In performing Bayesian analysis of a bonus-malus system (BMS) it is normal to choose a parametric structure, π 0 (λ), in the insurer's portfolio. According to Bayesian sensitivity analysis the structure function can be modelled by specifying a class Γ of priors instead of a single prior. In this paper, we examine the ranges of the relativities, i.e. δ π = E[λπ(λ|data)]/E[λπ(λ)], π ∈ Γ . We illustrate our method with data from [Astin Bulletin 10 (3) (1979) 274].

The Bayes premium is a quantity of interest in the actuarial collective risk model, under which certain hypotheses are assumed. The usual assumption of independence among risk profiles is very convenient from a computational point of view but is not always realistic. Recently, several authors in the field of actuarial and operational risks have examined the incorporation of some dependence in their models. In this paper, we approach this topic by using and developing a Farlie-Gumbel-Morgenstern (FGM) family of prior distributions with specified marginals given by standard two-sided power and gamma distributions. An alternative Poisson-Lindley distribution is also used to model the count data as the number of claims. For the model considered, closed expressions of the main quantities of interest are obtained, which permit us to investigate the behavior of the Bayes premium under the dependence structure adopted (Farlie-Gumbel-Morgenstern) when the independence case is included.

Seagrasses are angiosperm that composes the only group of vascular plants with the morphological and physiological characteristics necessary to carry out their entire life cycle submerged in seawater. These ecosystems fulfill a wide variety of ecological functions, including interactions with coral reefs and mangroves that modify the hydrodynamics of the environment, production of direct and indirect sources of food, stabilization of nutrients, production and stabilization of sediments, and high primary productivity. The objective of this study was to determine the primary productivity of Thalassia testudinum in the Los Petenes Campeche Biosphere Reserve (RBLP by its initials in Spanish) and identify the environmental factors involved in the process. In order to do this, the environmental conditions of the reserve were observed over the course of one year and the health status of T. testudinum was characterized on the basis of maximum quantum yield. While the productivity was estimated by the reconstruction technique. Finally, the environmental factors that influenced it were identified. It was found that T. testudinum has an average Fv/Fm fluorescence measurement of 0.75 ± 0.03 that indicates healthy, non-stressed plants. This is also reflected in its average total biomass of 1,519.28 gPS/m 2 , with 22% in flower and productivity of 25.84 leaves per year per plant. The highest productivity was presented in stations A2, A3, A4 and B1, whose zone is characterized by being shallow, high temperatures, lower salinity and higher concentration of nutrients, mainly PTporewater.Likewise, the RBLP has optimal environmental conditions for growth of the species under study, which is reflected in its high productivity when compared with other studies in the Gulf of Mexico and Yucatan peninsula. Seagrasses are excellent indicators of the health of marine ecosystems, which is why monitoring them is of vital importance to know the status of the environment and thus establish proposals for management, restoration and conservation.