Abstract Poisson distribution is a popular discrete model used to describe counting information, from which traditional control charts involving count data, such as the c and u charts, have been established in the literature. However, several studies recognize the need for alternative control charts that allow for data overdispersion, which can be encountered in many fields, including ecology, healthcare, industry, and others. The Bell distribution, recently proposed by Castellares et al. (2018), is a particular solution of a multiple Poisson process able to accommodate overdispersed data. It can be used as an alternative to the usual Poisson (which, although not nested in the Bell family, is approached for small values of the Bell distribution) Poisson, negative binomial, and COM-Poisson distributions for modeling count data in several areas. In this paper, we consider the Bell distribution to introduce two new exciting, and useful statistical control charts for counting processes, which are capable of monitoring count data with overdispersion. The performance of the so-called Bell charts, namely Bell-c and Bell-u charts, is evaluated by the average run length in numerical simulation. Some artificial and real data sets are used to illustrate the applicability of the proposed control charts.

Resumen En este artículo, discutimos varias propiedades matemáticas y métodos de estimación para una versión reparametrizada de la distribución ponderada de Lindley (RWL). La distribución RWL puede ser particularmente útil para modelar datos de confiabilidad (supervivencia) con función de tasa de riesgo en forma de bañera o creciente. El procedimiento inferencial para obtener las estimaciones de los parámetros se realiza mediante el enfoque de máxima verosimilitud considerando la censura aleatoria a la derecha. Se realizan extensas simulaciones numéricas para investigar y evaluar el rendimiento del método de estimación propuesto. Finalmente, la utilidad del modelo RWL se analiza mediante el uso de dos conjuntos de datos reales.

Abstract In this paper, we discuss several mathematical properties and estimation methods for a reparameterized version of the weighted Lindley (RWL) distribution. The RWL distribution can be particularly useful for modeling reliability (survival) data with bathtub-shaped or increasing hazard rate function. The inferential procedure to obtain the parameter estimates is conducted via the maximum likelihood approach considering random right-censoring. Extensive numerical simulations are carried out to investigate and evaluate the performance of the proposed estimation method. Finally, the potentiality of the RWL model is analyzed by employing two real data sets.

Abstract The gamma distribution has been extensively used in many areas of applications. In this paper, considering a Bayesian analysis we provide necessary and sufficient conditions to check whether or not improper priors lead to proper posterior distributions. Further, we also discuss sufficient conditions to verify if the obtained posterior moments are finite. An interesting aspect of our findings are that one can check if the posterior is proper or improper and also if its posterior moments are finite by looking directly in the behavior of the proposed improper prior. To illustrate our proposed methodology these results are applied in different objective priors.

Abstract: In this paper, we revisit the Wilson-Hilferty distribution and presented its mathematical properties such as the r-th moments and reliability properties. The parameters estimators are discussed using objective reference Bayesian analysis for both complete and censored data where the resulting marginal posterior intervals have accurate frequentist coverage. A simulation study is presented to compare the performance of the proposed estimators with the frequentist approach where it is observed a clear advantage for the Bayesian method. Finally, the proposed methodology is illustrated on three real datasets.

ABSTRACT In this paper, we discuss computational aspects to obtain accurate inferences for the parameters of the generalized gamma (GG) distribution. Usually, the solution of the maximum likelihood estimators (MLE) for the GG distribution have no stable behavior depending on large sample sizes and good initial values to be used in the iterative numerical algorithms. From a Bayesian approach, this problem remains, but now related to the choice of prior distributions for the parameters of this model. We presented some exploratory techniques to obtain good initial values to be used in the iterative procedures and also to elicited appropriate informative priors. Finally, our proposed methodology is also considered for data sets in the presence of censorship.

Tomato yellow leaf curl virus (TYLCV) is a major threat to tomato production in the tropics and sub-tropics around the world. The application of genetic engineering and pathogen derived resistance mechanisms to obtain tomatoes that are resistant to this pathogen is considered a promising alternative to the current protective practice against the virus. However, the development of transgenic tomato plants that are resistant to the virus is a resourceconsuming and time-consuming procedure, often with unpredictable efficiency, which hinders the evaluation of genetic designs. For this reason an assessment of the strategies against TYLCV replication preceding transgenic tomato development would ensure the protective potential of the candidate transgene. Attempting to circumvent this issue, the present study demonstrated the feasibility of using tobacco cell lines to study the consequences of c1 antisense expression on TYLCV replication. As a result, the transgenic tobacco cell lines were able to produce siRNA that is complementary to the c1 sequence and inhibited TYLCV multiplication, forecasting what would happen in transgenic plants harboring this antiviral strategy.

Tomato yellow leaf curl virus (TYLCV) constituye el mayor peligro para la producción de tomate en el mundo, principalmente en las regiones tropicales y subtropicales. La aplicación de la ingeniería genética y los mecanismos de resistencia derivada del patógeno para obtener tomates resistentes a este patógeno es considerada una alternativa promisoria en la práctica corriente de protección contra este virus. Sin embargo, el desarrollo de plantas transgénicas de tomate resistentes a virus es un procedimiento que consume mucho tiempo y recursos, y en la mayoría de las veces resulta impredecible su eficiencia, lo cual dificulta la evaluación de los diseños antivirales. Por ello la evaluación de las estrategias que inhiban la replicación de TYLCV en un sistema previo a la obtención de plantas de tomate transgénicas aseguraría el potencial protectivo del transgén candidato. En un intento por evadir el proceso de transformación de tomate en el presente trabajo se demostró la factibilidad de utilizar líneas celulares de tabaco para estudiar las consecuencias de la expresión del gen c1 en antisentido sobre la replicación de TYLCV. Como resultado las líneas celulares de tabaco fueron capaces de producir ARN de interferencia, complementarios a la secuencia del gen c1, e inhibieron la multiplicación de TYLCV, previendo lo que sucedería en las plantas transgénicas portadoras de esta estrategia antiviral.