Modified Kumaraswamy distributions for double bounded hydro-environmental data

Sagrillo, Murilo; Guerra, Renata Rojas; Bayer, Fábio M.

doi:10.1016/j.jhydrol.2021.127021

Cited by 13 publications

(6 citation statements)

References 23 publications

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“…In this section, we present an empirical analysis of the monthly UV (percentage of useful volume) time series of the Samuel water reservoir in the Rondônia State, Brazil. The UV is defined as the volume of water between the maximum and minimum normal operating levels (Operador Nacional do Sistema Elétrico 2022; Sagrillo et al 2021). The hydropower is the primary source of electric energy in Brazil, with an installed hydroelectric capacity representing about 64% of the National Interconnected System (SIN) in 2021 Sagrillo et al (2021).…”

Section: Percentage Of Useful Volume Applicationmentioning

confidence: 99%

“…The UV is defined as the volume of water between the maximum and minimum normal operating levels (Operador Nacional do Sistema Elétrico 2022; Sagrillo et al 2021). The hydropower is the primary source of electric energy in Brazil, with an installed hydroelectric capacity representing about 64% of the National Interconnected System (SIN) in 2021 Sagrillo et al (2021). Thus, the water resource management is important for the generation of electricity in the country.…”

Section: Percentage Of Useful Volume Applicationmentioning

confidence: 99%

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Inflated beta autoregressive moving average models

et al. 2023

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In this paper, we introduce the inflated beta autoregressive moving average (IβARMA) models for modeling and forecasting time series data that assume values in the intervals (0,1], [0,1) or [0,1]. The proposed model considers a set of regressors, an autoregressive moving average structure and a link function to model the conditional mean of inflated beta conditionally distributed variable observed over the time. We develop partial likelihood estimation and derive closed-form expressions for the score vector and the cumulative partial information matrix. Hypotheses testing, confidence interval, some diagnostic tools and forecasting are also proposed. We evaluate the finite sample performances of partial maximum likelihood estimators and confidence interval using Monte Carlo simulations. Two empirical applications related to forecasting hydro-environmental data are presented and discussed.

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Section: Percentage Of Useful Volume Applicationmentioning

confidence: 99%

Section: Percentage Of Useful Volume Applicationmentioning

confidence: 99%

Inflated beta autoregressive moving average models

et al. 2023

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“…where K is constant and Differentiating the log-likelihood function in ( 14) concerning and λ one can obtain [21]…”

Section: F Estimation Using Ranked Set Sampling (Rss) Techniques 1) M...mentioning

confidence: 99%

The Kumaraswamy Distribution: Statistical Properties and Application

Badra¹,

Mohammed²

2022

Int. J. Adv. Sci. Eng. Inf. Technol.

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Modeling and analyzing lifetime data is an important aspect of statistical work in various scientific and technological fields such as medicine, engineering, insurance, and finance. The modeling and analysis of lifetimes is an important aspect of statistical work in various scientific and technological fields. In recent years, inverted Kumaraswamy distribution has been used quite effectively to model many lifetime data. The most broadly applied statistical distribution is Kumaraswamy distribution in hydrological problems and many natural phenomena. The Kumaraswamy distribution (KD) is widely applied for modeling data in practical domains, such as medicine, engineering, economics, and physics. The present work proposes the Bayesian estimators of KD parameters through the use of type-II censoring data in this research the problem to estimate the unknown parameters of Kumaraswamy distribution with two parameters and λ, these estimates are a maximum likelihood of ordered observation and the Bayesian for the parameter of the Kumaraswamy distribution (KUD) depended on ranked set sampling (RSS) techniques. Both the simulated are inserted into real-life data sets and are considered to make a comparison between the estimation based on Maximum Likelihood estimators and Bayesian Estimation methods based on (RSS) techniques. For comparison purposes, we employed (100) mean square error and the criteria like AICC (Akaike information corrected criterion). Finally, the importance and flexibility of the new model of real data set are proved empirically.

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“…In the case of rates and proportions processes, as well as other processes whose variables of interest assume values in the range (0, 1), there is a well-represented class of models, the unit distributions family, which deals with this type of double-bounded data. Among the many existing unit distributions, it is noteworthy mentioning the power distribution, beta distribution [3], Kumaraswamy distribution [4], unit-logistic distribution [5], simplex distribution [6], unit-Weibull distribution [7,8], unit-Lindley distribution [9], unithalf-normal distribution [10], unit log-log distribution [11], modified Kumaraswamy and reflected modified Kumaraswamy distributions [12], unit-Teissier distribution [13], unit extended Weibull families of distributions [14], lognormal distribution [15], unit folded normal distribution [16], Marshall-Olkin reduced Kies distribution [17], and unit-Chen distribution [18].…”

Section: Introductionmentioning

confidence: 99%

Extending Normality: A Case of Unit Distribution Generated from the Moments of the Standard Normal Distribution

Concha-Aracena

Barrios-Blanco

Elal-Olivero

et al. 2022

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This paper presents an important theorem, which shows that, heading from the moments of the standard normal distribution, one can generate density functions originating a family of models. Additionally, we discussed that different random variable domains are achieved with transformations. For instance, we adopted the moment of order two, from the proposed theorem, and transformed it, which enabled us to exemplify this class as a unit distribution. We named it as Alpha-Unit (AU) distribution, which contains a single positive parameter α (AU(α)∈[0,1]). We presented its properties and demonstrated two estimation methods for the α parameter, the maximum likelihood estimator (MLE) and uniformly minimum-variance unbiased estimator (UMVUE) methods. In order to analyze the statistical consistency of the estimators, a Monte Carlo simulation study was carried out, in which the robustness was demonstrated. As a real-world application, we adopted two sets of unit data, the first regarding the dynamics of Chilean inflation in the post-military period, and the other one regarding the daily maximum relative humidity of the air in the Atacama Desert. In both cases presented, the AU model is competitive, whenever the data present a range greater than 0.4 and extremely heavy asymmetric tail. We compared our model with other commonly used unit models, such as the beta, Kumaraswamy, logit-normal, simplex, unit-half-normal, and unit-Lindley distributions.

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Modified Kumaraswamy distributions for double bounded hydro-environmental data

Cited by 13 publications

References 23 publications

Inflated beta autoregressive moving average models

Inflated beta autoregressive moving average models

The Kumaraswamy Distribution: Statistical Properties and Application

Extending Normality: A Case of Unit Distribution Generated from the Moments of the Standard Normal Distribution

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