applying two definitions of the union of if-events, p. grzegorzewski gave two generalizations of the inclusion-exclusion principle for if-events.in this paper we prove an inclusion-exclusion principle for if-states based on a method which can also be used to prove grzegorzewski's inclusion-exclusion principle for probabilities on if-events.finally, we give some applications of this principle by...

Simulated estimates for several proportions are needed in many simulation studies. We propose a method for controlling the length of a simulation run so that the proportions estimated satisfy a prespeciied precision requirement. The method applies the arcsin transform in order to generate conndence intervals with the desired width. The Bonferroni inequality is applied in a new way to construct ...

Holm’s method and Hochberg’s method for multiple testing can be viewed as step-down and step-up versions of the Bonferroni test. We show that both are special cases of partition testing. The difference is that, while Holm’s method tests each partition hypothesis using the largest order statistic, setting a critical value based on the Bonferroni inequality, Hochberg’s method tests each partition...

We present a unified approach to an important subclass of Bonferroni-type inequalities by considering so-called binomially bounded functions. Our main result associates with each binomially bounded function a Bonferroni-type inequality. By appropriately choosing this function, several well-known and new results are deduced.

This paper rigorously demonstrates that for any unequal income distribution, the well-known Gini index of inequality is bounded above by recently revived Bonferroni index. The bound exactly attained if and only out n incomes in society, − 1 poor are identical. boundedness theorem shown to possess a duality-type implication. These two metrics, popular members general class indices generated Aabe...

The computing power of modern workstations has made it possible to simulate many queueing systems interactively. Recent development in simulation software has mainly concentrated on interactive facilities. Unfortunately the precision of estimates has widely been overlooked in interactive simulation. In this paper we propose a method for controlling the pre-cisions of estimated means during an i...

A natural way of viewing an inequality or a poverty measure is in terms of the vector distance between an actual (empirical) distribution of incomes and some appropriately normative distribution (reflecting a perfectly equal distribution of incomes, or a distribution with the smallest mean that is compatible with a complete absence of poverty). Real analysis offers a number of distance function...

It is common for conclusions of empirical studies to depend on multiple significant outcomes. This practice may seem reasonable, but it has some unintended effects. In particular, the compound Type I error rate (the likelihood concluding that an effect exists when does not) can be much lower than individual studies. in itself not a problem since low desirable. However, there also accompanying d...