Error bounds in approximations of random sums using gamma-type operators

Survival probabilities in bivariate risk models, with application to reinsurance

“…In case of a single risk, a different interesting method to approximate compound distributions by discretisation is proposed in Sangüesa (2008).…”

Uniform error bounds for a continuous approximation of non-negative random variables

“…i , the error in the approximation can be controlled 'uniformly,' regardless of the distribution of M (see [16], Theorem 4.3). This effect is obvious when we choose M with a large expected value (our choice of a small p is for this reason -for larger values of p checked, L * 5 F is also better, but the difference is less appreciable).…”

“…Note that the first equality in (17) follows by recalling (2) and noting that ( M i=1 X i ) •t has the same distribution as M i=1 X •t i (see [16], Proposition 2.1). Actually, a more natural way (in this case) to compute (17) is to evaluate the LS transform of ( M i=1 X i ) •t and then apply (1) and (2).…”

“…(3) Also, in [16], error bounds for random sums of mixtures of gamma distributions were obtained, uniformly controlled on the parameters of the random summation index. In all of these papers, the measure of distance considered was the Kolmogorov (or sup-norm) distance.…”

Using Advanced Analytic Techniques to Optimize Cyber-Physical Defensive Plans in Sports Infrastructures and Facilities

“…The analysis of mathematical models includes tables, graphs, mathematical equations, logical statements, and verbal descriptions, which are means of describing system boundaries, system input, and output elements and their relationships, and any feedback between output and input variables to achieve the desired result of the relevant modeling [ 19 ]. Specifically, the different types of mathematical models of the system depending on the types of mathematical functions used in this modeling are presented below [ 20 , 21 ]: Algebraic equation: It can be obtained by adjusting a curve in empirical measurements; for example, Equation of differences: They can describe time-varying systems with delay, memory, multiple variables, and so on; for example, Normal differential equation: It can be obtained from processes of reduction or increase of the examined variable state; for example, where a , b are the system parameters. Integral equation (an equation in which an unknown function appears under an integral sign): Known relationships that can be captured in the form of integral; for example, Differential equation with some derivatives; for example, where S , t , h , R , P are the system parameters.…”