Despite the progress in conservation risk management, conservation organizations are reluctant to interface usable risk-diversification strategies with their decision-making processes. One reason for this reluctance is that the empirical models used to develop risk-diversification strategies need the expected returns on investment (ROIs) of target assets and their variances and covariances, and the probabilities of occurrence of the scenarios needed to calculate those statistics are almost always unknown. We examine how risk diversification for conservation is influenced by the probabilities assigned to uncertainty scenarios using a case study involving the conservation of biodiversity at the county level in the central and southern Appalachian region within the framework of modern portfolio theory. A comparison of risk-mitigating portfolios with bootstrapped and fixed probability distributions shows that introducing the flexibility of an unknown probability distribution of uncertainty scenarios allows conservation organizations to spread bets more than with the inflexibility of the fixed probability distribution, while also achieving higher expected ROIs per unit of risk on average. The improvement becomes more significant when conservation organizations are less risk averse.

Studies agree on a significant global mean sea level rise in the 20th century and its recent 21st century acceleration in the satellite record. At regional scale, the evolution of sea level probability distributions is often assumed to be dominated by changes in the mean. However, a quantification of changes in distributional shapes in a changing climate is currently missing. To this end, we propose a novel framework quantifying significant changes in probability distributions from time series data. The framework first quantifies linear trends in quantiles through quantile regression. Quantile slopes are then projected onto a set of four orthogonal polynomials quantifying how such changes can be explained by independent shifts in the first four statistical moments. The framework proposed is theoretically founded, general, and can be applied to any climate observable with close-to-linear changes in distributions. We focus on observations and a coupled climate model (GFDL-CM4). In the historical period, trends in coastal daily sea level have been driven mainly by changes in the mean and can therefore be explained by a shift of the distribution with no change in shape. In the modeled world, robust changes in higher order moments emerge with increasing $ {\mathrm{CO}}_2 $ concentration. Such changes are driven in part by ocean circulation alone and get amplified by sea level pressure fluctuations, with possible consequences for sea level extremes attribution studies.

Consider the coupon collector problem where each box of a brand of cereal contains a coupon and there are n different types of coupons. Suppose that the probability of a box containing a coupon of a specific type is $1/n$, and that we keep buying boxes until we collect at least m coupons of each type. For $k\geq m$ call a certain coupon a k-ton if we see it k times by the time we have seen m copies of all of the coupons. Here we determine the asymptotic distribution of the number of k-tons after we have collected m copies of each coupon for any k in a restricted range, given any fixed m. We also determine the asymptotic joint probability distribution over such values of k, and the total number of coupons collected.

Cumulative probability distributions of income for management scenarios involving four preharvest marketing strategies are subjected to stochastic dominance analysis to determine risk-efficient sets of strategies for different groups of farmers in North Florida. Results indicate that farmers should behave differently in their choice of marketing strategies according to their risk attitudes. Highly risk-averse farmers should prefer some forward contracting while low risk-averse and risk-loving farmers should prefer cash sales at harvest. Use of the futures markets leads to both higher income and greater risk than forward contracting but lower income and risk than cash sales.

In this paper we consider a reinsurance syndicate, assuming that Pareto optimal allocations exist. Under a continuity assumption on preferences, we show that a competitive equilibrium exists and is unique. Our conditions allow for risks that are not bounded, and we show that the most standard models satisfy our set of sufficient conditions, which are thus not restrictive. Our approach is to transform the analysis from an infinite dimensional to a finite dimensional setting.

We present a transformation for stochastic matrices and analyze theeffects of using it in stochastic comparison with the strong stochastic(st) order. We show that unless the given stochastic matrix is row diagonallydominant, the transformed matrix provides better st bounds on the steady state probability distribution.

The catch from bottom longline stations sampled from a series of research cruises around Lanzarote and Fuerteventura (Canary Islands, NE Atlantic) was analysed in terms of fish distribution, density and diversity. The distribution of the number of species and individuals caught per station appeared to fit well the Poisson and Exponential distribution function, respectively. In particular, the parameter of the Poisson’s distribution appeared to provide an index of the point (at station scale) diversity, and its confidence interval, allowing for statistical comparisons. The relationships between point diversity, the alpha diversity (in the depth strata) and the beta diversity (along the depth gradient) were investigated. Around the islands, the density and the point diversity of the predator fish declined with depth down to about 800 m and then increased in the deeper stratum. The alpha diversity was the lowest in the deeper stratum but the taxonomic distinctness was similar to that of shallower strata. The beta diversity showed some faunal breaks along the depth gradient. The carnivorous fish fauna can be understood as comprised of three major assemblages: shelf, upper slope and mid-slope that are different both in terms of species composition and point, alpha and beta diversities. The relevance of this simple method for ecological studies of fish assemblage in the context of non-trawlable grounds is discussed, in particular for the slope and other areas of established or developing deep-water fisheries.

It is shown that random variables X exist, not exponentially or geometrically distributed, such that

P{X – b ≧ x | X ≧ b} = P{X ≧ x}

for all x > 0 and infinitely many different values of b. A class of distributions having the given property is exhibited. We call them ALM distributions, since they almost have the lack-of-memory property. For a given subclass of these distributions some phenomena relating to service by an unreliable server are discussed.

We derive the representation of additive measures of information with the sum property under a regular generating function. This family of measures includes the Shanon entropy, directed/symmetric divergence and inaccuracy.

The following properties of entropies, as measures of expected information, seem natural. The amount of information expected from an experiment does not change if we add outcomes of zero probability (expansibility). The expected information is symmetric in the (probabilities of the) outcomes. The information expected from a combination of two experiments is less than or equal to the sum of the informations expected from the single experiments (subadditivity); equality holds here if the two experiments are independent (additivity).

In this paper it is shown that linear combinations of the Shannon and Hartley entropies and only these have the above properties. The Shannon and the Hartley entropies are also individually characterized.