A uniform asymptotic expansion for weighted sums of exponentials

J.S.H. van Leeuwaarden and N.M. Temme

Statistics & Probability Letters, 2011, vol. 81, issue 11, 1571-1579

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]

Keywords: Asymptotic; analysis; Saddle; point; approximation; Exponential; random; variables; Gumbel; distribution; Kolmogorov; distribution (search for similar items in EconPapers)
Date: 2011
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