Tables of cumulative distribution functions and percentiles of the standardized stable random variables |
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Authors: | Tsushung A Hua M Pourahmadi |
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Institution: | Department of Mathematical Sciences , Northern Illinois University , DeKalb, IL, 60115 |
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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 ) Z∝, values of P∝(z) … P(0<Z∝<z) for z … 0(.02)4.08 and ∝=.1(.2)1.9, as well as percentiles of these r.v.'s for ∝=.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, ß= ?1(.25)1 and ∝=.1(.2)1.9. These result sare compared with related results of others which were obtained by using different procedure and standardization. |
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Keywords: | stable random variable standardization series expansion integral representation numerical integration cumulative distribution functions percentiles |
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