Error Distributions in Navigation

1972 ◽  
Vol 25 (2) ◽  
pp. 250-252 ◽  
Author(s):  
J. B. Parker
Keyword(s):  
Normal Distribution ◽  
Frequency Distributions ◽  
Families Of Curves ◽  
Pearson Type ◽  
Error Distributions ◽  
The One ◽  
Two Parameter

Graduating error distributions by families of curves has a long and distinguished history. In seeking a class of frequency distributions which graduate navigational data, Anderson and Ellis are motivated by the well-known shortcomings of the normal distribution which so often fails to do justice to the data in the tails of the distribution. They generalize the one parameter (σ) zero-mean gaussian family to a two parameter (α, β) family which is in fact the Pearson Type VII class. They then observe that this class graduates published navigational distributions very wells.

Subjective Time Preference and Willingness to Pay for an Energy-Saving Durable Good

2001 ◽  
Vol 32 (3) ◽  
pp. 133-141 ◽  
Author(s):  
Gerrit Antonides ◽  
Sophia R. Wunderink
Keyword(s):  
Willingness To Pay ◽  
Energy Saving ◽  
Subjective Time ◽  
Durable Good ◽  
Discount Function ◽  
Hyperbolic Discount ◽  
The One ◽  
Two Parameter ◽  
Difference Effect ◽  
Better Than

Summary: Different shapes of individual subjective discount functions were compared using real measures of willingness to accept future monetary outcomes in an experiment. The two-parameter hyperbolic discount function described the data better than three alternative one-parameter discount functions. However, the hyperbolic discount functions did not explain the common difference effect better than the classical discount function. Discount functions were also estimated from survey data of Dutch households who reported their willingness to postpone positive and negative amounts. Future positive amounts were discounted more than future negative amounts and smaller amounts were discounted more than larger amounts. Furthermore, younger people discounted more than older people. Finally, discount functions were used in explaining consumers' willingness to pay for an energy-saving durable good. In this case, the two-parameter discount model could not be estimated and the one-parameter models did not differ significantly in explaining the data.

Theoretical accuracy of the last squares method in the isotope dilution analysis

1984 ◽  
Vol 49 (4) ◽  
pp. 805-820
Author(s):  
Ján Klas
Keyword(s):  
Least Squares ◽  
Isotope Dilution ◽  
Least Squares Method ◽  
Isotope Dilution Analysis ◽  
Straight Line ◽  
The One ◽  
Two Parameter ◽  
Theoretical Accuracy

The accuracy of the least squares method in the isotope dilution analysis is studied using two models, viz a model of a two-parameter straight line and a model of a one-parameter straight line.The equations for the direct and the inverse isotope dilution methods are transformed into linear coordinates, and the intercept and slope of the two-parameter straight line and the slope of the one-parameter straight line are evaluated and treated.

Performance limitation of networked systems with controller and communication filter co-design

2016 ◽  
Vol 40 (4) ◽  
pp. 1167-1176 ◽  
Author(s):  
Jie Wu ◽  
Xi-Sheng Zhan ◽  
Xian-He Zhang ◽  
Tao Han ◽  
Hong-Liang Gao
Keyword(s):  
Networked Systems ◽  
Channel Noise ◽  
Frequency Domain Method ◽  
Minimum Phase ◽  
Error Signal ◽  
Optimal Network ◽  
Performance Limitation ◽  
The One ◽  
Theoretical Results ◽  
Two Parameter

This paper addresses the performance limitation problem of networked systems by co-designing the controller and communication filter. The tracking performance index is measured by the energy of the error signal. Explicit expressions of the performance limitation are obtained by applying the controller and communication filter co-design, and the optimal network filter is obtained by applying the frequency domain method. It is shown that the performance limitation is closely related to the unstable poles and the non-minimum phase zeros of a given plant under the one-parameter compensator structure, whereas, under the two-parameter compensator structure, the performance limitation is unrelated to the unstable poles of a given plant. It is also demonstrated that the performance limitation can be improved and the effect of the channel noise can be eliminated by using the controller and communication filter co-design. Finally, some typical examples are presented to illustrate the theoretical results.

scholarly journals Regional parent flood frequency distributions in Europe – Part 2: Climate and scale controls

2014 ◽  
Vol 18 (11) ◽  
pp. 4391-4401 ◽  
Author(s):  
J. L. Salinas ◽  
A. Castellarin ◽  
S. Kohnová ◽  
T. R. Kjeldsen
Keyword(s):  
Flood Frequency ◽  
Mean Annual Precipitation ◽  
Annual Maximum ◽  
Catchment Scale ◽  
Frequency Distributions ◽  
Coefficient Of Skewness ◽  
Basin Area ◽  
Two Parameter ◽  
Parameter Distributions ◽  
Annual Maximum Series

Abstract. This study aims to better understand the effect of catchment scale and climate on the statistical properties of regional flood frequency distributions. A database of L-moment ratios of annual maximum series (AMS) of peak discharges from Austria, Italy and Slovakia, involving a total of 813 catchments with more than 25 yr of record length is presented, together with mean annual precipitation (MAP) and basin area as catchment descriptors surrogates of climate and scale controls. A purely data-based investigation performed on the database shows that the generalized extreme value (GEV) distribution provides a better representation of the averaged sample L-moment ratios compared to the other distributions considered, for catchments with medium to higher values of MAP independently of catchment area, while the three-parameter lognormal distribution is probably a more appropriate choice for drier (lower MAP) intermediate-sized catchments, which presented higher skewness values. Sample L-moment ratios do not follow systematically any of the theoretical two-parameter distributions. In particular, the averaged values of L-coefficient of skewness (L-Cs) are always larger than Gumbel's fixed L-Cs. The results presented in this paper contribute to the progress in defining a set of "process-driven" pan-European flood frequency distributions and to assess possible effects of environmental change on its properties.

scholarly journals Some New Fractional-Calculus Connections between Mittag–Leffler Functions

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 485 ◽  
Author(s):  
Hari M. Srivastava ◽  
Arran Fernandez ◽  
Dumitru Baleanu
Keyword(s):  
Experimental Data ◽  
Fractional Calculus ◽  
Fractional Derivative ◽  
Fractional Integral ◽  
Integral Expression ◽  
Potential Applications ◽  
The One ◽  
Two Parameter

We consider the well-known Mittag–Leffler functions of one, two and three parameters, and establish some new connections between them using fractional calculus. In particular, we express the three-parameter Mittag–Leffler function as a fractional derivative of the two-parameter Mittag–Leffler function, which is in turn a fractional integral of the one-parameter Mittag–Leffler function. Hence, we derive an integral expression for the three-parameter one in terms of the one-parameter one. We discuss the importance and applications of all three Mittag–Leffler functions, with a view to potential applications of our results in making certain types of experimental data much easier to analyse.

On Post-Critical Behavior of a Beam on an Elastic Foundation

2018 ◽  
Vol 18 (06) ◽  
pp. 1850082 ◽  
Author(s):  
Lidija Z. Rehlicki ◽  
Marko B. Janev ◽  
Branislava N. Novaković ◽  
Teodor M. Atanacković
Keyword(s):  
Total Energy ◽  
Elastic Foundation ◽  
Nonlinear Problem ◽  
Bifurcation Analysis ◽  
Nontrivial Solutions ◽  
Buckling Mode ◽  
Nonlinear Equilibrium ◽  
The Stability ◽  
The One ◽  
Two Parameter

In this paper, we analyze the nonlinear equilibrium equation corresponding to the two-parameter bifurcation problem arising in the stability analysis of an elastic simply supported beam on the Winkler type elastic foundation for the case when bimodal buckling occurs. We perform the bifurcation analysis of the nonlinear problem, by using Lyapunov–Schmidt reduction, thus obtaining the number of the nontrivial solutions to the nonlinear problem and qualitatively characterizing the solution patterns. We also give the formulation of the problem and bifurcation analysis from the total energy viewpoint and determine the energy of each bifurcating solution. We assert that the solution with the smallest energy is the one that will be observed in the post-critical state. For specific choice of parameters, the bifurcating solution in the form of the second buckling mode has the smallest total energy. The numerical results illustrating the theory are also provided.

scholarly journals On a family of prior distributions for a class of Bayesian search models

1993 ◽  
Vol 25 (03) ◽  
pp. 714-716
Author(s):  
K. D. Glazebrook
Keyword(s):  
Conjugate Prior ◽  
Prior Distributions ◽  
Search Models ◽  
New Family ◽  
Special Cases ◽  
The Family ◽  
The One ◽  
Two Parameters ◽  
Two Parameter ◽  
Conjugate Prior Distributions

We propose a two-parameter family of conjugate prior distributions for the number of undiscovered objects in a class of Bayesian search models. The family contains the one-parameter Euler and Heine families as special cases. The two parameters may be interpreted respectively as an overall success rate and a rate of depletion of the source of objects. The new family gives enhanced flexibility in modelling.

ONE-PARTY QUANTUM-ERROR-CORRECTING CODES FOR UNBALANCED ERRORS: PRINCIPLES AND APPLICATION TO QUANTUM DENSE CODING AND QUANTUM SECURE DIRECT COMMUNICATION

2010 ◽  
Vol 08 (04) ◽  
pp. 697-719 ◽  
Author(s):  
KAI WEN ◽  
GUI LU LONG
Keyword(s):  
Quantum Secure Direct Communication ◽  
Error Correcting Codes ◽  
General Definition ◽  
Dense Coding ◽  
Quantum Dense Coding ◽  
Direct Communication ◽  
Error Distributions ◽  
General Correspondence ◽  
The One ◽  
Quantum Error

In this article, we present unbalanced-quantum-error-correcting codes (one-party QECCs) — a novel idea for correcting unbalanced quantum errors. In some quantum communication tasks using entangled pairs, the error distributions between two parts of the pairs are unbalanced, and one party holds the whole entangled pairs at the final stage, and he or she is able to perform joint measurements on the pairs. In this situation the proposed one-party QECCs can improve error correction by allowing a higher-tolerated error rate. We have established the general correspondence between linear classical codes and the one-party QECCs, and we have given the general definition for these types of quantum-error-correcting codes. It has been shown that the one-party QECCs can correct errors as long as the error threshold is not larger than 0.5. They work even for fidelity less than 0.5 as long as it is larger than 0.25. We give several concrete examples of the one-party QECCs. We provide the applications of the one-party QECCs in quantum dense coding, so that it can function in noisy channels. As a result, a large number of quantum secure direct communication protocols based on dense coding are also able to be protected by this new type of one-party QECCs.

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