Topic
Unit interval
About: Unit interval is a research topic. Over the lifetime, 1251 publications have been published within this topic receiving 21132 citations. The topic is also known as: [0,1] & 0 to 1.
Papers published on a yearly basis
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Papers
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TL;DR: The betareg package is described which provides the class of beta regressions in the R system for statistical computing and incorporates features such as heteroskedasticity or skewness which are commonly observed in data taking values in the standard unit interval, such as rates or proportions.
Abstract: The class of beta regression models is commonly used by practitioners to model variables that assume values in the standard unit interval (0, 1). It is based on the assumption that the dependent variable is beta-distributed and that its mean is related to a set of regressors through a linear predictor with unknown coefficients and a link function. The model also includes a precision parameter which may be constant or depend on a (potentially different) set of regressors through a link function as well. This approach naturally incorporates features such as heteroskedasticity or skewness which are commonly observed in data taking values in the standard unit interval, such as rates or proportions. This paper describes the betareg package which provides the class of beta regressions in the R system for statistical computing. The underlying theory is briefly outlined, the implementation discussed and illustrated in various replication exercises.
2,199 citations
TL;DR: A function to help in the ordering of fuzzy subsets of the unit interval is introduced, which is the integral of the mean of the level sets associated with the fuzzy subset.
1,456 citations
1 Jan 2003
TL;DR: It is shown that the class of positive, monotonically decreasing functions on the unit interval leads to kernels and corresponding regularization operators and can be found as a special case of the reasoning.
Abstract: We introduce a family of kernels on graphs based on the notion of regularization operators. This generalizes in a natural way the notion of regularization and Greens functions, as commonly used for real valued functions, to graphs. It turns out that diffusion kernels can be found as a special case of our reasoning. We show that the class of positive, monotonically decreasing functions on the unit interval leads to kernels and corresponding regularization operators.
1,109 citations
TL;DR: An infinite sequence of finite or denumerable limit sets is found for a class of many-to-one transformations of the unit interval into itself and the structure and order of occurrence is universal for the class.
616 citations
1 Jan 1980
TL;DR: In this paper, the extended interval space IR can be used to write formulas, theorems, and proofs in a closed form, without using the left and right interval bounds.
Abstract: This paper shows, how the extended Interval Space IR can be used to write formulas, theorems, and proofs in a closed form, ie without using the left and right interval bounds So a basic generalization and moreover a simplification and improvement of the theorems and proofs is achieved
341 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 11 |
| 2024 | 17 |
| 2023 | 37 |
| 2022 | 112 |
| 2021 | 55 |
| 2020 | 73 |