This study introduces the bucket plot, a visual tool to detect skewness and kurtosis in a continuously distributed random variable. The plot can be applied to both moment and centile skewness and kurtosis. The bucket plot is used to detect skewness and kurtosis either in a response variable, or in the residuals from a fitted model as a diagnostic tool by which to assess the adequacy of a fitted distribution to the response variable regarding skewness and kurtosis. We demonstrate the bucket plot in nine simulated skewness and kurtosis scenarios, and the usefulness of the plot is shown in a real-data situation.

Regression models with probit and logit link functions are the most frequently used for binary response variables. However, traditional approaches may not be adequate when data are unbalanced. This paper deals with standard skew-probit regression models. Parameters were estimated through a new Bayesian approach which consists of the use of Hamiltonian Monte Carlo (HMC) and the original likelihood function. Simulation studies assessed the efficiency of the estimation method and the sensitivity of prior distributions for parameters related to asymmetry calculating the RMSE (root mean square error). The proposed estimation method was compared when used for detecting outliers. The results show that the proposed method is more efficient than INLA and is successful in the recovery of true parameter values. The sensitivity study enabled the proposal of a new prior distribution configuration for the asymmetry parameter, and the randomized quantile residual proved to be more suitable for detecting outliers. The methodology was applied to a diabetes dataset towards illustrating the results.

The appropriate use of auxiliary information in sample surveys increases the efficiency of estimator for parameter of interest. In this paper, we have proposed an exponential type estimator for the population mean of a sensitive study variable based on an optional randomized response model by using the known information on a non-sensitive auxiliary variable. Expressions for the bias and the mean square error (MSE) of the proposed estimator are derived, up to first order of approximation. For this proposed estimator, efficiency comparisons with the existing estimators have been carried out both theoretically and numerically. It has been shown that our proposed estimator perform better than the existing estimators based on the same optional randomized response model even for the small correlation between auxiliary variable and study variable. To support the results obtained, we have also studied the performance of the proposed exponential estimator using simulation technique.

Functional Data Analysis is known for its application in several fields of science. In some cases, functional datasets are constituted by spatially indexed curves. The primary goal of this paper is to supply a straightforward and precise approach to interpolate these curves, that is, the aim is to estimate a curve at an unmonitored location. It is proven that the best linear unbiased estimator for this unsampled curve is the solution of a linear system, where the coefficients and the constant terms of the system are formed using a function called trace-variogram. In this paper, we propose using Legendre-Gauss quadrature to estimate the trace-variogram. This estimator’s suitable numerical properties are shown in simulation studies for normal and non-normal datasets. Simulation results indicated that the proposed methodology outperforms the established estimation procedure. An $\mathtt{R}$ package was built and is available at the CRAN repository. The novel estimation methodology is illustrated with a real dataset on temperature curves from 35 weather stations in Canada.

Growth curve mixture models for longitudinal data are often developed on the conditional mean of a response, focusing only on the central section of the distribution. There is, however, an increasing desire to provide holistic information on different parts of the distribution of the response such as lower and higher quantiles. This article presents quantile regression analysis within the framework of growth curve models by jointly analyzing time to an event and longitudinal data with multiphasic features. The multiphasic patterns are accounted for at different quantiles by modeling heterogeneous growth trajectories which show gradual changes from a declining trend to an increasing trend over time within latent classes. Thus, we assess these important features of longitudinal data using bent-cable models along with a joint modeling of time to event process and response process. The proposed methods are illustrated using a real data set from an AIDS clinical study.

Discretization of continuous-time diffusion processes is a widely recognized method for sampling. However, it seems to be a considerable restriction when the potentials are often required to be smooth (gradient Lipschitz). This paper studies the problem of sampling through Euler discretization, where the potential function is assumed to be a mixture of weakly smooth distributions and satisfies weakly dissipative. We establish the convergence in Kullback–Leibler (KL) divergence with the number of iterations to reach ϵ-neighborhood of a target distribution in only polynomial dependence on the dimension. We relax the degenerated convex at infinity conditions of (Erdogdu and Hosseinzadeh (2020)) and prove convergence guarantees under Poincaré inequality or non-strongly convex outside the ball. In addition, we also provide convergence in ${\mathit{L}}_{\mathit{\beta }}$-Wasserstein metric for the smoothing potential.

In this work, we define the cumulative past Fisher (CPF) information and the relative cumulative past Fisher (RCRF) information measures for parameter as well as for the distribution function of the underlying random variables. We show that these cumulative past Fisher information measures can be expressed in terms of the reversed hazard rate function. We also define three extensions of the CPF information measure. Further, we study these cumulative information measures and their Bayes versions for some well-known models used in reliability, economics and survival analysis. The associated results reveal some interesting connections between the proposed Fisher type information measures with some well-known information divergences and reliability measures.

In this paper, we propose a log-symmetric survival model with cure fraction, considering that the distributions of lifetimes for susceptible individuals belong to the log-symmetric class of distributions. This class has continuous, strictly positive, and asymmetric distributions, including the log-normal, log-Student-t, Birnbaum–Saunders, log-logistic I, log-logistic II, contaminated log-normal, log-power-exponential, and log-slash distributions. The log-symmetric class is quite flexible and allows for including bimodal distributions and outliers. It has two parameters interpreted directly as location and scale, where the location is the median, which is a robust measure in the presence of outliers and quite informative in survival analysis. The proposed model includes explanatory variables through the parameter associated with the cure fraction. We evaluate the performance of such model through extensive simulation studies and consider a real data application to evaluate the effect of factors on the immunity to leprosy reactions in patients with Hansen’s disease.

In this paper, we consider the problem of trajectory fitting estimation for a class of stochastic differential equations with small Lévy noises based on continuous-time observations. The consistency, the rate of convergence, and asymptotic distribution of the trajectory fitting estimator are established as a small dispersion coefficient tends to zero.

This paper extends the multivariate skew t distributions with independent logistic skewing functions (MSTIL) introduced in Kwong and Nadarajah (Methodology and Computing in Applied Probability 24 (2022) 1669–1691) to finite mixture models (FM-MSTIL). A stochastic EM-type algorithm is proposed for fitting the FM-MSTIL, and a divisive hierarchical algorithm is proposed for initialisations and model selections. We show that the model can outperform other finite mixture models in the literature for some simulated data sets. The performance of the FM-MSTIL in cluster analysis is also investigated. We show that the FM-MSTIL-R, a nested version of the FM-MSTIL, performs well for automatic gating tasks on some flow cytometry data sets in the FlowCap-I challenge. The FM-MSTIL-R achieved a better overall score than all other competing algorithms in the original challenge. An efficient implementation of the FM-MSTIL is available as an R package in GitHub.

The Gompertz–Makeham model was introduced as an extension of the Gompertz model in the second half of the 19th century by the British actuary William M. Makeham. Since then, this model has been successfully used in biology, actuarial science, and demography to describe mortality patterns in numerous species (including humans), determine policies in insurance, establish actuarial tables and growth models. In this paper, we derive some structural properties of the Gompertz–Makeham model in statistics, demography, and actuarial sciences, and present some other ones already introduced in the literature. All structural properties we provide are expressed in closed-form, which eliminates the need to evaluate them with numerical integration directly. In addition, we study the estimation of the Gompertz–Makeham model parameters through the discrete Poisson and Bell distributions. In particular, we verify that the recently introduced discrete Bell distribution can be an interesting alternative to the Poisson distribution, mainly because it is suitable to deal with over dispersion, unlike the Poisson distribution. On the basis of real mortality datasets, we compute the remaining life expectancy for several countries and verify that the Gompertz–Makeham model, especially under the Bell distribution, provides proper results to deal with human mortality in practice.