Survival probability and ruin probability of a risk model

In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special casc cxponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.

LAPLACE TRANSFORM OF THE SURVIVAL PROBABILITY UNDER SPARRE ANDERSEN MODEL

In this paper a class of risk processes in which claims occur as a renewal process is studied. A clear expression for Laplace transform of the survival probability is well given when the claim amount distribution is Erlang distribution or mixed Erlang distribution. The expressions for moments of the time to ruin with the model above are given.

Survival Probability of the Quantum Walk with Phase Parameters on the Two-Dimensional Trapped Lattice

We investigate the time dependence of the survival probability of quantum walks governed by Fibonacci walks with phase parameters on the trapped two-dimensional lattice. We have shown that the survival probability of the quantum walk decays with time obey to the stretched exponential law for all initial states of walkers. We have also shown that stretched exponential decay parameter β can be arranged by phase parameter combination. Obtained numerical results show that phase parameters can be used as a control parameter to determine the decay rate of the survival probability of the quantum walk.

Determining exact survival probability by setting discrete random variables in E. Sparre Andersen’s model

In this work,we propose an alternative to the Pollaczek-Khinchine formula for the ultimate time survival(or ruin)probability calculation in exchange for a few assumptions on the random variables that generate the renewal risk model.More precisely,we demonstrate the expressibility of the distribution function n P(sup n≥1^(n)∑_(i=1)(X_(i)-cθ_(i))<u),u∈N_(0)using the roots of the probability-generating function,expectation E(X-cθ)X-cθ,and probability mass function of.We assume that the random X_(1),X_(2),...cθ_(1),cθ_(2),...variables of the mutually independent sequences and are cθc>0 X cθindependent copies of X and respectively,wherein,and are independent,θnonnegative,and integer.We also assume that the support of is finite.To illustrate the applicability of the proven theoretical statements we present a few numerical outputs when the mentioned random variables adopt some particular distributions.

Multi-stage emergency medicine logistics system optimization based on survival probability

Using sudden cardiac deaths as an example and maximizing survival rate as the goal, this paper studies the influence of multi-stage medical logistics system optimization on the survival rate of sudden illness. A distribution model of survival is built, drone and ambulance arrival probability over time are discussed, a formula is proposed for maximum possible survival rate based on the probability of emergency medical logistics reaching the patient, and the results are analyzed using empirical data fitting distribution and numerical experiments performed with the model. The model is discussed as a reference point for management decision making by changing model parameters. Results show that compared to using current ambulance vehicles, ambulance drones delivering medical equipment for first aid on-site in emergencies can significantly increase survival rate, and the effect of collaborative multi-stage logistics optimization is better than that of any single stage logistics response optimization. Simulation results show that the medical rescue logistics service radius, speed, loading capacity and performance of ambulance drones impact the probability of survival, and there is an optimal service radius depending on the shape of probability distribution, which provides new information for management decisions.

On a Nonparametric Estimator for the Finite Time Survival Probability with Zero Initial Surplus

In this paper, we consider the estimation of the finite time survival probability in the classical risk model when the initial surplus is zero. We construct a nonparametric estimator by Fourier inversion and kernel density estimation method. Under some mild assumptions imposed on the kernel, bandwidth and claim size density, we derive the order of the bias and variance, and show that the estimator has asymptotic normality property. Some simulation studies show that the estimator performs quite well in the finite sample setting.

Effects of N/Z on survival probability of heavy nuclei

The excitation functions of the evaporation residue formation probability of three heavy nuclei ^194pb, ^200Pb and ^206pb are calculated by using a Langevin equation coupled with a statistical decay model. The results show that the neutron-to-proton ratio （N/Z） of a compound nucleus has an effect on survival probability and this effect becomes larger with increasing N/Z. This is because the fission barrier and the pre-saddle particle emission depend on the N/Z ratio of the system.

Analysis of survival probability based on superasymmetric reaction systems

The survival probability of an excited compound nucleus was studied using two different approaches of the washing out of shell effects with excitation energy based on a superasymmetric reaction system.The estimated evaporation residue cross sections based on the two different methods are compared with the available experimental data.Both methods are in agreement with the experimental data to a certain extent for some specific reactions and emission channels.

Factors affecting post-release survival and dispersal of reintroduced Crested Ibis(Nipponia nippon)in Tongchuan City,China

Reintroduction has become a common conservation management tool to restore endangered species in their historical range.However,many attempts have failed to establish self-sustaining populations in the wild.The success of reintroductions could be improved by varying release strategies.Therefore,it is vital to determine the factors influencing reintroduction outcomes.To better understand the post-release settlement and to optimize the release strategy of the Crested Ibis(Nipponia nippon),we quantified the effects of age,sex,acclimation duration,and the timing of release events on post-release survival and dispersal distance for the released Crested Ibis in Tongchuan City,Shaanxi Province,using a generalized linear mixed effect modeling approach.Our results indicate that 40–56.3%of the released individuals survived the first year following release.Mortality was attributable to flight collisions,starvation,disease,and unknown reasons.The post-release survival probability of ibises showed a negative association with age(estimate=-0.186;95%CI:-0.350 to-0.022;P=0.026),and post-release dispersal distance was affected by the timing of release event(estimate=0.718;95%CI:0.025 to1.253;P=0.042).However,sex and acclimation period duration did not cause detectable differences in postrelease survival probability and dispersal distance.Based on our results,optimal release strategies for establishing a reintroduced population of the Crested Ibis include:(1)release of sub-adults biased and sex ratio balanced initial groups;(2)release during the non-breeding season;and(3)food supplementation immediately after release.

RANDOMIZATION METHOD OF DETERMINISTIC EQUATION FOR PROBABILITY FRACTURE MECHANICS

In order to obtain any probability of survival for crack growth life, a randomization method of deterministic equation for probability fracture mechanics is presented. According to this method, the deterministic equation of fracture mechanics is randomized to stochastic equation, and the parameters of the stochastic equation are estimated by means of the statistics. Three new kinds of random models to gain the p d a/ d N Δ K curve and the γ p d a/ d N Δ K curve (confidence level probability of survival fatigue crack growth rate stress intensity factor range curve) are proposed by using this randomization method. And the p d a/ d N Δ K curves and the γ p d a/ d N Δ K curves determined by these three models are discussed and compared according to the treatment result of the experimental data from CT specimens. From examples, it is found that the three deterministic fatigue crack growth rate equations determined by these models are very near and in agreement with the traditional deterministic fatigue crack growth rate equation, and these models are effectively and easily used to treat fatigue crack growth rate data.

On single particle breakage behavior of crushable weathered sands

This paper presents an experimental study on single particle breakage behavior of crushable weathered sands by a number of single particle uniaxial compression tests to comprehensively investigate the characteristics of single particle breakage,the probability of survival of single particle,and the effects of particle size and weathering on single particle strengths.The behavior of single particle under uniaxial compression falls into the mixed five phases:damage by chipping,elastic deformation,fragmentation by partial fracture,breakage by splitting,and the residuals,demonstrating the complexity and variability of the tensile strengths of single particles.The behavior of single particle breakage was quantified herein by the initial fracture and failure strengths of single particle.The probability of survival decreased as the characteristic stresses increased.An increase in the particle size or weathering number of single particle resulted in a reduction in the probability of survival of single particle.For a given probability of survival,the difference in the initial fracture characteristic stress and failure characteristic stress decreased with increasing particle size but showed a complex change with increasing weathering number.The probability of survival showed greater variability for the normalized initial fracture characteristic stress than for the normalized failure characteristic stress,implying that the initial fracture stresses of single particles diverged more than the failure stresses of the particles.The average initial fracture and failure characteristic stresses,and the initial fracture and failure characteristic stresses corresponding to 1/e(37%)survival of single particles decreased while increasing particle size or weathering number,but the decrease showed a sharper rate for smaller single particles with a lower weathering number.The ln-ln coordinates showed a linear representation of the failure characteristic stress and particle size,verifying the applicability of Weibull theory to single particle breakage.However,weathering resulted in downward translation and slight rotation of the linear relation of the failure characteristic stress and particle size in the ln-ln coordinates.

Thermodynamic Formulation of Living Systems and Their Evolution II

In the previous paper [1], the application of the general thermodynamic theory was considered to biological systems. The nature of living matter has been presented from the mesoscopic to the macroscopic point of view, for different time scales (ontogenetic and phylogenetics). Herein, we continue with this application, and present three characteristics of life in the form of statements or postulates. The first characteristic describes the probability of survival against aging. In particular, the behaviour of life is shown as an independent mode of aging. The second characteristic refers to the adaptation of the species according to the environment. The relationship between the phenomenon of organic homeostasis and the origin of the clinical parameters that define health is highlighted. And finally, the third characteristic applies the principle of negentropy to describe evolution. A representative model is given as an example of each postulate.

Heavy ion fusion of spherical nuclei

We study the experimental and theoretical fusion reactions of compound nuclei synthesized using different projectile-target systems,among which at least one projectile/target nucleus is spherical.The first part of this study analyses the fusion cross sections obtained using different projectile-target combinations in the synthesis of polonium(Po),thorium(Th),and nobelium(No).In the second part of this study,we suggest the fusion reaction to synthesize the superheavy element Z=122.We select three nuclei,polonium(Po),thorium(Th),and nobelium(No),which are synthesized using various projectile-target combinations.We also investigate fusion reactions such as^(90)Zr(^(208)Pb,2n)^(296)122.This study may be a milestone in the synthesis of the superheavy element Z=122.

THE RANGE OF RANDOM WALK ON TREES AND RELATED TRAPPING PROBLEM

This paper treats of the range of the simple random walk on trees and a related trapping problem. The strong law of large numbers and the central limit theorem for the range, and some asymptotic behaviour for the mean trapping time and survival probability are presented.