Stochastic inequalities for weighted sum of two random variables independently and identically distributed as exponential

YILMAZ M., Topcu B.

STATISTICS & PROBABILITY LETTERS, cilt.78, sa.18, ss.3152-3158, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 78 Sayı: 18
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1016/j.spl.2008.05.038
  • Dergi Adı: STATISTICS & PROBABILITY LETTERS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.3152-3158
  • Ankara Üniversitesi Adresli: Evet

Özet

Let X and Y be two random variables which are independently and identically distributed (i.i.d.) as exponential. Given two nonnegative numbers a and b, it is of interest to establish bounds on the tail probability of aX + bY, i.e. P (aX + bY > t). The present work attempts to provide first some basic inequalities for P (aX + bY > t) and then shows that this probability increases in (a. b) defined on the set D = {(a, b) : a(2) + b(2) = 1, a > b} for some t. This result is further supported and enhanced by numerical computation. (C) 2008 Elsevier B.V. All rights reserved.