This paper studies the goodness of fit test for the bivariate Hermite distribution. Specifically, we propose and study a Cramér-von Mises-type test based on the empirical probability generation function. The bootstrap can be used to consistently estimate the null distribution of the test statistics. A simulation study investigates the goodness of the bootstrap approach for finite sample sizes.

In this paper, we study the asymptotic behavior of the sequential empirical process and the sequential empirical copula process, both constructed from residuals of multivariate stochastic volatility models. Applications for the detection of structural changes and specification tests of the distribution of innovations are discussed. It is also shown that if the stochastic volatility matrices are diagonal, which is the case if the univariate time series are estimated separately instead of being jointly estimated, then the empirical copula process behaves as if the innovations were observed; a remarkable property. As a by-product, one also obtains the asymptotic behavior of rank-based measures of dependence applied to residuals of these time series models.

The two-parameter distribution introduced by Kumaraswamy (1980) is a very flexible alternative to the Beta distribution with the same (0,1) support. Originally proposed in the field of hydrology, it has subsequently received a good deal of positive attention in both the theoretical and applied statistics literatures. Interestingly, the problem of testing formally for the appropriateness of the Kumaraswamy distribution appears to have received little or no attention to date. To fill this gap, in this paper we apply the “biased transformation” methodology proposed by Raschke (2009) to several standard goodness-of-fit tests based on the empirical distribution function. A simulation study reveals that these (modified) tests perform well in the context of the Kumaraswamy distribution, in terms of both low size distortion, and respectable power. In particular, the “biased transformation” Anderson-Darling test dominates the other tests that are considered.

Energy distance is used to eigenvalue distributions in this new Wishart distribution study, providing a new perspective on high-dimensional data. Multivariate statistics relies on Wishart distribution to explain covariance matrices. This analysis shows how degrees of freedom and covariance matrix configurations affect eigenvalue dispersion. We use energy distance based on eigenvalue distributions to assess Wishart distribution differences without the "curse of dimensionality" via extensive simulation simulations. This approach improves measurement accuracy and processing efficiency in distribution comparisons and enables new analytical pathways in scientific fields that need data covariance comprehension. Our results show that degrees of freedom and matrix structure considerably affect energy distances, expanding the theoretical framework and practical applications of statistical models.

A new discrete distribution for count data called extended biparametric Waring (EBW) distribution is developed. Its name is related to the fact that, in a specific configuration of its parameters, it can be seen as a biparametric version of the univariate generalized Waring (UGW) distribution, a well-known model for the variance decomposition into three components: randomness, liability and proneness. Unlike the UGW distribution, the EBW can model both overdispersed and underdispersed data sets. In fact, the EBW distribution is a particular case of a UWG distribution when its first parameter is positive; otherwise, it is a particular case of a Complex Triparametric Pearson (CTP) distribution. Hence, this new model inherits most of their properties and, moreover, it helps to solve the identification problem in the variance components of the UGW model. We compare the EBW with the UGW by a simulation study, but also with other over and underdispersed distributions through the Kullback-Leibler divergence. Additionally, we have carried out a simulation study in order to analyse the properties of the maximum likelihood parameter estimates. Finally, some application examples are included which show that the proposed model provides similar or even better results than other models, but with fewer parameters.

Pinus occidentalis, Swartz is the primary timber species in the Dominican Republic (DR). Despite its economic importance, studies conducted on this species are very scarce, making it difficult to estimate current inventory levels. This study aims to enhance the accuracy of estimating total bole volume of P. occidentalis in different ecological zones (EZs) within La Sierra, evaluating and comparing two established volume equations—combined variable and Schumacher-Hall—across nine modeling variants (MVs). An indicator variables analysis determined the necessity of distinct equations for two EZs. Fitting included both linear and nonlinear models. Our comprehensive statistical analysis included goodness-of-fit metrics to evaluate each model variant's performance rigorously. Modeling variant SH02 was most effective in the Dry Ecological Zone, showing superior performance in both fitting and validation phases. Similarly, SH03 emerged as the best fit for the Combined Intermediate and Humid Ecological Zones, achieving the lowest overall ranking sum among tested variants. The SH equation variants SH02 and SH03, provide reliable and precise volume estimations, allowing optimization of forestry management practices for P. occidentalis trees. The SH models outperformed the CV model variants' consistency in parameter estimation. This tailored approach employed ensures more accurate volume predictions, which is crucial for sustainable management and conservation efforts.

Precipitation during a specific return period plays an important role in the design of hydraulic infrastructure. The traditional approach involves collecting annual maximum precipitation data from a station, then subjecting it to statistical probability distributions (PDFs), and finally selecting the one with the lowest value in a goodness-of-fit test (e.g., Kolmogorov-Smirnov). Nevertheless, this methodology assumes current data, leaving uncertainty regarding its suitability for outdated data. The aim of this study is to compare the probability density functions (e.g., Normal, Log Normal, Pearson III) with the machine learning algorithm known as Random Forest (RF) for calculating precipitation at different return periods, using the province of Arequipa in Peru as the study area, through 5 stations located in different parts of the province. This comparison was conducted using the RMSE metric in both methods to evaluate their performance, resulting in RF having a lower RMSE than PDFs in most cases in calculating precipitation for return periods of 2, 5, 10, 20, 50 and 100 years for the studied stations.

This paper focuses on the so-called proportional intensity-based software reliability models (PI-SRMs), which are extensions of the common non homogeneous Poisson process (NHPP)-based SRMs, and describe the probabilistic behavior of software fault-detection process by incorporating the time-dependent software metrics data observed in the development process. Especially we generalize the seminal PI-SRM in Rinsaka, Shibata and Dohi (2006) by introducing eleven well-known fault-detection time distributions, and investigate their goodness-of-fit and predictive performances. In numerical illustrations with four data sets collected in real software development projects, we utilize the maximum likelihood estimation to estimate model parameters with three time-dependent covariates; test execution time, failure identification work and computer time-failure identification, and examine the performances of our PI SRMs in comparison with the existing NHPP-based SRMs without covariates. It is shown that our PI-STMs could give better goodness-of-fit and predictive performances in many cases.