DISTRIBUTION OF THE SUM OF INDEPENDENT RIGHT TRUNCATED NEGATIVE BINOMIAL VARIATES

G. S. LINGAPPAIAH[1]

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ABSTRACT:
This paper deals with the negative binomial variables with the distribution (k
+ j – 1) q^{j},

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.

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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.