Extinction in a branching process: Why some of the fittest strategies cannot guarantee survival

The fitness of a biological strategy is typically measured by its expected reproductive rate, the first moment of its offspring distribution. However, strategies with high expected rates can also have high probabilities of extinction. A similar situation is found in gambling and investment, where strategies with a high expected payoff can also have a high risk of ruin. We take inspiration from the gambler's ruin problem to examine how extinction is related to population growth. Using moment theory we demonstrate how higher moments can impact the probability of extinction. We discuss how moments can be used to find bounds on the extinction probability, focusing on s-convex ordering of random variables, a method developed in actuarial science. This approach generates "best case" and "worst case" scenarios to provide upper and lower bounds on the probability of extinction. Our results demonstrate that even the most fit strategies can have high probabilities of extinction.Comment: Best case extrema adde

Stationary-excess operator and convex stochastic orders

The present paper aims to point out how the stationary-excess operator and its iterates transform the s-convex stochastic orders and the associated moment spaces. This allows us to propose a new unified method on constructing s-convex extrema for distributions that are known to be t-monotone. Both discrete and continuous cases are investigated. Several extremal distributions under monotonicity conditions are derived. They are illustrated with some applications in insurance.Insurance risks; s-convex stochastic orders; Extremal distributions; t-monotone distributions; Stationary-excess operator; Discrete and continuous versions.

Behavioral sciences and auto-transformations of functions

The two goals of the present article are: 1) To define transformations (named here as auto-transformations) of the probability density functions of random variables (or other functions) into similar functions having smaller sizes of their domains. 2) To research and outline basic features of these transformations. In particular, auto-transformations from infinite to finite domains are analyzed. The goals are caused by the well-known problems of behavioral sciences

Behavioral sciences and auto-transformations of functions

The two goals of the present article are: 1) To define transformations (named here as auto-transformations) of the probability density functions of random variables (or other functions) into similar functions having smaller sizes of their domains. 2) To research and outline basic features of these transformations. In particular, auto-transformations from infinite to finite domains are analyzed. The goals are caused by the well-known problems of behavioral sciences

Can forbidden zones for the expectation explain noise influence in behavioral economics and decision sciences?

The present article is devoted to discrete random variables that take a limited number of values in finite closed intervals. I prove that if non-zero lower bounds exist for the variances of the variables, then non-zero bounds or forbidden zones exist for their expectations near the boundaries of the intervals. This article is motivated by the need in rigorous theoretical support for the analysis of the influence of scattering and noise on data in behavioral economics and decision sciences

Can forbidden zones for the expectation explain noise influence in behavioral economics and decision sciences?

The present article is devoted to discrete random variables that take a limited number of values in finite closed intervals. I prove that if non-zero lower bounds exist for the variances of the variables, then non-zero bounds or forbidden zones exist for their expectations near the boundaries of the intervals. This article is motivated by the need in rigorous theoretical support for the analysis of the influence of scattering and noise on data in behavioral economics and decision sciences

Macroscopic analogs of quantum-mechanical phenomena and auto-transformations of functions

The two main goals of the present article are: 1) To prove an existence theorem for forbidden zones for the expectations of real-valued random variables. 2) To define transformations (named here as auto-transformations) of the probability density functions (PDFs) of random variables into similar PDFs having smaller sizes of their domains and to outline their basic features. Such transformations can be used also for functions beyond the scope of the probability theory. The goals are caused by the well-known problems of behavioral sciences, e.g., by the underweighting of high and the overweighting of low probabilities, risk aversion, the Allais paradox, etc

Behavioral economics and auto-images of distributions of random variables

Distributions of random variables defined on finite intervals were considered in connection with some problems of behavioral economics. To develop the results obtained for finite intervals, auto-image distributions of random variables defined on infinite or semi-infinite intervals are proposed in this article. The proposed auto-images are intended for constructing reference auto-image distributions for preliminary considerations and estimates near the boundaries of semi-infinite intervals and on finite intervals

Behavioral economics and auto-images of distributions of random variables

Distributions of random variables defined on finite intervals were considered in connection with some problems of behavioral economics. To develop the results obtained for finite intervals, auto-image distributions of random variables defined on infinite or semi-infinite intervals are proposed in this article. The proposed auto-images are intended for constructing reference auto-image distributions for preliminary considerations and estimates near the boundaries of semi-infinite intervals and on finite intervals