STOCHASTIC ORDERING OF LIFETIMES OF PARALLEL AND SERIES SYSTEMS COMPRISING HETEROGENEOUS DEPENDENT COMPONENTS WITH GENERALIZED BIRNBAUM-SAUNDERS DISTRIBUTIONS

2020 ◽  
pp. 1-17
Author(s):  
Mehdi Amiri ◽  
Narayanaswamy Balakrishnan ◽  
Ahad Jamalizadeh
Keyword(s):  
Lower Bounds ◽  
Stochastic Ordering ◽  
Upper And Lower Bounds ◽  
Dependence Structure ◽  
Archimedean Copulas ◽  
Survival Functions ◽  
Stochastic Orderings ◽  
Special Cases ◽  
Series Systems ◽  
Skew Normal

In this paper, we discuss stochastic orderings of lifetimes of two heterogeneous parallel and series systems with heterogeneous dependent components having generalized Birnbaum–Saunders distributions. The comparisons presented here are based on the vector majorization of parameters. The ordering results are established in some special cases for the generalized Birnbaum–Saunders distribution based on the multivariate elliptical, normal, t, logistic, and skew-normal kernels. Further, we use these results by considering Archimedean copulas to model the dependence structure among systems with generalized Birnbaum–Saunders components. These results have been used to derive some upper and lower bounds for survival functions of lifetimes of parallel and series systems.

scholarly journals Positive solutions and eigenvalues of conjugate boundary value problems

1999 ◽  
Vol 42 (2) ◽  
pp. 349-374 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Martin Bohner ◽  
Patricia J. Y. Wong
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Positive Solutions ◽  
Lower Bounds ◽  
Boundary Value ◽  
Upper And Lower Bounds ◽  
Special Cases ◽  
Image Position

We consider the following boundary value problemwhere λ > 0 and 1 ≤ p ≤ n – 1 is fixed. The values of λ are characterized so that the boundary value problem has a positive solution. Further, for the case λ = 1 we offer criteria for the existence of two positive solutions of the boundary value problem. Upper and lower bounds for these positive solutions are also established for special cases. Several examples are included to dwell upon the importance of the results obtained.

scholarly journals Bounds on Rényi and Shannon Entropies for Finite Mixtures of Multivariate Skew-Normal Distributions: Application to Swordfish (Xiphias gladius Linnaeus)

Entropy ◽  
2016 ◽  
Vol 18 (11) ◽  
pp. 382 ◽  
Author(s):  
Javier Contreras-Reyes ◽  
Daniel Cortés
Keyword(s):  
Mixture Models ◽  
Lower Bounds ◽  
Metric Spaces ◽  
Asymptotic Expression ◽  
Approximate Entropy ◽  
Upper And Lower Bounds ◽  
Normal Mixture ◽  
Normal Mixture Models ◽  
Xiphias Gladius ◽  
Skew Normal

Mixture models are in high demand for machine-learning analysis due to their computational tractability, and because they serve as a good approximation for continuous densities. Predominantly, entropy applications have been developed in the context of a mixture of normal densities. In this paper, we consider a novel class of skew-normal mixture models, whose components capture skewness due to their flexibility. We find upper and lower bounds for Shannon and Rényi entropies for this model. Using such a pair of bounds, a confidence interval for the approximate entropy value can be calculated. In addition, an asymptotic expression for Rényi entropy by Stirling’s approximation is given, and upper and lower bounds are reported using multinomial coefficients and some properties and inequalities of L p metric spaces. Simulation studies are then applied to a swordfish (Xiphias gladius Linnaeus) length dataset.

Predicting Behavior from Intention-to-Buy Measures: The Parametric Case

1995 ◽  
Vol 32 (2) ◽  
pp. 176-191 ◽  
Author(s):  
Albert C. Bemmaor
Keyword(s):  
Lower Bounds ◽  
Probabilistic Model ◽  
New Products ◽  
New Product ◽  
Upper And Lower Bounds ◽  
Purchase Intent ◽  
Business Markets ◽  
Special Cases ◽  
Predicting Behavior ◽  
Parametric Case

The author develops a probabilistic model that converts stated purchase intents into purchase probabilities. The model allows heterogeneity between nonintenders and intenders with respect to their probability to switch to a new “true” purchase intent after the survey, thereby capturing the typical discrepancy between overall mean purchase intent and subsequent proportion of buyers (bias). When the probability to switch of intenders is larger (smaller) than that of nonintenders, the overall mean purchase intent overestimates (underestimates) the proportion of buyers. As special cases, the author derives upper and lower bounds on proportions of buyers from purchase intents data and shows the consistency of those bounds with observed behavior, except in predictable cases such as new products and business markets. However, a straightforward modification of the model deals with new product purchase forecasts.

scholarly journals Fully-Dynamic and Kinetic Conflict-Free Coloring of Intervals with Respect to Points

2019 ◽  
Vol 29 (01) ◽  
pp. 49-72
Author(s):  
Mark de Berg ◽  
Tim Leijsen ◽  
Aleksandar Markovic ◽  
André van Renssen ◽  
Marcel Roeloffzen ◽  
...  
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Worst Case ◽  
Insertions And Deletions ◽  
Coloring Problem ◽  
Trade Offs ◽  
Special Cases ◽  
The Cost ◽  
Case Number

We introduce the fully-dynamic conflict-free coloring problem for a set [Formula: see text] of intervals in [Formula: see text] with respect to points, where the goal is to maintain a conflict-free coloring for [Formula: see text] under insertions and deletions. A coloring is conflict-free if for each point [Formula: see text] contained in some interval, [Formula: see text] is contained in an interval whose color is not shared with any other interval containing [Formula: see text]. We investigate trade-offs between the number of colors used and the number of intervals that are recolored upon insertion or deletion of an interval. Our results include: a lower bound on the number of recolorings as a function of the number of colors, which implies that with [Formula: see text] recolorings per update the worst-case number of colors is [Formula: see text], and that any strategy using [Formula: see text] colors needs [Formula: see text] recolorings; a coloring strategy that uses [Formula: see text] colors at the cost of [Formula: see text] recolorings, and another strategy that uses [Formula: see text] colors at the cost of [Formula: see text] recolorings; stronger upper and lower bounds for special cases. We also consider the kinetic setting where the intervals move continuously (but there are no insertions or deletions); here we show how to maintain a coloring with only four colors at the cost of three recolorings per event and show this is tight.

scholarly journals Optimal L(h,k)-Labeling of Regular Grids

2006 ◽  
Vol Vol. 8 ◽  
Author(s):  
Tiziana Calamoneri
Keyword(s):  
Lower Bounds ◽  
Negative Integer ◽  
Upper And Lower Bounds ◽  
Vertex Coloring ◽  
Small Interval ◽  
Regular Grids ◽  
Special Cases ◽  
Hexagonal Grids ◽  
International Audience ◽  
The Difference

International audience The L(h, k)-labeling is an assignment of non negative integer labels to the nodes of a graph such that 'close' nodes have labels which differ by at least k, and 'very close' nodes have labels which differ by at least h. The span of an L(h,k)-labeling is the difference between the largest and the smallest assigned label. We study L(h, k)-labelings of cellular, squared and hexagonal grids, seeking those with minimum span for each value of k and h ≥ k. The L(h,k)-labeling problem has been intensively studied in some special cases, i.e. when k=0 (vertex coloring), h=k (vertex coloring the square of the graph) and h=2k (radio- or λ -coloring) but no results are known in the general case for regular grids. In this paper, we completely solve the L(h,k)-labeling problem on regular grids, finding exact values of the span for each value of h and k; only in a small interval we provide different upper and lower bounds.

scholarly journals Favorite-Candidate Voting for Eliminating the Least Popular Candidate in a Metric Space

2020 ◽  
Vol 34 (02) ◽  
pp. 1894-1901
Author(s):  
Xujin Chen ◽  
Minming Li ◽  
Chenhao Wang
Keyword(s):  
Lower Bounds ◽  
Metric Space ◽  
Social Value ◽  
Upper And Lower Bounds ◽  
Worst Case ◽  
The Social ◽  
Special Cases ◽  
Worst Case Ratio ◽  
The One

We study single-candidate voting embedded in a metric space, where both voters and candidates are points in the space, and the distances between voters and candidates specify the voters' preferences over candidates. In the voting, each voter is asked to submit her favorite candidate. Given the collection of favorite candidates, a mechanism for eliminating the least popular candidate finds a committee containing all candidates but the one to be eliminated. Each committee is associated with a social value that is the sum of the costs (utilities) it imposes (provides) to the voters. We design mechanisms for finding a committee to optimize the social value. We measure the quality of a mechanism by its distortion, defined as the worst-case ratio between the social value of the committee found by the mechanism and the optimal one. We establish new upper and lower bounds on the distortion of mechanisms in this single-candidate voting, for both general metrics and well-motivated special cases.

Optimal L(j,k)-Edge-Labeling of Regular Grids

2015 ◽  
Vol 26 (04) ◽  
pp. 523-535 ◽  
Author(s):  
Tiziana Calamoneri
Keyword(s):  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Regular Grids ◽  
Triangular Grids ◽  
Minimum Value ◽  
Special Cases ◽  
Common Endpoint ◽  
Positive Integers ◽  
Edge Labeling

Given a graph [Formula: see text] and two positive integers j and k, an [Formula: see text]-edge-labeling is a function f assigning to edges of E colors from a set [Formula: see text] such that [Formula: see text] if e and e′ are adjacent, i.e. they share a common endpoint, [Formula: see text] if e and e′ are not adjacent and there exists an edge adjacent to both e and e′. The aim of the [Formula: see text]-edge-labeling problem consists of finding a coloring function f such that the value of [Formula: see text] is minimum. This minimum value is called [Formula: see text]. This problem has already been studied on hexagonal, squared and triangular grids, but mostly not coinciding upper and lower bounds on [Formula: see text] have been proposed. In this paper we close some of these gaps or find better bounds on [Formula: see text] in the special cases [Formula: see text] and [Formula: see text]. Moreover, we propose tight [Formula: see text]-edge-labelings for eight-regular grids.

Multiple Solutions of Generalized Multipoint Conjugate Boundary Value Problems

1999 ◽  
Vol 6 (6) ◽  
pp. 567-590
Author(s):  
Patricia J. Y. Wong ◽  
Ravi P. Agarwal
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Lower Bounds ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Upper And Lower Bounds ◽  
Special Cases

Abstract We consider the boundary value problem 𝑦(𝑛) (𝑡) = 𝑃(𝑡, 𝑦), 𝑡 ∈ (0, 1) 𝑦(𝑗) (𝑡𝑖) = 0, 𝑗 = 0, . . . , 𝑛𝑖 – 1, 𝑖 = 1, . . . , 𝑟, where 𝑟 ≥ 2, 𝑛𝑖 ≥ 1 for 𝑖 = 1, . . . , 𝑟, and 0 = 𝑡1 < 𝑡2 < ⋯ < 𝑡𝑟 = 1. Criteria are offered for the existence of double and triple ‘positive’ (in some sense) solutions of the boundary value problem. Further investigation on the upper and lower bounds for the norms of these solutions is carried out for special cases. We also include several examples to illustrate the importance of the results obtained.

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hui Lei ◽  
Gou Hu ◽  
Zhi-Jie Cao ◽  
Ting-Song Du
Keyword(s):  
Lower Bounds ◽  
Hypergeometric Functions ◽  
Upper And Lower Bounds ◽  
Weighted Inequalities ◽  
Convex Mappings ◽  
Special Means

Abstract The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings. Moreover, we give the upper and lower bounds for the weighted inequalities via products of two different mappings. Some applications of the presented results to special means are also provided.

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