Modelling the frequency of events is a significant problem that has received a lot of attention in recent years. Discrete probability distributions such as the Poisson, Negative Binomial, Geometric, and Poisson-Lindley are commonly used for this purpose. However, these traditional distributions often exhibit limited flexibility in capturing the complexity of real-world count data. In this regard, we study the New Discrete XLindley distribution introduced by (Maya et al., 2024) and discussed its various structural properties. A Bayesian analysis is conducted to enhance the inferential understanding of the model. To address the presence of excess zeros in count data, we propose a zero-inflated extension of the New Discrete XLindley model. Parameters are estimated using the Maximum Likelihood Estimation method, and the performance of the estimators is assessed via simulation studies. The practical relevance of the proposed model is demonstrated through its application to a real-life dataset. Finally, a Likelihood Ratio Test is employed to test the significance of the zero-inflation parameter, providing strong evidence in support of the extended model. Overall, the zero-inflated New Discrete XLindley model offers a flexible and effective tool for modeling zero-inflated count data.

This paper focuses on evaluating allocation strategies in portfolio management, specifically examining methods for determining asset weights. The study emphasizes the covariance matrix, a critical component in constructing risk-based portfolios, including minimum volatility, inverse volatility, equal risk contribution, and maximum diversification portfolios. The primary aim is to analyzethe robustness and sensitivity ofthese strategies under potential misspecifications or errors in the covariance matrix. Using a Dynamic Conditional Correlation model and a Monte Carlo simulation approach, a large set of covariance matrices is generated. Risk-based allocation strategies are then applied to these simulated matrices, and robustness is assessed by quantifying deviations between actual and simulated allocations. Furthermore, the study estimates the probability of model accuracy and incorporates this into two conventional risk measures. These adjusted measures account for the risk of covariance misspecification, providing a normalized and more reliable evaluation of portfolio performance. This approach enhances the interpretability and robustness of risk metrics in the presence of estimation errors, offering valuable insights for portfolio optimization under realistic uncertainty conditions.

In this paper, a wide class of generalized geometric distribution is introduced and we name this class of distributions as “the alpha generalized geometric distribution (AGGD)". Several important distributions are obtained as a special cases of this proposed model. Important distributional properties such as generating functions, moments, recursive relations of the proposed distribution are examined. Parameter estimation using maximum likelihood is discussed. Three well-known data sets, having long tails, are analyzed and the results of fitting by various models are provided. Further, the generalized likelihood ratio test procedure is considered for testing the significance of the parameters of the GGD. Finally, performance of the different estimation methods are compared by means of a Monte Carlo simulation.

Variable selection is important for making sense with (ultra) high-dimensional data. Penalized least squares such as the LASSO, elastic-net and the correlation based elastic-net (L1CP) are popular methods for carrying out variable selection and estimation simultaneously. This study proposes a modified version of the L1CP motivated by reasons similar to that given by Zou and Hastie (2005) where the naïve elastic net was rescaled to give the elastic net. The scaling transformation is derived such that the double shrinkage caused by applying two penalties is undone thereby reducing bias. The derived scaling transformations are found to depend on the correlations among the predictors. A robust worst-case quadratic solver is used to obtain estimates. An evaluation of the proposed method which is referred to as CL1CP alongside the L1CP, LASSO and elastic-net through simulation studies illustrate the advantages of the CL1CP compared to the other alternatives considered especially in correct selection of sparse models. In terms of variable selection, estimation and prediction accuracy the proposed CL1CP performs favourably compared to the L1CP, LASSO and elastic-net especially for “grouped-variables” selection. Results from applications to two real life datasets corroborate the findings from simulation studies.

In the last decade the practice of combining longitudinal surveys with administrative data has been affirmed, enabling the integration of the complementary advantages offered by these two data sources. In this perspective, the paper describes a pilot study conducted in 2015 involving deterministic matching and integration between a retrospective panel survey carried out on a representative sample of households living in the province of Trento (Italy) and the register data from the provincial section of the administrative archive of INPS (the Italian social security agency). The aim was to create a comprehensive database for the study of work histories. Through the survey we address the main limitation of INPS data, which do not cover the universe of workers and jobseekers. Conversely, the administrative data, providing richer and more reliable information on most work episodes and instances of subsidized unemployment, help mitigate one of the most significant sources of errors in the panel surveys, i.e. the distortions caused by memory bias.

In factor screening experiments with limited resources, it is common for practitioners to cut down the number of runs N and choose a supersaturated design for the experiment. In the past two decades, E(s2)-optimality has been one of the most important criteria used to choose a supersaturated design. We show that the definition E(s2)-optimal supersaturated designs X for N ≡ 2 (mod 4) runs and m ≥ N factors are not unique by showing that XX⊤ allows for multiple non-isomorphic possibilities for most values of m. For N = 10 and 12 ≤ m ≤ 114 we list all possible E(s2)-optimal designs.