Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series A, Pt. 2, 180--187

REAL ZEROS OF A RANDOM ALGEBRAIC POLYNOMIAL

By

N. N. NAYAK, College of Basic Science and Humanities

And

S. BAGH, Sambalpur University

 

SUMMARY. Let Nn (w ) be the number of real zeros of a random algebraic polynomial f(t) = S ni=0 x i (w ) t4 = 0, where the coefficients x i 's are independent, identically distributed random variables belonging to the domain of attraction of the symmetric stable law. It is proved that P{ w : Nn (w ) ³ l1n(256(l2 n)5/4)-1}> 1-321 e(l2 n )3/2 (l1n)-1

.

AMS (1980) subject classification. 60G99

Key words and phrases. Number of real zeros, random algebraic polynomial, domain of attraction

FULL PAPER.

This article in Mathematical Reviews.