On central versus factorial moments
Ramalingam Shanmugam · South African Statistical Journal · 1984
For many probability distributions, especially in the case of discrete distributions, it is relatively easy to find factorial moments. Relations exist (see Comtet, 1974, p. 160) between factorial and ordinary moments. Using such relations, ordinary moments are found first customarily in order to have central moments. Needless to mention, central moments play a key role in statistical inference. In this paper we introduce two numbers with their properties and establish, using these numbers, direct relations between factorial and central moments. We illustrate our results for modified power series distributions.