Allocating hot standbys to randomly weighted k-out-of-n: G systems

In industrial engineering applications, randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems can model many reliability systems whose components may contribute unequally and randomly to the systems’ performance. This paper investigates optimal allocations of hot standbys for [Formula: see text]-out-of-[Formula: see text]: G systems with random weights. First, optimal allocation policies are presented by maximizing the total capacity according to the usual stochastic ordering and the expectation ordering when the system is constituted by independent and heterogeneous components accompanied with independent random weights. Second, we investigate hot standbys allocation for randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems with right [left] tail weakly stochastic arrangement increasing random weights in the sense of the usual stochastic ordering [increasing concave ordering]. Simulation studies are provided to illustrate our theoretical findings as well. These established results can provide useful guidance for system designers on how to introduce hot standbys in randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems in order to enhance their total capacities.

Assessment of Natural and Forest Reclaimed Forage Lands in Semi-Desert Conditions in Southern Russia

Haphazard use of pastures has become one of the factors of disturbance of their natural vegetation. Therefore, forest reclamation works were carried out and significant areas of strip plantations of shrubs were created in the Caspian Sea region in the mid-20th century. In the arid zone of Russia, one of the most important tasks in the field of scientific provision of protective afforestation is the improvement of methods and techniques of arrangement, increasing longevity and environmental, agricultural, and utilitarian efficiency of plantations. This study aims to determine the long-term impact of afforestation on the functioning of pasture ecosystems. The influence of tree and shrub layer on biodiversity and productivity of vegetation cover of pastures was also studied. The research objects are plantations growing on the reclaimed pastures. The research is based on the materials of biomonitoring and field experiments using standard methods of forest inventory and geobotanical survey. Rectangular-shaped test plots of 0.25–0.30 ha were laid out for the study of forest plots. Test plots were used for a detailed description of the location, soil composition, time, method, and technology of plantation development, as well as a comprehensive assessment of the growth and longevity of tree and shrub crops. Data from key plots were used to study the successional processes of vegetation cover. The research results have shown that deep plowing preparation of soil to obtain high results in rooting, preservation, and growth of shrub species has an advantage over other soil preparation technologies in the semi-desert zone. It was found that the shrub layer up to 45 years old retains its productive and generative abilities. Pasture protection belts from Haloxylon aphyllum and reclamation and fodder plantations from Krascheninnikovia ceratoides and Calligonum aphyllum have a high cenosis potential and stability. In this case study, in semi-arid regions, afforestation with shrubs is the best way to improve and restore pastures. For citation: Rybashlykova L.P., Lepesko V.V. Assessment of Natural and Forest Reclaimed Forage Lands in Semi-Desert Conditions in Southern Russia. Lesnoy Zhurnal [Russian Forestry Journal], 2021, no. 3, pp. 37–48. DOI: 10.37482/0536-1036-2021-3-37-48

ORDERING PROPERTIES OF EXTREME CLAIM AMOUNTS FROM HETEROGENEOUS PORTFOLIOS

In the context of insurance, the smallest and largest claim amounts turn out to be crucial to insurance analysis since they provide useful information for determining annual premium. In this paper, we establish sufficient conditions for comparing extreme claim amounts arising from two sets of heterogeneous insurance portfolios according to various stochastic orders. It is firstly shown that the weak supermajorization order between the transformed vectors of occurrence probabilities implies the usual stochastic ordering between the largest claim amounts when the claim severities are weakly stochastic arrangement increasing. Secondly, sufficient conditions are established for the right-spread ordering and the convex transform ordering of the smallest claim amounts arising from heterogeneous dependent insurance portfolios with possibly different number of claims. In the setting of independent multiple-outlier claims, we study the effects of heterogeneity among sample sizes on the stochastic properties of the largest and smallest claim amounts in the sense of the hazard rate ordering and the likelihood ratio ordering. Numerical examples are provided to highlight these theoretical results as well. Not only can our results be applied in the area of actuarial science, but also they can be used in other research fields including reliability engineering and auction theory.

ON HETEROGENEITY IN THE INDIVIDUAL MODEL WITH BOTH DEPENDENT CLAIM OCCURRENCES AND SEVERITIES

It is a common belief for actuaries that the heterogeneity of claim severities in a given insurance portfolio tends to increase its dangerousness, which results in requiring more capital for covering claims. This paper aims to investigate the effects of orderings and heterogeneity among scale parameters on the aggregate claim amount when both claim occurrence probabilities and claim severities are dependent. Under the assumption that the claim occurrence probabilities are left tail weakly stochastic arrangement increasing, the actuaries' belief is examined from two directions, i.e., claim severities are comonotonic or right tail weakly stochastic arrangement increasing. Numerical examples are provided to validate these theoretical findings. An application in assets allocation is addressed as well.

Increasing convex order on generalized aggregation of SAI random variables with applications

In this paper we study general aggregation of stochastic arrangement increasing random variables, including both the generalized linear combination and the standard aggregation as special cases. In terms of monotonicity, supermodularity, and convexity of the kernel function, we develop several sufficient conditions for the increasing convex order on the generalized aggregations. Some applications in reliability and risks are also presented.