A Three-Parameter Binomial Approximation

Continuous approximation of binomial lattices

A systematic analysis of a continuous version of a binomial lattice, containing a real parameter γ and covering the Toda field equation as γ → ∞, is carried out in the framework of group theory. The symmetry algebra of the equation is derived. Reductions by one–dimensional and two–dimensional subalgebras of the symmetry algebra and their corresponding subgroups, yield notable field equations in...

Confidence Intervals for the Binomial Parameter

ON NEGATIVE BINOMIAL APPROXIMATION TO k-RUNS

The distributions of the run occurrences for a sequence of independent and identically distributed (i.i.d.) experiments are usually obtained by combinatorial methods (see Balakrishnan and Koutras (2002, Chapter 5)) and the resulting formulae are often very tedious, while the distributions for non i.i.d. experiments are generally intractable. It is therefore of practical interest to find a suita...

Stirling's Approximation for Central Extended Binomial Coefficients

We derive asymptotic formulae for central polynomial coefficients, a generalization of binomial coefficients, using the distribution of the sum of independent uniform random variables and the CLT. 1 Stirling’s formula and binomial coefficients For a nonnegative integer m, Stirling’s formula m! ∼ √ 2πm (m e )m , where e is Euler’s number, yields an approximation of the central binomial coefficie...

Multivariate Poisson–Binomial approximation using Stein’s method

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...