

Inverse Gaussian ◽

New Family ◽

Tail Distribution ◽

Zero Values ◽

The Mean ◽

Positive Support

There are some generalizations of the classical exponential distribution in the statistical literature that have proven to be helpful in numerous scenarios. Some of these distributions are the families of distributions that were proposed by Marshall and Olkin and Gupta. The disadvantage of these models is the impossibility of fitting data of a bimodal nature of incorporating covariates in the model in a simple way. Some empirical datasets with positive support, such as losses in insurance portfolios, show an excess of zero values and bimodality. For these cases, classical distributions, such as exponential, gamma, Weibull, or inverse Gaussian, to name a few, are unable to explain data of this nature. This paper attempts to fill this gap in the literature by introducing a family of distributions that can be unimodal or bimodal and nests the exponential distribution. Some of its more relevant properties, including moments, kurtosis, Fisher’s asymmetric coefficient, and several estimation methods, are illustrated. Different results that are related to finance and insurance, such as hazard rate function, limited expected value, and the integrated tail distribution, among other measures, are derived. Because of the simplicity of the mean of this distribution, a regression model is also derived. Finally, examples that are based on actuarial data are used to compare this new family with the exponential distribution.

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AGN evolution as seen in spectral lines: The case of narrow-line Seyfert 1s

Proceedings of the International Astronomical Union ◽

10.1017/s1743921320002653 ◽

2019 ◽

Vol 15 (S356) ◽

pp. 94-94

Author(s):

Marco Berton

Keyword(s):

Active Galactic Nuclei ◽

Galactic Nuclei ◽

Spectroscopic Studies ◽

Spectral Lines ◽

Narrow Line ◽

Line Profiles ◽

Line Shapes ◽

Fundamental Information ◽

Line Region ◽

Gaussian Samples

AbstractLine profiles can provide fundamental information on the physics of active galactic nuclei (AGN). In the case of narrow-line Seyfert 1 galaxies (NLS1s) this is of particular importance since past studies revealed how their permitted line profiles are well reproduced by a Lorentzian function instead of a Gaussian. This has been explained with different properties of the broad-line region (BLR), which may present more pronounced turbulent motions in NLS1s with respect to other AGN. We investigated the line profiles in a recent large NLS1 sample classified using SDSS, and we divided the sources into two subsamples according to their line shapes, Gaussian or Lorentzian. The line profiles seem to separate all the properties of NLS1s. Black hole mass, Eddington ratio, [OIII] luminosity, and Fe II strength are all very different in the Lorentzian and Gaussian samples, as well as their position on the quasar main sequence. We interpret this in terms of evolution within the class of NLS1s. The Lorentzian sources may be the youngest objects, while Gaussian profiles may be typically associated to more evolved objects. Further detailed spectroscopic studies are needed to fully confirm our hypothesis.

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