This paper presents and first scientifically substantiates the generalized theory of binomial number systems (BNS) method their formation for reliable digital signal processing (DSP), transmission, data storage. The is obtained based on general positional (PNS) with conditions functions converting BNS a binary alphabet, also allowing to generate matrix BNS, linear-cyclic, multivalued systems. G...

The difference between two binomial proportions is commonly used in applied research. Since many studies encounter incomplete data, proper methods to analyze such data are needed. Here, we present a multiple imputation (MI) procedure for constructing confidence interval using Newcombe’s method, which known have better coverage probability when compared with Wald’s method. We use both convention...

The binomial tree method, first proposed by Cox, Ross, and Rubinstein [Journal of Financial Economics, 7 (1979), pp. 229–263], is one of the most popular approaches to pricing options. By introducing an additional path-dependent variable, such methods can be readily extended to the valuation of path-dependent options. In this paper, using numerical analysis and the notion of viscosity solutions...

In this paper, we investigate the use of assessments of conditional previsions for modeling prior information on the parameter of a binomial model as a way of obtaining non-vacuous posterior previsions via natural extension. More specifically, we argue that a useful method for obtaining an imprecise prevision for the parameter θ of a binomial model, given a sample of size n showing r successes,...

We introduce the negative binomial states with negative binomial distribution as their photon number distribution. They reduce to the ordinary coherent states and Susskind-Glogower phase states in different limits. The ladder and displacement operator formalisms are found and they are essentially the Perelomov’s su(1, 1) coherent states via its Holstein-Primakoff realisation. These states exhib...

Using the Stein-Chen method some upper bounds in Poisson approximation for distributions of row-wise triangular arrays of independent negative-binomial distributed random variables are established in this note.