Some Comments on the Compound Binomial Model

Roos Compound binomial approximations

We consider the approximation of the convolution product of not necessarily identical probability distributions qj I + pjF , (j = 1, . . . , n), where, for all j , pj = 1 − qj ∈ [0, 1], I is the Dirac measure at point zero, and F is a probability distribution on the real line. As an approximation, we use a compound binomial distribution, which is defined in a one-parametric way: the number of t...

Some comments on the cuff.

This issue of RESPIRATORY CARE includes a detailed study of a novel device to maintain a stable pressure within the cuff of an endotracheal tube (ETT).1 Why all the bother? Why do ETTs need cuffs anyway? These seem like silly questions on the surface. A certain level of occlusion between the tracheal wall and the ETT is necessary for positive-pressure ventilation. But what level of occlusion is...

Some Comments on Qis3

On the Gerber-shiu Penalty Function for the Compound Binomial Risk Model with Delayed Claims

Abstract: In this paper we consider the Gerber-Shiu penalty function in the compound binomial risk model with time-correlated claims. It is assumed that each main claim will induce a by-claim but the occurrence of the by-claim may be delayed with a certain probability. Formulas for the probability generating function of the penalty function are obtained, together with the expression for the pen...

Some Comments on Professor

In a recent issue, this journal published an article by Professor Robert S. Summers reviewing and commenting critically upon a recent book by Professor H. L. A. Hart of Oxford entitled The Concept of Law. Among other things, Professor Summers criticized Professor Hart for stressing rules to the neglect of other elements of a legal system and for succumbing to reductionist tendencies in the anal...