DISTRIBUTION OF THE SUM OF INDEPENDENT RIGHT TRUNCATED NEGATIVE BINOMIAL VARIATES

G. S. LINGAPPAIAH[1]

 

§    ABSTRACT: This paper deals with the negative binomial variables with the distribution (k + j – 1) qj,

  j

j=0,1,...,m where m is the right truncation point. Distribution of the sum of such t-independent right truncated variables is the object of this paper. There are three sets of parameters, q1,...,qt; m1, ..., mt and k1,...,kt. First, the mean and variance for this the general case when all the three sets of parameters are different among themselves, are put in closed forms. A small table gives the actual E(x) and var (x) for low values of these parameters. Next, for a special case when all the three sets of parameters are equal among themselves, distribution of the sum is expressed in terms of L-numbers. Some recurrence relations are given to generate theses L-numbers. A small table gives these generated L-number for few values of mi’s, qi’s and ki’s.

§    KEYWORDS: Truncation; negative binomial variates; L-numbers; distribution of the sum;

AMS Classification: 62 F 15.

 



[1] Departament of Mathematics & Statistics – Sir George Williams Campus – Concordia University – 1455 de Maisonneuve Boulevard West – Quebec – H3G – 1M8.