An unusual stochastic order relation with some applications in sampling and epidemic theory

Lefèvre, Claude; Picard, Philippe

doi:10.2307/1427496

Cited by 11 publications

(4 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For an arbitrary s, the s-convex order compares the s-th right-tail distribution functions of random variables that have the same first s − 1 moments. In the case of discrete distributions, this class of orders was studied in Lefèvre and Picard (1993), Fishburn and Lavalle (1995), Lefèvre and Utev (1996), Denuit and Lefèvre (1997) and Denuit el al. (1999aDenuit el al.…”

Section: Introductionmentioning

confidence: 99%

Stationary-excess operator and convex stochastic orders

Lefèvre

Loisel

2010

Insurance: Mathematics and Economics

View full text Add to dashboard Cite

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.MSC: primary 60E15, 62P05; secondary 60E10

show abstract

Section: Introductionmentioning

confidence: 99%

Stationary-excess operator and convex stochastic orders

Lefèvre

Loisel

2010

Insurance: Mathematics and Economics

View full text Add to dashboard Cite

show abstract

“…Lefèvre and Picard [6] and Daley [4] gave an analogous result to Theorem 5 for SIR epidemics of this type. Consider two independent within-household SIR epidemics that differ only in their infectious period distributions.…”

Section: Sir Within-household Epidemicsmentioning

confidence: 77%

The Probability of Containment for Multitype Branching Process Models for Emerging Epidemics

Spencer

O’Neill

2011

J. Appl. Probab.

View full text Add to dashboard Cite

This paper is concerned with the definition and calculation of containment probabilities for emerging disease epidemics. A general multitype branching process is used to model an emerging infectious disease in a population of households. It is shown that the containment probability satisfies a certain fixed point equation which has a unique solution under certain conditions; the case of multiple solutions is also described. The extinction probability of the branching process is shown to be a special case of the containment probability. It is shown that Laplace transform ordering of the severity distributions of households in different epidemics yields an ordering on the containment probabilities. The results are illustrated with both standard epidemic models and a specific model for an emerging strain of influenza.

show abstract

“…Thus, to obtain the result it suffices to apply a comparison result given in Property 4.2 of Lefèvre and Picard (1993).…”

Section: )mentioning

confidence: 99%

“…A few other properties used in the paper (but not recalled here) were derived in Lefèvre and Picard (1993) and Picard and Lefèvre (2003).…”

Section: A1 Abel-gontcharoff Polynomialsmentioning

confidence: 99%

Nonstationarity and randomization in the Reed-Frost epidemic model

Lefèvre

Picard

2005

J. Appl. Probab.

Self Cite

View full text Add to dashboard Cite

The purpose of this paper is to determine the exact distribution of the final size of an epidemic for a wide class of models of susceptible-infective-removed type. First, a nonstationary version of the classical Reed-Frost model is constructed that allows us to incorporate, in particular, random levels of resistance to infection in the susceptibles. Then, a randomized version of this nonstationary model is considered in order to take into account random levels of infectiousness in the infectives. It is shown that, in both cases, the distribution of the final number of infected individuals can be obtained in terms of Abel-Gontcharoff polynomials. The new methodology followed also provides a unified approach to a number of recent works in the literature.

show abstract

An unusual stochastic order relation with some applications in sampling and epidemic theory

Cited by 11 publications

References 17 publications

Stationary-excess operator and convex stochastic orders

Stationary-excess operator and convex stochastic orders

The Probability of Containment for Multitype Branching Process Models for Emerging Epidemics

Nonstationarity and randomization in the Reed-Frost epidemic model

Contact Info

Product

Resources

About