Browsing by Author "Jerez-Lillo, Nixon"

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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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    Power-law distribution in pieces: a semi-parametric approach with change point detection
    (2024) Ramos, Pedro L.; Jerez-Lillo, Nixon; Segovia, Francisco A.; Egbon, Osafu A.; Louzada, Francisco
    Piecewise models play a crucial role in statistical analysis as they allow the same pattern to be adjusted over different regions of the data, achieving a higher quality of fit than would be obtained by fitting them all at once. The standard piecewise linear distribution assumes that the hazard rate is constant between each change point. However, this assumption may be unrealistic in many applications. To address this issue, we introduce a piecewise distribution based on the power-law model. The proposed semi-parametric distribution boasts excellent properties and features a non-constant hazard function between change points. We discuss parameter estimates using the maximum likelihood estimators (MLEs), which yield closed-form expressions for the estimators and the Fisher information matrix for both complete and randomly censored data. Since MLEs can be biased for small samples, we derived bias-corrected MLEs that are unbiased up to the second order and also have closed-form expressions. We consider a profiled MLE approach to estimate change points and construct a hypothesis test to determine the number of change points. We apply our proposed model to analyze the survival pattern of monarchs in the Pharaoh dynasties. Our results indicate that the piecewise power-law distribution fits the data well, suggesting that the lifespans of pharaonic monarchs exhibit varied survival patterns.