There is ever growing demand of modeling overdispersed count data generated by various disiplines. Excessive number of zeros and heterogeneity in the population are two main sources of the overdispersion problem. Development of new count models that are more flexible than conventional Poisson model is thus necessary in order to address such sources. This study fullfils this need by proposing a new heterogeneous Poisson model with a capture of excess zeros, namely zero-inflated Poisson–Ailamujia (ZIPA) model. In line with the aim of curing overdispersion, a censored variant of this newly suggested model is also here developed. An extensive simulation study is conducted to assess the performances of both forms of new models in terms of bias, precision and accuracy measures. Additionally, two real world applications are presented to illustrate practical implications of zero-inflated (censored) Poisson–Ailamujia models in comparison to some alternatives.

The functional law of the iterated logarithm is obtained for solutions of stochastic differential equations with random coefficients.

In this note, we establish when the bivariate discrete Schur-constant models possess the Sibuya-type aging property. It happens that the corresponding class is large, solving the counterpart of classical Sincov’s functional equation on the set of nonnegative integers.

In this paper, we develop a new survival model induced by discrete frailty with Katz distribution. The new model encompasses as particular cases the mixture cure rate model and promotion cure rate model and has a proportional hazards structure when the covariates are modeled through mean frailty. Furthermore, we construct a regression model to evaluate the effects of covariates on both the cured fraction and risk of the event of interest. We discuss inference aspects of the proposed model in a classical approach, where an expectation maximization algorithm is developed to determine the maximum likelihood estimates of the models parameters. Finally, the model is fully illustrated with a dataset on cervical cancer.

The analysis of means (ANOM) is a method that can compare the mean of each treatment to the overall mean. According to the graphical result of a statistical data analysis, we can specify which one is different from another. One of the assumptions of the classical ANOM model is that the variances are equal. However, it is not always true for the practice. To solve unknown and unequal population variances, Nelson and Dudewicz (2002) proposed a two-stage sampling procedure. However, additional samples need to be added in the second stage of the two-stage sampling procedure, so it is not practical all the time due to limited time and insufficient budget. Thus, under heteroscedasticity, we applied Chen and Lam’s (1989) single-stage sampling procedure to solve the drawback of the two-stage sampling procedure. In addition, we also provided an illustrative example and critical values for practical uses. In order to make the procedure user-friendly, we built an interface by using R Shiny.

A fully parametric estimation procedure is proposed for robust estimation of the structural parameter in a functional comparative calibration model, under normality. The proposed estimator is obtained, based on maximum Lq-likelihood approach, first replacing the incidental parameters by estimators depending on the structural parameter. The estimator, called MLqE, depends on a single distortion parameter q, which controls the balance between robustness and efficiency. If q tends to 1, the maximum likelihood estimator (MLE) is obtained. The estimation procedure can be implemented easily by a simple and fast reweighting algorithm. For applying the method to practical and real-data scenarios, a data-based choice of an appropriate value of q is proposed. Consistency and asymptotic normality is established and the covariance matrix is given. The influence function is derived, to show the local robustness properties. Theoretical properties, ease of implementabiliy and empirical results on simulated and real data show the satisfactory behavior of the MLqE and its vantages over the MLE in presence of observations discordant with the assumed model.

Three new mixed-effects regressions models using an extended Weibull distribution are defined for repeated measures, and their parameters are estimated by maximum likelihood. Monte Carlo simulations report the accuracy of the maximum likelihood estimators and the distribution of the quantile residuals in these regressions. The usefulness of the proposed regressions is illustrated in differential and integral class from the Exact Sciences Department at the University of São Paulo (Brazil) with the objective of showing a pedagogical alternative of learning diagnostic methodology as a game approach. The results indicate that the questions correctly answered by the students took less time to be solved than those incorrectly answered. In addition, the algebraic application and multiple representation questions has the lowest percentages of correct answers and, in general, the longest time to be solved. So, it is possible to note that the used game approach enables the identification of possible difficult points in a class and provides the teacher with the opportunity of search for different strategies to reduce these difficulties faced by differential and integral calculus students when entering higher education, which often result from basic education.

We propose a stochastic model for evolution through mutation and natural selection of a population that evolves on a ${\mathbb{T}}_{\mathit{d}}^{+}$ tree. We think of this model as a way of describing the evolution fitness landscape of a population. We obtain sharp and distinct conditions on the set of parameters for extinction and survival.

The third-order response surface designs are designs used to estimate the parameters of the third-order polynomial model. In this paper, the orthogonal uniform composite designs that combine two-level orthogonal array and four-level uniform design denoted by ${\mathrm{OUCD}}_4$ for estimating the parameters of the third-order models are proposed. The ${\mathrm{OUCD}}_4$ are good space-filling and efficient designs, that uses resolution IV as the initial design, provide more flexible run sizes, have the ability to execute in-depth analysis and perform multiple analysis with different parts of the data for cross-validation.

This paper proposes partially linear models with random errors following p-order autoregressive (AR) with skew-normal errors. The maximum likelihood estimators are derived from the Expectation-Maximization algorithm, which have analytic expressions for the M and E-steps. The estimation of the effective degrees of freedom concerning the nonparametric component are obtained based on a linear smoother. The conditional quantile residuals are used for the construction of simulated confidence bands to assess departures from the error assumptions, as well as autocorrelation and partial autocorrelation graphs are considered to check adequacy of the AR error structure. A simulation study is carried out to evaluate the efficiency of the EM algorithm. Finally, the methodology is illustrated by a real data set on cardiovascular mortality.

In this paper, we proposed a new cure rate model based on the Nielsen distribution. This model has a simple form for the probability generating function, it includes as a particular case the logarithmic distribution and it is a proposal recently discussed in greater detail in the literature, so its application within the context of cure models is very attractive. The model is parameterized directly in the cure rate, facilitating the comparison among other cure rate models in the literature also parameterized in this term. The estimation is approached based on a Bayesian paradigm. A real data set is considered to illustrate the performance of our proposal.