A Note on the Convolution of Uniform Distributions

Olds, Edwin G.

doi:10.1214/aoms/1177729446

Cited by 35 publications

(12 citation statements)

References 2 publications

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“…A q-value is assigned to each gene based on the null model in which the rank-sum statistic is formed by adding n integers randomly from a uniform distribution, with replacement. The exact closed-form expression for the distribution of the rank-sum statistic for uniform variates is known and can be used with great accuracy for sums of discrete ranks when the number of genes is large [31]. …”

Section: Methodsmentioning

confidence: 99%

Developmental and Extracellular Matrix-Remodeling Processes in Rosiglitazone-Exposed Neonatal rat Cardiomyocytes

et al. 2014

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Objective The objective of this study was to investigate the effects of rosiglitazone (Avandia®) on gene expression in neonatal rat ventricular myocytes. Materials & methods Myocytes were exposed to rosiglitazone ex vivo. The two factors examined in the experiment were drug exposure (rosiglitazone and dimethyl sulfoxide vs dimethyl sulfoxide), and length of exposure to drug (1/2 h, 1 h, 2 h, 4 h, 6 h, 8 h, 12 h, 18 h, 24 h, 36 h and 48 h). Results Transcripts that were consistently expressed in response to the drug were identified. Cardiovascular system development, extracellular matrix and immune response are represented prominently among the significantly modified gene ontology terms. Conclusion Hmgcs2, Angptl4, Cpt1a, Cyp1b1, Ech1 and Nqo1 mRNAs were strongly upregulated in cells exposed to rosiglitazone. Enrichment of transcripts involved in cardiac muscle cell differentiation and the extracellular matrix provides a panel of biomarkers for further analysis in the context of adverse cardiac outcomes in humans.

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Section: Methodsmentioning

confidence: 99%

Developmental and Extracellular Matrix-Remodeling Processes in Rosiglitazone-Exposed Neonatal rat Cardiomyocytes

et al. 2014

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“…Lagrange used generating functions based on to obtain the distribution of T ([9, pages 603-612], [10, page 283] [12][13][14], [15, pages 362-363], [16,17]). Others utilize the convolution integral for sums and mathematical induction ([4, page 225], [11, pages 190-191 and 244-246], [18]). The distribution of the sum of uniform random variables that may have differing domains is found in [18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

“…Others utilize the convolution integral for sums and mathematical induction ([4, page 225], [11, pages 190-191 and 244-246], [18]). The distribution of the sum of uniform random variables that may have differing domains is found in [18][19][20][21]. Sums of dependent uniform random variables are examined in [22,23].…”

Section: Introductionmentioning

confidence: 99%

A Geometric Derivation of the Irwin-Hall Distribution

Marengo

Farnsworth

Stefanic

2017

International Journal of Mathematics and Mathematical Sciences

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The Irwin-Hall distribution is the distribution of the sum of a finite number of independent identically distributed uniform random variables on the unit interval. Many applications arise since round-off errors have a transformed Irwin-Hall distribution and the distribution supplies spline approximations to normal distributions. We review some of the distribution's history. The present derivation is very transparent, since it is geometric and explicitly uses the inclusion-exclusion principle. In certain special cases, the derivation can be extended to linear combinations of independent uniform random variables on other intervals of finite length. The derivation adds to the literature about methodologies for finding distributions of sums of random variables, especially distributions that have domains with boundaries so that the inclusion-exclusion principle might be employed.

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“…Surprisingly, the general distribution of the mean of a sample of n where each has been drawn from a different rectangular distribution does not seem to have received much attention in the literature. The distribution of the sum, which is in effect the same problem, has been proved by induction by Olds (1952).…”

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confidence: 93%

The Frequency Distribution of the Sample Mean Where Each Member of the Sample is Drawn from a Different Rectangular Distribution

Roach¹

1963

Biometrika

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A Note on the Convolution of Uniform Distributions

Cited by 35 publications

References 2 publications

Developmental and Extracellular Matrix-Remodeling Processes in Rosiglitazone-Exposed Neonatal rat Cardiomyocytes

Developmental and Extracellular Matrix-Remodeling Processes in Rosiglitazone-Exposed Neonatal rat Cardiomyocytes

A Geometric Derivation of the Irwin-Hall Distribution

The Frequency Distribution of the Sample Mean Where Each Member of the Sample is Drawn from a Different Rectangular Distribution

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