Browsing by Author "Ramos, Pedro Luiz"

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    Improved process capability assessment through semiparametric piecewise modeling
    (2024) Soares, Vinicius da Costa; Jerez-Lillo, Nixon; Ferreira, Paulo Henrique; Ramos, Pedro Luiz
    Piecewise models have gained popularity as a useful tool in reliability and quality control/monitoring, particularly when the process data deviates from a normal distribution. In this study, we develop maximum likelihood estimators (MLEs) for the process capability indices, denoted as $ C_{pk} $ Cpk, $ C_{pm} $ Cpm, $ C<^>{*}_{pm} $ Cpm & lowast; and $ C_{pmk} $ Cpmk, using a semiparametric model. To remove the bias in the MLEs with small sample sizes, we propose a bias-correction approach to obtain improved estimates. Furthermore, we extend the proposed method to situations where the change-points in the density function are unknown. To estimate the model parameters efficiently, we employ the profiled maximum likelihood approach. Our simulation study reveals that the suggested method yields accurate estimates with low bias and mean squared error. Finally, we provide real-world data applications to demonstrate the superiority of the proposed procedure over existing ones.
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    On the posterior property of the Rician distribution
    (2024) Achire, Enrique; Ramos, Eduardo; Ramos, Pedro Luiz
    The Rician distribution, a well-known statistical distribution frequently encountered in fields like magnetic resonance imaging and wireless communications, is particularly useful for describing many real phenomena such as signal process data. In this paper, we introduce objective Bayesian inference for the Rician distribution parameters, specifically the Jeffreys rule and Jeffreys prior are derived. We proved that the obtained posterior for the first priors led to an improper posterior while the Jeffreys prior led to a proper distribution. To evaluate the effectiveness of our proposed Bayesian estimation method, we perform extensive numerical simulations and compare the results with those obtained from traditional moment-based and maximum likelihood estimators. Our simulations illustrate that the Bayesian estimators derived from the Jeffreys prior provide nearly unbiased estimates, showcasing the advantages of our approach over classical techniques. Additionally, our framework incorporates the S.A.F.E. principles - Sustainable, Accurate, Fair, and Explainable - ensuring robustness, fairness, and transparency in predictive modelling.
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    POWER LAWS DISTRIBUTIONS IN OBJECTIVE PRIORS
    (2023) Ramos, Pedro Luiz; Rodrigues, Francisco A.; Ramos, Eduardo; Dey, Dipak K.; Louzada, Francisco
    Using objective priors in Bayesian applications has become a common way of analyzing data without using subjective information. Formal rules are usually used to obtain these prior distributions, and the data provide the dominant infor-mation in the posterior distribution. However, these priors are typically improper, and may lead to an improper posterior. Here, for a general family of distribu-tions, we show that the objective priors obtained for the parameters either follow a power law distribution, or exhibit asymptotic power law behavior. As a result, we observe that the exponents of the model are between 0.5 and 1. Understand-ing this behavior allows us to use the exponent of the power law directly to verify whether such priors lead to proper or improper posteriors. The general family of distributions we consider includes essential models such as the exponential, gamma, Weibull, Nakagami-m, half-normal, Rayleigh, Erlang, and Maxwell Boltzmann dis-tributions, among others. In summary, we show that understanding the mechanisms that describe the shape of a prior provides essential information that can be used to understand the properties of posterior distributions.
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    The impacts of climate change on rainfall modeling in the Pantanal of Mato Grosso do Sul
    (2021) Pobocikova, Ivana; de Souza, Amaury; Abreu, Marcel Carvalho; De Oliveira-Junior, Jose Francisco; dos Santos, Cicero Manoel; Pinto Lins, Tayna Maria; Aristone, Flavio; Ramos, Pedro Luiz
    The most significant and influential meteorological element in environmental conditions and human activities is precipitation. The objective of this study was to adjust eight probability distributions to monthly, seasonal and annual rainfall data in the Pantanal of Mato Grosso do Sul, Brazil, using a time series of data (1983-2013) by the National Meteorological Water Agency (ANA). The performance evaluation of different probability distribution models was assessed by the quality of fit of the selected probability distributions for precipitation data. Quality tests as chi-square, Kolmogorov-Smirnov (KS) and Anderson-arling (AD), the information criteria as Akaike (AIC) and the Bayesian criterion (BIC) were used. Then the mean root square error (RMSE) and the coefficient of determination (R2) were applied. The analyzes were made monthly, annually and by seasons. The 3-parameter Lognormal distribution performs the best for all twelve months and provides the best-fit to the monthly rainfall data. Thus characterizing a dry period that runs from May to September and a rainy period between the months of October and April, it was observed that the 3-parameter Lognormal distribution has best adjustment for spring and summer, and for winter and autumn the 2-parameter Gamma and 3-parameter Gamma distribution performed better. For annual observations, the function that best fits is 3-parameter Weibull distribution.