An urn model study of variability within a compartment

Bernard, S.R.

doi:10.1007/bf02462924

Cited by 23 publications

(2 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We turn now to a variability problem for an urn model with successive reinforcement-depletions of random size. The model was introduced by Bernard (1977) to describe the dilution over time of some material, such as radioactive atoms, within some region. In Bernard's original model, the reinforcement-depletion sizes are constant; following an extension proposed by Shenton (1981), we suppose here that these sizes are random.…”

Section: A Reinforcement-depletion Urn Modelmentioning

confidence: 99%

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

Lefèvre

Picard

1993

Advances in Applied Probability

View full text Add to dashboard Cite

One expects, intuitively, that the total damage caused by an epidemic increases, in a certain sense, with the infection intensity exerted by the infectives during their lifelength. The original object of the present work is to make precise in which probabilistic terms such a statement does indeed hold true, when the spread of the disease is described by a collective Reed–Frost model and the global cost is represented by the final size and severity. Surprisingly, this problem leads us to introduce an order relation for -valued random variables, unusual in the literature, based on the descending factorial moments. Further applications of the ordering occur when comparing certain sampling procedures through the number of un-sampled individuals. In particular, it is used to reinforce slightly comparison results obtained earlier for two such samplings.

show abstract

Section: A Reinforcement-depletion Urn Modelmentioning

confidence: 99%

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

Lefèvre

Picard

1993

Advances in Applied Probability

View full text Add to dashboard Cite

show abstract

“…What is the distribution of red and white balls ? Bernard [1] studied this model paying particular attention to means and variances when radioiodine is injected into animals. If the reinforcement of red balls in the urn at each cycle is large it seems likely that the variance of red balls at a subsequent stage will be large (small) if the number randomly removed at each stage is large (small).…”

Section: Introductionmentioning

confidence: 99%

A reinforcement-depletion urn model: A contiguity case

Bowman

Shenton

1986

Ann Inst Stat Math

View full text Add to dashboard Cite

SummaryAn urn contains balls of s different colors. The problem of the reinforcement of a specified color and random depletion of balls has been considered by Bernard (1977, Bull. Math. Biol., 39, 463-470) and Shenton (1981, Bull. Math. Biol., 43, 327-340), (1983, Bull. Math. Biol., 45, 1-9). Here we consider a special relation between a reinforcement and depletion, leading to a hypergeometric distribution.

show abstract

Advances in Urn Models during the Past Two Decades

Kotz

Balakrishnan

1997

Advances in Combinatorial Methods and Applications to Probability and Statistics

View full text Add to dashboard Cite

An urn model study of variability within a compartment

Cited by 23 publications

References 2 publications

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

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

A reinforcement-depletion urn model: A contiguity case

Advances in Urn Models during the Past Two Decades

Contact Info

Product

Resources

About