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Consider two parallel systems with their independent components' lifetimes following heterogeneous exponentiated generalized gamma distributions, where the heterogeneity is in both shape and scale parameters. We then obtain the usual stochastic (reversed hazard rate) order between the lifetimes of two systems by using the weak submajorization order between the vectors of shape parameters and the p-larger (weak supermajorization) order between the vectors of scale parameters, under some restrictions on the involved parameters. Further, by reducing the heterogeneity of parameters in each system, the usual stochastic (reversed hazard rate) order mentioned above is strengthened to the hazard rate (likelihood ratio) order. Finally, two characterization results concerning the comparisons of two parallel systems, one with independent heterogeneous generalized exponential components and another with independent homogeneous generalized exponential components, are derived. These characterization results enable us to find some lower and upper bounds for the hazard rate and reversed hazard rate functions of a parallel system consisting of independent heterogeneous generalized exponential components. The results established here generalize some of the known results in the literature, concerning the comparisons of parallel systems under generalized exponential and exponentiated Weibull models. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the usual stochastic and reversed hazard rate orders between the series and parallel systems from two sets of independent heterogeneous exponentiated Weibull components. We also obtain the results concerning the convex transform orders between parallel systems and obtain necessary and sufficient conditions under which the dispersive and usual stochastic orders, and the right spread and increasing convex orders between the lifetimes of the two systems are equivalent. Finally, in the multiple-outlier exponentiated Weibull models, based on weak majorization and p-larger orders between the vectors of scale and shape parameters, some characterization results for comparing the lifetimes of parallel and series systems are also established, respectively. The results of this paper can be used in practical situations to find various bounds for the important aging characteristics of these systems. [ABSTRACT FROM AUTHOR]

As a dynamic system in which different factors affect human performance via dynamic interactions, mental workload needs a dynamic measure to monitor its factors and evidence in a complicated system, an approach that is lacking in the literature. The present study introduces a system dynamics-based model for designing feedback mechanisms related to the mental workload through literature review and content analysis of the previous studies. A human-based archetype of mental workload was detected from the data collection process. The archetype is presented at various stages, including dynamic theory, behavior over time, leverage points and model verification. The real validation of the dynamic model was confirmed in an urban train simulator. The dynamic model can be used to analyze the long-term behavior of the mental workload. Decision-makers can benefit from the developed archetypes in evaluating the dynamic impact of their decisions on accident prevention in the complicated systems. [ABSTRACT FROM AUTHOR]

Consider two (n − r + 1)-out-of-n systems, one with independent and non-identically distributed components and another with independent and identically distributed components. When the lifetimes of components follow the proportional hazard rates model, we establish a necessary and sufficient condition for the usual stochastic order to hold between the lifetimes of these two systems. For the special case of r = 2, some generalized forms of this result to the hazard rate, dispersive and likelihood ratio orders are also obtained. Moreover, for the case when the lifetimes of components follow the proportional reversed hazard rates model, we derive some similar results for comparing the lifetimes of two systems. Applications of the established results to different situations are finally illustrated. [ABSTRACT FROM AUTHOR]

This article introduces a k-Inflated Negative Binomial mixture distribution/regression model as a more flexible alternative to zero-inflated Poisson distribution/regression model. An EM algorithm has been employed to estimate the model's parameters. Then, such new model along with a Pareto mixture model have employed to design an optimal rate-making system. Namely, this article employs number/size of reported claims of Iranian third party insurance dataset. Then, it employs the k-Inflated Negative Binomial mixture distribution/regression model as well as other well developed counting models along with a Pareto mixture model to model frequency/severity of reported claims in Iranian third party insurance dataset. Such numerical illustration shows that: (1) the k-Inflated Negative Binomial mixture models provide more fair rate/pure premiums for policyholders under a rate-making system; and (2) in the situation that number of reported claims uniformly distributed in past experience of a policyholder (for instance k1 = 1 and k2 = 1 instead of k1 = 0 and k2 = 2). The rate/pure premium under the k-Inflated Negative Binomial mixture models are more appealing and acceptable. [ABSTRACT FROM AUTHOR]

In this work, we discuss some stochastic comparisons of two aggregate claim amounts. Applications of our results to the value-at-risk and tail-value-at-risk are also mentioned. It is also shown that the aggregate claim amounts of risks exhibiting a weak form of dependence known as positive cumulative dependence (negatively associated) is larger (smaller) in convex order than the corresponding aggregate claim amounts under the theoretical independence assumption. The obtained results show that the correlations between individual risks increase stop-loss premiums corresponding to aggregate claim amounts. The results established here complete and extend the results of Barmalzan, Payandeh Najafabadi, and Balakrishnan (2017, Theory of Probability and its Applications, to appear). [ABSTRACT FROM AUTHOR]

This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process. By approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equation). Application of our findings has been given though a simulation study. [ABSTRACT FROM AUTHOR]

LetX1, …,Xnbe independent random variables withXi∼EWG(α, β, λi,pi),i= 1, …,n, andY1, …,Ynbe another set of independent random variables withYi∼EWG(α, β, γi,qi),i= 1, …,n. The results established here are developed in two directions. First, under conditionsp1= ⋅⋅⋅ =pn=q1= ⋅⋅⋅ =qn=p, and based on the majorization andp-larger orders between the vectors of scale parameters, we establish the usual stochastic and reversed hazard rate orders between the series and parallel systems. Next, for the case λ1= ⋅⋅⋅ = λn= γ1= ⋅⋅⋅ = γn= λ, we obtain some results concerning the reversed hazard rate and hazard rate orders between series and parallel systems based on the weak submajorization between the vectors of (p1, …,pn) and (q1, …,qn). The results established here can be used to find various bounds for some important aging characteristics of these systems, and moreover extend some well-known results in the literature. [ABSTRACT FROM AUTHOR]

Credibility formula has been developed in many fields of actuarial sciences. Based upon Payandeh (2010), this article extends concept of credibility formula to relatively premium of a given rate-making system. More precisely, it calculates Payandeh’s (2010) credibility factor for zero-inflated Poisson gamma distributions with respect to several loss functions. A comparison study has been given. [ABSTRACT FROM PUBLISHER]

In contrast to scalar Riemann–Hilbert problems, a general matrix Riemann–Hilbert problem cannot be solved in terms of Sokhotskyi–Plemelj integrals. As far as the authors know, the exact solutions are known for a class of homogeneous matrix Riemann–Hilbert problems with commutative and factorable kernels. This article considered matrix Riemann–Hilbert problems in which all the partial indices are zero and the logarithms of the components of the kernels and their non-homogeneous vectors are exponential-type (equivalently, band-limited) functions. Then, it develops exact solutions for such matrix Riemann–Hilbert problems. Applications in a class of spectral factorizations and a class of the Wiener–Hopf system of integrations are given. [ABSTRACT FROM PUBLISHER]

The classical Bonus-Malus System (BMS) determines the next year level of a policyholder based upon his/her current level along with the number of his/her claims during the current period. Moreover, such systems do not take into account other information, such as age, sex, etc., to determine the policyholder's level. This article employs the sophisticated Hidden Markov Model along with the ordinal logistic regression to introduce a Dynamic Bonus-Malus System (DBMS) which the policyholder's level considers as a hidden state. Then the exact level of a policyholder has been estimated by using the ordinal logistic regression model, which is developed based upon exactly collected observations along with negative binomial-inverse Gaussian distribution and the hidden Markov model. An application of such DMBS in Iranian automobile insurance has been given. [ABSTRACT FROM AUTHOR]

Consider the problem of solving, approximately, a Wiener-Hopf integral equation ∫ο∞ g(θ)k(x - θ)dθ = f (x), x ≥ 0 in g; with certain conditions on k and f (see below). We use the well known and powerful Riemann-Hilbert problem to develop two techniques to solve, approximately, the Wiener-Hopf integral equation. One of the approximations is based upon the Shannon sampling theorem, which provides a sharp approximation, when applicable. Estimation bounds and application in statistics are given. [ABSTRACT FROM AUTHOR]

Consider the problem of solving a Riemann–Hilbert problem with ‘zero index’. Abraham (2000, IMA J. Appl. Math., 65, 257–281) suggested to replace a possibly complicated kernel of a homogeneous Riemann–Hilbert problem with a Padé approximant that uniformly approximates the original kernel. Abraham's procedure fails whenever the kernel cannot be approximated uniformly by a Padé approximant (see Example 1). This article (i) provides an approximation technique to approximate solutions of a non-homogeneous Riemann–Hilbert problem with zero index in Lp(ℝ) (1 < p < ∞) sense, which improves the result by Abraham in two directions (weaker conditions on approximating functions and solutions for a non-homogeneous Riemann–Hilbert problem with zero index). Also, we discussed an interesting case p = ∞ (uniformly approximation). (ii) Using the Egoroff's theorem provides a pointwise approximate solutions for a class of non-homogeneous Riemann–Hilbert problem with zero index. (iii) Using the Shannon sampling theorem provides explicit solutions for certain non-homogeneous Riemann–Hilbert problems with zero index. Some approximations which exploiting this fact will be discussed. (iv) Applications to integral equations are given. [ABSTRACT FROM PUBLISHER]