scholarly journals On Occurrences of F-S Strings in Linearly and Circularly Ordered Binary Sequences

2010 ◽  
Vol 47 (1) ◽  
pp. 157-178 ◽  
Author(s):  
Frosso S. Makri
Keyword(s):  
Waiting Time ◽  
Applied Research ◽  
Random Variables ◽  
Upper Bounds ◽  
Binary Sequences ◽  
Mean Values ◽  
Numerical Examples ◽  
Binary Trials ◽  
Binary Random Variables ◽  
Theoretical Results

Consider a sequence of exchangeable or independent binary trials ordered on a line or on a circle. The statistics denoting the number of times an F-S string of length (at least) k1 + k2, that is, (at least) k1 failures followed by (at least) k2 successes in n such trials, are studied. The associated waiting time for the rth occurrence of an F-S string of length (at least) k1 + k2 in linearly ordered trials is also examined. Exact formulae, lower/upper bounds and approximations are derived for their distributions. Mean values and variances of the number of occurrences of F-S strings are given in exact formulae too. Particular exchangeable and independent sequences of binary random variables, used in applied research, combined with numerical examples clarify further the theoretical results.

scholarly journals On Occurrences of F-S Strings in Linearly and Circularly Ordered Binary Sequences

2010 ◽  
Vol 47 (01) ◽  
pp. 157-178
Author(s):  
Frosso S. Makri
Keyword(s):  
Waiting Time ◽  
Applied Research ◽  
Random Variables ◽  
Upper Bounds ◽  
Binary Sequences ◽  
Mean Values ◽  
Numerical Examples ◽  
Binary Trials ◽  
Binary Random Variables ◽  
Theoretical Results

Consider a sequence of exchangeable or independent binary trials ordered on a line or on a circle. The statistics denoting the number of times an F-S string of length (at least) k 1 + k 2, that is, (at least) k 1 failures followed by (at least) k 2 successes in n such trials, are studied. The associated waiting time for the rth occurrence of an F-S string of length (at least) k 1 + k 2 in linearly ordered trials is also examined. Exact formulae, lower/upper bounds and approximations are derived for their distributions. Mean values and variances of the number of occurrences of F-S strings are given in exact formulae too. Particular exchangeable and independent sequences of binary random variables, used in applied research, combined with numerical examples clarify further the theoretical results.

THE MEAN WAITING TIME FOR A PATTERN

1999 ◽  
Vol 13 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Sheldon M. Ross
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Waiting Time ◽  
Random Variables ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Mean Waiting Time ◽  
The Mean ◽  
Mean Time

Consider a sequence of independent and identically distributed random variables along with a specified set of k-vectors. We present an expression for E [T], the mean time until the last k observed random variables fall within this set. Not only can this expression often be used to obtain bounds on E[T], it also gives rise to an efficient way of approximating E[T] by a simulation. Specific lower and upper bounds for E[T] are also derived. These latter bounds are given in terms of a parameter, and a Markov chain Monte Carlo approach to approximate this parameter by a simulation is indicated. The results of this paper are illustrated by considering the problem of determining the mean time until a sequence of k-valued random variables has a run of size k that encompasses each value.

scholarly journals The Kaldor–Kalecki stochastic model of business cycle

2011 ◽  
Vol 16 (2) ◽  
pp. 191-205 ◽  
Author(s):  
Gabriela Mircea ◽  
Mihaela Neamt¸u ◽  
Dumitru Opris
Keyword(s):  
Hopf Bifurcation ◽  
Business Cycle ◽  
Stochastic Model ◽  
Local Stability ◽  
Mean Values ◽  
Numerical Examples ◽  
Investment Demand ◽  
The Mean ◽  
Theoretical Results

This paper is concerned with the deterministic and the stochastic delayed Kaldor–Kalecki nonlinear business cycle models of the income. They will take into consideration the investment demand in the form suggested by Rodano. The existence of the Hopf bifurcation is studied and the direction and the local stability of the Hopf bifurcation is also taken into consideration. For the stochastic model, the dynamics of the mean values and the square mean values of the model’s variables are set. Numerical examples are given to illustrate our theoretical results.

scholarly journals An Inventory Model under Trapezoidal Type Demand, Weibull-Distributed Deterioration, and Partial Backlogging

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Lianxia Zhao
Keyword(s):  
Sensitivity Analysis ◽  
Waiting Time ◽  
Optimal Solution ◽  
Inventory Model ◽  
Partial Backlogging ◽  
Inventory Models ◽  
Numerical Examples ◽  
Replenishment Policy ◽  
Demand Rate ◽  
Theoretical Results

This paper studies an inventory model for Weibull-distributed deterioration items with trapezoidal type demand rate, in which shortages are allowed and partially backlogging depends on the waiting time for the next replenishment. The inventory models starting with no shortage is are to be discussed, and an optimal inventory replenishment policy of the model is proposed. Finally, numerical examples are provided to illustrate the theoretical results, and a sensitivity analysis of the major parameters with respect to the optimal solution is also carried out.

scholarly journals New bounds for the minimum eigenvalue of 𝓜-tensors

2017 ◽  
Vol 15 (1) ◽  
pp. 296-303 ◽  
Author(s):  
Jianxing Zhao ◽  
Caili Sang
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Minimum Eigenvalue ◽  
Numerical Examples ◽  
Theoretical Results

Abstract A new lower bound and a new upper bound for the minimum eigenvalue of an 𝓜-tensor are obtained. It is proved that the new lower and upper bounds improve the corresponding bounds provided by He and Huang (J. Inequal. Appl., 2014, 2014, 114) and Zhao and Sang (J. Inequal. Appl., 2016, 2016, 268). Finally, two numerical examples are given to verify the theoretical results.

scholarly journals Path Analysis for Binary Random Variables

2021 ◽  
pp. 004912412110312
Author(s):  
Martina Raggi ◽  
Elena Stanghellini ◽  
Marco Doretti
Keyword(s):  
Random Variables ◽  
Standard Errors ◽  
Marginal Effect ◽  
Direct And Indirect Effects ◽  
Direct Effects ◽  
P Values ◽  
Recursive System ◽  
Binary Random Variables ◽  
Log Odds ◽  
Research Questions

The decomposition of the overall effect of a treatment into direct and indirect effects is here investigated with reference to a recursive system of binary random variables. We show how, for the single mediator context, the marginal effect measured on the log odds scale can be written as the sum of the indirect and direct effects plus a residual term that vanishes under some specific conditions. We then extend our definitions to situations involving multiple mediators and address research questions concerning the decomposition of the total effect when some mediators on the pathway from the treatment to the outcome are marginalized over. Connections to the counterfactual definitions of the effects are also made. Data coming from an encouragement design on students’ attitude to visit museums in Florence, Italy, are reanalyzed. The estimates of the defined quantities are reported together with their standard errors to compute p values and form confidence intervals.

Some remarks on probability inequalities for sums of bounded convex random variables

1975 ◽  
Vol 12 (1) ◽  
pp. 155-158 ◽  
Author(s):  
M. Goldstein
Keyword(s):  
Convex Function ◽  
Exponential Convergence ◽  
Random Variables ◽  
Upper Bounds ◽  
Independent Random Variables ◽  
Probability Inequalities ◽  
Continuous Convex Function ◽  
Bounded Convex

Let X1, X2, · ··, Xn be independent random variables such that ai ≦ Xi ≦ bi, i = 1,2,…n. A class of upper bounds on the probability P(S−ES ≧ nδ) is derived where S = Σf(Xi), δ > 0 and f is a continuous convex function. Conditions for the exponential convergence of the bounds are discussed.

scholarly journals Edge detection with trigonometric polynomial shearlets

2021 ◽  
Vol 47 (1) ◽  
Author(s):  
Kevin Schober ◽  
Jürgen Prestin ◽  
Serhii A. Stasyuk
Keyword(s):  
Edge Detection ◽  
Trigonometric Polynomial ◽  
Two Dimensions ◽  
Characteristic Functions ◽  
Numerical Examples ◽  
Special Cases ◽  
Periodic Characteristic ◽  
Boundary Curves ◽  
Theoretical Results ◽  
De La Vallée Poussin

AbstractIn this paper, we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vallée Poussin-type wavelets are able to detect step discontinuities along boundary curves of periodic characteristic functions. Motivated by recent results for discrete shearlets in two dimensions, we provide lower and upper estimates for the magnitude of the corresponding inner products. In the proof, we use localization properties of trigonometric polynomial shearlets in the time and frequency domain and, among other things, bounds for certain Fresnel integrals. Moreover, we give numerical examples which underline the theoretical results.

scholarly journals Stability Analysis of Impulsive Control Systems with Finite and Infinite Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xuling Wang ◽  
Xiaodi Li ◽  
Gani Tr. Stamov
Keyword(s):  
Control Systems ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Infinite Delays ◽  
Impulsive Control Systems ◽  
Stable Matrix ◽  
Theoretical Results

This paper studies impulsive control systems with finite and infinite delays. Several stability criteria are established by employing the largest and smallest eigenvalue of matrix. Our sufficient conditions are less restrictive than the ones in the earlier literature. Moreover, it is shown that by using impulsive control, the delay systems can be stabilized even if it contains no stable matrix. Finally, some numerical examples are discussed to illustrate the theoretical results.

scholarly journals Stochastic orders for a multivariate Pareto distribution

2021 ◽  
Vol 29 (1) ◽  
pp. 53-69
Author(s):  
Luigi-Ionut Catana
Keyword(s):  
Pareto Distribution ◽  
Random Variables ◽  
Stochastic Orders ◽  
Distribution Family ◽  
Theoretical Results

Abstract In this article we give some theoretical results for equivalence between different stochastic orders of some kind multivariate Pareto distribution family. Weak multivariate orders are equivalent or imply different stochastic orders between extremal statistics order of two random variables sequences. The random variables in this article are not neccesary independent.

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