New Fuzzy Extensions on Binomial Distribution

On extensions of fuzzy topologies

The concept of fuzzy topological spaces was introduced in [2] and ever since this introduction much research has been done in this area. In this note we introduce the concept of extension of fuzzy topological spaces as done for topological spaces in [1,7]. Let (X, T) be a fuzzy topological space and T C T*. Then T* will be called a simple extension of T iff there exists a 6 $T such that T* = {A...

Binomial Sampling and the Binomial Distribution

This is a good place to point out that these are only (approximating) , and not full truth. models Truth is not a model. A model, by definition, is an approximation (and not truth). In fact, out of a few million coin flips, one or more coins will remain standing on edge – that is truth. The binomial model does not allow such reality. The idea is more easily understood for the outcomes “dead" or...

On Hypergeometric Generalized Negative Binomial Distribution

On Littlewood's Estimate for the Binomial Distribution

We correct a theorem of J. E. Littlewood which gives an approximation for the tail of the binomial distribution. We also present several new approximations which are less accurate but have wider scope. One of them gives an estimate with relative error uniformly 0(11 a) over all values of all the parameters, where a is the standard deviation. For some types of probability calculations, the famil...

Distribution-Sensitive Binomial Queues

A new priority queue structure is introduced, for which the amortized time to insert a new element isO(1) while that for the minimumextraction is O(logK). K is the average, taken over all the deleted elements x, of the number of elements that are inserted during the lifespan of x and are still in the heap when x is removed. Several applications of our structure are mentioned.