arXiv subjects

Andreas Nordvall Lagerås

Publications and source records attributed to Andreas Nordvall Lagerås.

5 recordsLinked to original sources

arXiv2009

Analytical and easily calculated expressions for continuous commutation functions under Gompertz-Makeham mortality

It is known, but perhaps not well-known, that when the mortality is assumed to be of Gompertz-Makeham-type, the expected remaining life-length and the commutation functions used for calculating the expected values of various types of life insurances can be expressed with an incomplete gamma function with a negative shape parameter. This is not of much use if ones software cannot calculate these values. The aim of this note is to show that one can express the commutation functions using only the exponential function, the (ordinary) gamma function and the gamma distribution function, which are all implemented in common statistical and spreadsheet software. This eliminates the need to evaluate the commutation functions and expected remaining life-length with numerical integration.

math.PR↗

arXiv2008

A note on the component structure in random intersection graphs with tunable clustering

We study the component structure in random intersection graphs with tunable clustering, and show that the average degree works as a threshold for a phase transition for the size of the largest component. That is, if the expected degree is less than one, the size of the largest component is a.a.s. of logarithmic order, but if the average degree is greater than one, a.a.s. a single large component of linear order emerges, and the size of the second largest component is at most of logarithmic order.

math.PR↗

arXiv2007

Supercritical general branching processes conditioned on extinction are subcritical

It is well known that a simple, supercritical Bienaymé-Galton-Watson process turns into a subcritical such process, if conditioned to die out. We prove that the corresponding holds true for general, multi-type branching, where child-bearing may occur at different ages, life span may depend upon reproduction, and the whole course of events is thus affected by conditioning upon extinction.

math.PR↗

arXiv2007

Epidemics on random graphs with tunable clustering

In this paper, a branching process approximation for the spread of a Reed-Frost epidemic on a network with tunable clustering is derived. The approximation gives rise to expressions for the epidemic threshold and the probability of a large outbreak in the epidemic. It is investigated how these quantities varies with the clustering in the graph and it turns out for instance that, as the clustering increases, the epidemic threshold decreases. The network is modelled by a random intersection graph, in which individuals are independently members of a number of groups and two individuals are linked to each other if and only if they share at least one group.

math.PR↗

arXiv2007

A population model for $Λ$-coalescents with neutral mutations

Bertoin and Le Gall (2003) introduced a certain probability measure valued Markov process that describes the evolution of a population, such that a sample from this population would exhibit a genealogy given by the so-called $Λ$-coalescent, or coalescent with multiple collisions, introduced independently by Pitman (1999) and Sagitov (1999). We show how this process can be extended to the case where lineages can experience mutations. Regenerative compositions enter naturally into this model, which is somewhat surprising, considering a negative result by M{ö}hle (2007).

math.PR↗