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A uniform asymptotic expansion for weighted sums of exponentials

Author

Listed:
  • van Leeuwaarden, J.S.H.
  • Temme, N.M.

Abstract

We consider the random variable Zn,[alpha]=Y1+2[alpha]Y2+...+n[alpha]Yn, with and Y1,Y2,... independent and exponentially distributed random variables with mean one. The distribution function of Zn,[alpha] is in terms of a series with alternating signs, causing great numerical difficulties. Using an extended version of the saddle point method, we derive a uniform asymptotic expansion for that remains valid inside ([alpha]>=-1/2) and outside ([alpha]

Suggested Citation

  • van Leeuwaarden, J.S.H. & Temme, N.M., 2011. "A uniform asymptotic expansion for weighted sums of exponentials," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1571-1579, November.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:11:p:1571-1579
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