Tables and graphs of the stable probability density functions

Holt, Donald R.; Crow, Edwin L.

doi:10.6028/jres.077b.017

Cited by 66 publications

(53 citation statements)

References 7 publications

(11 reference statements)

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“…It seems impossible to express stable probability densities, p (x), in a closed form (graphs and tables are in reference [34] , and so on. Now we shall map our minimal coupling model of Section 2 to this mathematics.…”

Section: Levy Distributionsmentioning

confidence: 99%

Phenomenological treatment of dynamic glass transition heterogeneity

Donth¹

1999

Acta Polym.

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Section: Levy Distributionsmentioning

confidence: 99%

Phenomenological treatment of dynamic glass transition heterogeneity

Donth¹

1999

Acta Polym.

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“…stable density they were able to check their results against Holt and Crow's tables [20] for a = 1/4, 1/2, and 3/4. However, these tables are given to four places in fixed arithmetic.…”

Section: Qa(z) = E -Cos(zu)dumentioning

confidence: 99%

“…When a satisfactory value of a is determined, using eq (18), we may find r from the relation (19) wherefm is the frequency in Hz at which the peak maximum occurs. Finally, since an estimate of the peak height will generally be available, the estimate of the parameter A can be found from (20) where relevant values of M(a) are given in table 5. The first three data points were used to estimate the peak location and height.…”

Section: Application To Polymer Physicsmentioning

confidence: 99%

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Stable law densities and linear relaxation phenomena

Dishon¹,

Weiss²,

Bendler³

1985

J. RES. NATL. BUR. STAN.

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Stable law distributions occur in the description of the linear dielectric behavior of polymers, the motion of carriers in semi-conductors, the statistical behavior of neurons, and many other phenomena. No accurate tables of these distributions or algorithms for estimating the parameters in these relaxation models exist. In this paper we present tables of the functions Q.(Z)= J rea cos(zu)duVa()= e sin(zu)du together with related functional properties of zQa(z). These are useful in the estimation of the parameters in relaxation models for polymers and related materials. Values of the integral Qa(z) are given for a=0.01, 0.02(0.02)0.1(0.1)1.0(0.2)2.0 and those of V(z) are given for a=0.0(0.01)0.l(0.1)2.0. A variety of methods was used to obtain six place accuracy. The tables can be used to sequentially estimate the three parameters appearing in the Williams-Watts model of relaxation. An illustration of this method applied to data in the literature is given.

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“…(The density function for positive 0 values may be obtained by reflection of these curves about the vertical axis.) The figure has been modified from one in Holt and Crow (1973) and has been purposely selected to have a relatively low 01 value to emphasize how the curve changes as 0 changes, although noticeable changes in the location of the mode are discernable up to a = 1.75 and beyond. (At a = 2, the family of curves combines into a single normal distribution symmetrically distributed about the origin.)…”

Section: Measurement Of Trading Performancementioning

confidence: 99%

Stable distributions, futures prices, and the measurement of trading performance

Cornew¹,

Town²,

Crowson³

1984

Journal of Futures Markets

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n recent years there has been a growing awareness that futures prices and I other economic price series are not well described by normal probability distributions. Accordingly, a number of different investigators (Mandelbrot, 1963; Roll, 1968,1971;Dusak, 1973;Mann and Heifner, 1976, and others who have worked outside the futures price area) have considered the determination of parameters to fit one or another members of the family of stable distributions to an underlying economic price series. Here, we have used stable distributions to fit futures price series (including foreign exchange price series) from US.-regulated exchanges and have compared the results obtained against those obtained from fitting the same data series with normal distributions. In total, daily price series from 18 different futures markets were considered. These included 12 different metals, livestock, agricultural and world commodities (duplicate gold and silver contracts from different exchanges were reviewed), and four different currencies. They represent the most comprehensive selection of different futures contracts yet analyzed in this way. In contrast to previous measurements of this type, symmetry of the underlying price distributions was not an a priori assumption. The data series selected were all of long duration, having time periods ranging from three to nine years with each containing between 807 and 2291 data points.

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Tables and graphs of the stable probability density functions

Cited by 66 publications

References 7 publications

Phenomenological treatment of dynamic glass transition heterogeneity

Phenomenological treatment of dynamic glass transition heterogeneity

Stable law densities and linear relaxation phenomena

Stable distributions, futures prices, and the measurement of trading performance

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