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On some joint distributions in fluctuation theory |
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| Authors: | Jagdish Saran Kanwar Sen |
| Institution: | S.V. College, Aligarh, India;University of Delhi, India |
| Abstract: | For non-negative integral valued interchangeable random variables v1, v2,…,vn, Takács (1967, 70) has derived the distributions of the statistics ?n' ?1n' ?(c)n and ?(-c)n concerning the partial sums Nr = v1 + v2 + ··· + vrr = 1,…,n. This paper deals with the joint distributions of some other statistics viz., (α(c)n, δ(c)n, Zn), (β(c)n, Zn) and (β(-c)n, Zn) concerning the partial sums Nr = ε1 + ··· + εrr = 1,2,…,n, of geometric random variables ε1, ε2,…,εn. |
| Keywords: | Interchangeable Random Variables Partial Sums Random Walk Path Composed Path Bernoulli Trials |
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