Weighted averages with random proportions that are jointly uniformly distributed over the unit simplex

Soltani, Aboozar; Homei, Hazhir

doi:10.1016/j.spl.2009.01.009

“…For the same type of measures, the notion of exact order is defined in [14] and [15] and determined for hypergeometric series. When λ is a positive integer, the random weighted average of independent random variables gives rise to generalized Stieltjes transforms of continuous probability measures which may be written as products of Stieltjes transforms [23,24,27]). In the recent paper [18], generalized Stieltjes transforms appear as transmutation operators between the solutions of the hypergeometric differential equation.…”

Section: Remindermentioning

confidence: 99%

Generalized Stieltjes Transforms of Compactly-Supported Probability Distributions: Further Examples

Демни

¹

2016

SIGMA

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Abstract. For two families of beta distributions, we show that the generalized Stieltjes transforms of their elements may be written as elementary functions (powers and fractions) of the Stieltjes transform of the Wigner distribution. In particular, we retrieve the examples given by the author in a previous paper and relating generalized Stieltjes transforms of special beta distributions to powers of (ordinary) Stieltjes ones. We also provide further examples of similar relations which are motivated by the representation theory of symmetric groups. Remarkably, the power of the Stieltjes transform of the symmetric Bernoulli distribution is a generalized Stietljes transform of a probability distribution if and only if the power is greater than one. As to the free Poisson distribution, it corresponds to the product of two independent Beta distributions in [0, 1] while another example of Beta distributions in [−1, 1] is found and is related with the Shrinkage process. We close the exposition by considering the generalized Stieltjes transform of a linear functional related with Humbert polynomials and generalizing the symmetric Beta distribution.

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“…Let us follow Lemma 4.1 to find a simple method to get the distribution of Z 2 . The work of Soltani and Homei (2009b) leads us to the following lemma.…”

Section: Tsp Random Variablesmentioning

confidence: 99%

Two-Sided Power Random Variables

Homei

2012

Preprint

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0

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“…By letting X 1 and X 2 to have identical distributions, he derived that: (i) for X 1 and X 2 on [−1, 1], Z is uniform on [−1, 1] if and only if X 1 and X 2 have arcsin distribution; and (ii) Z possesses the same distribution as X 1 and X 2 if and only if X 1 and X 2 are degenerated or have a Cauchy distribution. Soltani and Homei (2009a) extended Van Assche's results as follows: They put X 1 , • • • , X n to be independent, and considered for n ≥ 2…”

Section: Introductionmentioning

confidence: 99%

“…By letting X 1 and X 2 to have identical distributions, he derived that: (i) for X 1 and X 2 on [−1, 1], Z is uniform on [−1, 1] if and only if X 1 and X 2 have arcsin distribution; and (ii) Z possesses the same distribution as X 1 and X 2 if and only if X 1 and X 2 are degenerated or have a Cauchy distribution. Soltani and Homei (2009a) extended Van Assche's results as follows: They put X 1 , · · · , X n to be independent, and considered for n ≥ 2 S n (R 1 , ..., R n−1 ) = R 1 X 1 + R 2 X 2 + · · · + R n−1 X n−1 + R n X n , (1.1) 1], and U (0) = 0. Soltani and Roozegar (2012), defined fairly large classes of randomly weighted average (RWA) distributions by using new random weights.…”

Section: Introductionmentioning

confidence: 99%

A novel extension of randomly weighted averages

Homei

¹

2014

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We study a well-known problem concerning a random variable Z uniformly distributed between two independent random variables. A new extension has been introduced for this problem and fairly large classes of randomly weighted average distributions are identified by their generalized Stieltjes transforms. In this article we employ the Schwartz distribution theory for finding distributions of this extension; we also study some of their properties.

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Weighted averages with random proportions that are jointly uniformly distributed over the unit simplex

Cited by 13 publications

References 6 publications

Generalized Stieltjes Transforms of Compactly-Supported Probability Distributions: Further Examples

Generalized Stieltjes Transforms of Compactly-Supported Probability Distributions: Further Examples

Two-Sided Power Random Variables

A novel extension of randomly weighted averages

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