Ch. A. Charalambides

A New Kind of Numbers Appearing in the n-Fold Convolution of Truncated Binomial and Negative Binomial Distributions

In the present paper the numbers

Abel series distributions with applications to fluctuations of sample functions of stochastic processes

C(m,n,s)

The asymptotic normality of certain combinatorial distributions

appearing in the n-fold convolution of truncated binomial and negative binomial distributions (see T. Cacoullos and Ch. Charalambides [1]) are introduced by \[ C(m,n,s) = \frac{1}{{n!}}[\Delta ^n (sx)_m ]_{x = 0}, \quad m,n\,{\text{positive integers and}}\,s\,{\text{a real number}} \] where

Some Properties and Applications of the Differences of the Generalized Factorials

\Delta

On the q-differences of the generalized q-factorials

denotes the difference operator and

Minimum variance unbiased estimation for the zero class truncated bivariate poisson and logarithmic series distributions

(sx)_m = sx(sx - 1) \cdots (sx - m + 1)

On bivariate generalized binomial and negative binomial distributions

is the usual falling factorial. This definition is shown to be equivalent to that given in [1]. A recurrence relation for these numbers, useful for tabulation purposes, is obtained. The difference equation is solved by using the exponential generating function of the numbers

Gould series distributions with applications to fluctuations of sums of random variables

C(m,n,s)

Bivariate Generalized Discrete Distributions and Bipartitional Polynomials

; a third expression of these numbers is concluded. Relations between Stirling, Lah and C-numbers and limiting expressions containing these numbers are also derived. Finally, some applications of the numbers

ON A GENERALIZED EULERIAN DISTRIBUTION

C(m,n,s)