The probability density functions fitting to the discrete probability functions has always been needed, and very important. This paper is fitting the continuous curves which are probability density functions to the binomial probability functions, negative binomial geometrics, poisson and hypergeometric. The main key in these fittings is the use of the derivative concept and common differential ...

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* We are grateful for helpful comments from Salih Neftci. The comments of an anonymous referee were enormously beneficial. We are grateful for support from the Schweger Fund. Remaining errors are our own.

Let be a complex variable. We associate a polynomial in , denoted M N , to any two molecular species M = M (X) and N = N (X) by means of a binomial-type expansion of the form

We study repeated games with frequent actions and frequent imperfect public signals, where the signals are aggregates of many discrete events, such as sales or tasks. The high-frequency limit of the equilibrium set depends both on the probability law governing the discrete events and on how many events are aggregated into a single signal. When the underlying events have a binomial distribution,...

Creating valid and reliable classroom tests are very important to an instructor for assessing student performance, achievement and success in the class. The same principle applies to the State Exit and Classroom Exams conducted by the instructors, state and other agencies. One powerful technique available to the instructors for the guidance and improvement of instruction is the test item analys...

In this paper, characterizations of the binomial, negative binomial, geometric, Poisson binomial, Hermite and Poisson distributions are done through their factorial cumulants.

Likert items and scales are often used in human subject studies to measure subjective responses of subjects to the treatment levels. In the field of human-robot interaction (HRI), with few widely accepted quantitative metrics, researchers often rely on Likert items and scales to evaluate their systems. However, there is a debate on what is the best statistical method to evaluate the differences...