Circadian and ultradian oscillations in bilateral rhythms of the crayfish chelipeds.

Circadian systems are composed of multiple oscillatory elements that contain both circadian and ultradian oscillations. The relationships between these components maintain a stable temporal function in organisms. They provide a suitable phase to recurrent environmental changes and ensure a suitable temporal sequence of their own functions. Therefore, it is necessary to identify these interactions. Because a circadian rhythm of activity can be recorded in each crayfish cheliped, this paired organ system was used to address the possibility that two quasi-autonomous oscillators exhibiting both circadian and ultradian oscillations underlie these rhythms. The presence of both oscillations was found, both under entrainment and under freerunning. The following features of interactions between these circadian and ultradian oscillations were also observed: (a) circadian modal periods could be a feature of circadian oscillations under entrainment and freerunning; (b) the average period of the rhythm is a function of the proportions between the circadian and ultradian oscillations; (c) the release of both populations of oscillations of Zeitgeber effect results in the maintenance or an increase in their number and frequency under freerunning conditions. These circadian rhythms of activity can be described as mixed probability distributions containing circadian oscillations, individual ultradian oscillations, and ultradian oscillations of Gaussian components. Relationships among these elements can be structured in one of the following six probability distributions: Inverse Gaussian, gamma, Birnbaum-Saunders, Weibull, smallest extreme value, or Laplace. It should be noted that at one end of this order, the inverse Gaussian distribution most often fits the freerunning rhythm segments and at the other end, the Laplace distribution fits only the segments under entrainment. The possible relationships between the circadian and ultradian oscillations of crayfish motor activity rhythms and between the probability distributions of their periodograms are discussed. Also listed are some oscillators that could interact with cheliped rhythms.

A family of bimodal distributions generated by distributions with positive support.

Bimodal data sets are very common in different areas of knowledge. The crude birth rates data, fish length data, egg diameter data, the eruption and interruption times of the Old Faithful geyser, are examples of this type of data. In this paper, a new class of symmetric density functions for modeling bimodal data as described above are presented. From density functions with support on [ 0 , + ∞ ) , the symmetry is getting by reflecting the density function in the negative semi-axis with their respective normalization. In this way, if the primitive density function is unimodal, then the resulting density will be bimodal. We introduce asymmetry parameters and study their behavior, in particular the values of their modes and some other statistical values of interest. The cases for densities generated by Gamma, Weibull, Log-normal, and Birnbaum-Saunders densities, among others are studied. Statistical inference is performed from a classical perspective. A small simulation study to evaluate the benefits and limitations of the new proposal. In addition, an application to a data set related to the fetal weight in grams obtained through ultrasound in a sample of 500 units is also presented; the results show the great usefulness of the model in practical situations.

Modeling Mortality Based on Pollution and Temperature Using a New Birnbaum-Saunders Autoregressive Moving Average Structure with Regressors and Related-Sensors Data.

Environmental agencies are interested in relating mortality to pollutants and possible environmental contributors such as temperature. The Gaussianity assumption is often violated when modeling this relationship due to asymmetry and then other regression models should be considered. The class of Birnbaum-Saunders models, especially their regression formulations, has received considerable attention in the statistical literature. These models have been applied successfully in different areas with an emphasis on engineering, environment, and medicine. A common simplification of these models is that statistical dependence is often not considered. In this paper, we propose and derive a time-dependent model based on a reparameterized Birnbaum-Saunders (RBS) asymmetric distribution that allows us to analyze data in terms of a time-varying conditional mean. In particular, it is a dynamic class of autoregressive moving average (ARMA) models with regressors and a conditional RBS distribution (RBSARMAX). By means of a Monte Carlo simulation study, the statistical performance of the new methodology is assessed, showing good results. The asymmetric RBSARMAX structure is applied to the modeling of mortality as a function of pollution and temperature over time with sensor-related data. This modeling provides strong evidence that the new ARMA formulation is a good alternative for dealing with temporal data, particularly related to mortality with regressors of environmental temperature and pollution.

Birnbaum-Saunders sample selection model.

The sample selection bias problem occurs when the outcome of interest is only observed according to some selection rule, where there is a dependence structure between the outcome and the selection rule. In a pioneering work, J. Heckman proposed a sample selection model based on a bivariate normal distribution for dealing with this problem. Due to the non-robustness of the normal distribution, many alternatives have been introduced in the literature by assuming extensions of the normal distribution like the Student-t and skew-normal models. One common limitation of the existent sample selection models is that they require a transformation of the outcome of interest, which is common R + -valued, such as income and wage. With this, data are analyzed on a non-original scale which complicates the interpretation of the parameters. In this paper, we propose a sample selection model based on the bivariate Birnbaum-Saunders distribution, which has the same number of parameters that the classical Heckman model. Further, our associated outcome equation is R + -valued. We discuss estimation by maximum likelihood and present some Monte Carlo simulation studies. An empirical application to the ambulatory expenditures data from the 2001 Medical Expenditure Panel Survey is presented.

Fatigue-life distributions for reaction time data.

The family of fatigue-life distributions is introduced as an alternative model of reaction time data. This family includes the shifted Wald distribution and a shifted version of the Birnbaum-Saunders distribution. Although the former has been proposed as a way to model reaction time data, the latter has not. Hence, we provide theoretical, mathematical and practical arguments in support of the shifted Birnbaum-Saunders as a suitable model of simple reaction times and associated cognitive mechanisms.

Birnbaum-Saunders frailty regression models: Diagnostics and application to medical data.

In survival models, some covariates affecting the lifetime could not be observed or measured. These covariates may correspond to environmental or genetic factors and be considered as a random effect related to a frailty of the individuals explaining their survival times. We propose a methodology based on a Birnbaum-Saunders frailty regression model, which can be applied to censored or uncensored data. Maximum-likelihood methods are used to estimate the model parameters and to derive local influence techniques. Diagnostic tools are important in regression to detect anomalies, as departures from error assumptions and presence of outliers and influential cases. Normal curvatures for local influence under different perturbations are computed and two types of residuals are introduced. Two examples with uncensored and censored real-world data illustrate the proposed methodology. Comparison with classical frailty models is carried out in these examples, which shows the superiority of the proposed model.