Tables of cumulative distribution functions and percentiles of the standardized stable random variables Academic Article uri icon

abstract

  • It is shown that Zolotarev's (1964) integral representation of the cumulative distribution function (c.d.f.) of stable random variables and the IMSL subroutine DCADRE (for numerical integration) provide a natural and practically simple method for finding the values of c.d.f., the percentiles and the density function of such random variables. For symmetric stable random variables (r.v.s) Za, values of Pa(z) = P(0 Za Z) for z = 0(.02)4.08 and a = 1(.2).9, as well as percentiles of these r.v.'s for a = 5(.1)2 and the percentage points. 6. 7(.05).85(.025).9(.01).96(.005). 995, are presented. For asymmetric stable r.v.'s we present values of their c.d.f.'s for z = 0(.1)4, $ = - 1(.25)1 and a =.1(.2)1.9. These results are compared with related results of others which were obtained by using different procedure and standardization. 1984, Taylor & Francis Group, LLC. All rights reserved.

published proceedings

  • Communications in Statistics - Simulation and Computation

author list (cited authors)

  • Hua, T. A., & Pourahmadi, M.

citation count

  • 2

complete list of authors

  • Hua, Tsushung A||Pourahmadi, M

publication date

  • January 1, 1984 11:11 AM