MRM-applicable measures for the power function of the second order

Kubo, Izumi; Kuo, Hui-Hsiung; Namli, Suat

doi:10.31390/cosa.5.4.03

Cited by 4 publications

(3 citation statements)

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“…[9][10][11][12] Since the first two cases are extremal and have been discussed in previous papers, we will exclude them in this paper. On the contrary, the case κ = 2 can be included in the general cases.…”

Section: Classes Of Mrm-applicable Measures For Power Function Of Genmentioning

confidence: 99%

Classes of MRM-Applicable Measures for the Power Function of General Order

Kubo

Kuo

Namli

2013

Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

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The authors have previously studied multiplicative renormalization method (MRM) for generating functions of orthogonal polynomials. In particular, they have determined all MRM-applicable measures for renormalizing functions h(x) = ex, h(x) = (1 - x)-κ, κ = 1/2, 1, 2. For the cases h(x) = ex and (1 - x)-1, there are very large classes of MRM-applicable measures. For the other two cases κ = 1/2, 2, MRM-applicable measures belong to special classes of a certain kind of beta distributions. In this paper, we determine all MRM-applicable measures for h(x) = (1 - x)-κ with κ ≠ 0, 1, 1/2.

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Section: Classes Of Mrm-applicable Measures For Power Function Of Genmentioning

confidence: 99%

Classes of MRM-Applicable Measures for the Power Function of General Order

Kubo

Kuo

Namli

2013

Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

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“…There are few examples of known distributions that are distributions of RWA on the form (1.1), S n , and there is not any examples, to the best of our knowledge, that are distributions of RWA on the form (1.2), S n:n 1 ,...,n k−1 . Roozegar and Soltani [6] used the investigations of [4] and [5] on the connection between ST and GST of two distributions and introduce new classes of power semicircle laws that are RWA S n distributions. In this paper we introduce new classes of RWA S n:n 1 ,...,n k−1 distributions.…”

Section: Introductionmentioning

confidence: 99%

“…In this section we present some special examples of distributions that are randomly weighted average distributions given in (1.2).Other examples of RWA S n distributions in case of r 1 = r 2 = • • • = r k = 1 and k = n can be found in[6]. For the first and second examples, we use the results of[5]. Let X 1 , X 2 and R be independent random variables with beta(1/2, 1/2), beta(m−1/2, m−1/2) and beta(1, m−1) distributions, respectively.…”

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confidence: 99%

Certain Family of Some Beta Distributions Arising from Distribution of Randomly Weighted Average

Roozegar¹

2015

Preprint

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We give the exact distribution of the average of n independent beta random variables weighted by the selected cuts of (0, 1) by the order statistics of a random sample of size n − 1 from the uniform distribution U (0, 1), for each n. A new integral transformation that is similar to generalized Stieltjes transform is given with various properties. The result of Soltani and Roozegar [On distribution of randomly ordered uniform incremental weighted averages: Divided difference approach. Statist Probab Lett. 2012;82(5):10121020] with this new transform and also integral representation of the Gauss-hypergeometric function in some parts are employed to achieve the exact distribution. Several examples of the new family are investigated.

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