in this research, a new control policy for the acceptance sampling problem is introduced. decision is made based on the number of defectives items in an inspected batch. the objective of the model is to find a constant control level that minimizes the total costs, including the cost of rejecting the batch, the cost of inspection and the cost of defective items. the optimization is performed by ...

The pricing models of American-type path-dependent options are of degenerate parabolic obstacle problems. The binomial tree method is the most popular approach to pricing options. For some special cases, this method is modified in order to make it feasible. The main purpose of this paper is, using numerical analysis and the notion of viscosity solutions, to show the uniform convergence of the b...

Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item splitting, these new created denominator of series contain 1 to 4 odd factors of binomial coefficients. As the result of splitting items, some identities of series of numbers values ...

The paper is concerned with the accuracy in total variation of the approximation of the distribution of a sum of independent Bernoulli distributed random d–vectors by the product distribution with Poisson marginals which has the same mean. The best results, obtained using generating function methods, are those of Roos (1998, 1999). Stein’s method has so far yielded somewhat weaker bounds. We de...

For a prime p and binomial axk+bxl with 1 ≤ l < k < 1 32 (p−1) 2 3 , we use Stepanov’s method to obtain the bound ∣∣∣∣∣ p−1 ∑ x=1 ep(ax k + bx) ∣∣∣∣∣ max { 1, l∆− 1 3 } 1 4 k 1 4 p 3 4 , where ∆ = k−l (k,l,p−1) .

We develop a general method for computing logarithmic and log-gamma expectations of distributions. As a result, we derive series expansions and integral representations of the entropy for several fundamental distributions, including the Poisson, binomial, beta-binomial, and negative binomial distributions. Our results also establish connections between the entropy functions and to the Riemann z...