Matemática

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On a goodness-of-fit test for normality with unknown parameters and type-II censored data
(2010-07) Castro-Kuriss, Claudia; Kelmansky, Diana M.; Leiva, Víctor; Martínez, Elena J.
"We propose a new goodness-of-fit test for normal and lognormal distributions with unknown parameters and type-II censored data. This test is a generalization of Michael's test for censored samples, which is based on the empirical distribution and a variance stabilizing transformation. We estimate the parameters of the model by using maximum likelihood and Gupta's methods. The quantiles of the distribution of the test statistic under the null hypothesis are obtained through Monte Carlo simulations. The power of the proposed test is estimated and compared to that of the Kolmogorov-Smirnov test also using simulations. The new test is more powerful than the Kolmogorov-Smirnov test in most of the studied cases. Acceptance regions for the PP, QQ and Michael's stabilized probability plots are derived, making it possible to visualize which data contribute to the decision of rejecting the null hypothesis. Finally, an illustrative example is presented."
On some goodness-of-fit tests and their connection to graphical methods with uncensored and censored data
(2019) Castro-Kuriss, Claudia; Huerta, Mauricio; Leiva, Víctor; Tapia, Alejandra
"In this work, we present goodness-of-fit tests related to the Kolmogorov-Smirnov and Michael statistics and connect them to graphical methods with uncensored and censored data. The Anderson-Darling test is often empirically more powerful than the Kolmogorov-Smirnov test. However, the former one cannot be related to graphical tools by means of probability plots, as the Kolmogorov-Smirnov test does. The Michael test is, in some cases, more powerful than the Anderson-Darling and Kolmogorov- Smirnov tests and can also be related to probability plots.We consider the Kolmogorov-Smirnov and Michael tests for detecting whether any distribution is suitable or not to model censored or uncensored data. We conduct numerical studies to show the performance of these tests and the corresponding graphical tools. Some comments related to big data and lifetime analysis, under the context of this study, are provided in the conclusions of this work."
A truncated version of the birnbaum-saunders distribution with an application in financial risk
(2010-01) Ahmed, Syed Ejaz; Castro-Kuriss, Claudia; Flores, Esteban; Leiva, Víctor; Sanhueza, Antonio
"In many Solvency and Basel loss data, there are thresholds or deductibles that affect the analysis capability. On the other hand, the Birnbaum-Saunders model has received great attention during the last two decades and it can be used as a loss distribution. In this paper, we propose a solution to the problem of deductibles using a truncated version of the Birnbaum-Saunders distribution. The probability density function, cumulative distribution function, and moments of this distribution are obtained. In addition, properties regularly used in insurance industry, such as multiplication by a constant (inflation effect) and reciprocal transformation, are discussed. Furthermore, a study of the behavior of the risk rate and of risk measures is carried out. Moreover, estimation aspects are also considered in this work. Finally, an application based on real loss data from a commercial bank is conducted."

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