$L^\infty $ Error Bounds in Partial Deconvolution of the Inverse Gaussian Pulse

1985 ◽  
Vol 45 (6) ◽  
pp. 1029-1038 ◽  
Author(s):  
Alfred S. Carasso ◽  
Nelson N. Hsu
Keyword(s):  
Error Bounds ◽  
Gaussian Pulse ◽  
Inverse Gaussian

Remaining useful life estimation: a review on stochastic process-based approaches

2020 ◽  
Vol 14 ◽  
Author(s):  
Dangbo Du ◽  
Jianxun Zhang ◽  
Xiaosheng Si ◽  
Changhua Hu
Keyword(s):  
Stochastic Process ◽  
Health Management ◽  
Remaining Useful Life ◽  
Future Trends ◽  
Prognostics And Health Management ◽  
Inverse Gaussian ◽  
Life Estimation ◽  
Inverse Gaussian Process ◽  
Pros And Cons ◽  
Useful Life

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.

scholarly journals Metric Fourier Approximation of Set-Valued Functions of Bounded Variation

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Elena E. Berdysheva ◽  
Nira Dyn ◽  
Elza Farkhi ◽  
Alona Mokhov
Keyword(s):  
Fourier Series ◽  
Bounded Variation ◽  
Error Bounds ◽  
Metric Spaces ◽  
Hausdorff Metric ◽  
Dirichlet Kernel ◽  
Partial Sums ◽  
Functions Of Bounded Variation ◽  
Moduli Of Continuity ◽  
Fourier Approximation

AbstractWe introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet kernel using the newly defined weighted metric integral. We derive error bounds for these approximants. As a consequence, we prove that the sequence of the partial sums converges pointwisely in the Hausdorff metric to the values of the approximated set-valued function at its points of continuity, or to a certain set described in terms of the metric selections of the approximated multifunction at a point of discontinuity. Our error bounds are obtained with the help of the new notions of one-sided local moduli and quasi-moduli of continuity which we discuss more generally for functions with values in metric spaces.

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

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.

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

Symmetry ◽  
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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