Alessandro Barbiero

Simulating Ordinal Data

The increasing use of ordinal variables in different fields has led to the introduction of new statistical methods for their analysis. The performance of these methods needs to be investigated under a number of experimental conditions. Procedures to simulate from ordinal variables are then required. In this article, we deal with simulation from multivariate ordinal random variables. We propose a new procedure for generating samples from ordinal random variables with a prespecified correlation matrix and marginal distributions. Its features are examined and compared with those of its main competitors. A software implementation in R is also provided along with examples of its application.

An imputation method for categorical variables with application to nonlinear principal component analysis

The problem of missing data in building multidimensional composite indicators is a delicate problem which is often underrated. An imputation method particularly suitable for categorical data is proposed. This method is discussed in detail in the framework of nonlinear principal component analysis and compared to other missing data treatments which are commonly used in this analysis. Its performance vs. these other methods is evaluated throughout a simulation procedure performed on both an artificial case, varying the experimental conditions, and a real case. The proposed procedure is implemented using R.

Interval estimators for reliability: the bivariate normal case

This paper proposes procedures to provide confidence intervals (CIs) for reliability in stress–strength models, considering the particular case of a bivariate normal set-up. The suggested CIs are obtained by employing either asymptotic variances of maximum-likelihood estimators or a bootstrap procedure. The coverage and the accuracy of these intervals are empirically checked through a simulation study and compared with those of another proposal in the literature. An application to real data is provided.

Confidence Intervals for Reliability of Stress-Strength Models in the Normal Case

In this article, we propose some procedures to get confidence intervals for the reliability in stress-strength models. The confidence intervals are obtained either through a parametric bootstrap procedure or using asymptotic results, and are applied to the particular context of two independent normal random variables. The performance of these estimators and other known approximate estimators are empirically checked through a simulation study which considers several scenarios.

A sequential distance-based approach for imputing missing data: Forward Imputation

Missing data recurrently affect datasets in almost every field of quantitative research. The subject is vast and complex and has originated a literature rich in very different approaches to the problem. Within an exploratory framework, distance-based methods such as nearest-neighbour imputation (NNI), or procedures involving multivariate data analysis (MVDA) techniques seem to treat the problem properly. In NNI, the metric and the number of donors can be chosen at will. MVDA-based procedures expressly account for variable associations. The new approach proposed here, called Forward Imputation, ideally meets these features. It is designed as a sequential procedure that imputes missing data in a step-by-step process involving subsets of units according to their “completeness rate”. Two methods within this context are developed for the imputation of quantitative data. One applies NNI with the Mahalanobis distance, the other combines NNI and principal component analysis. Statistical properties of the two methods are discussed, and their performance is assessed, also in comparison with alternative imputation methods. To this purpose, a simulation study in the presence of different data patterns along with an application to real data are carried out, and practical hints for users are also provided.

An R package for the simulation of correlated discrete variables

ABSTRACT A package for the stochastic simulation of discrete variables with assigned marginal distributions and correlation matrix is presented and discussed. The simulating mechanism relies upon the Gaussian copula, linking the discrete distributions together, and an iterative scheme recovering the correlation matrix for the copula that ensures the desired correlations among the discrete variables. Examples of its use are provided as well as three possible applications (related to probability, sampling, and inference), which illustrate the utility of the package as an efficient and easy-to-use tool both in statistical research and for didactic purposes.

Data Transformation for Confidence Interval Improvement: An Application to the Estimation of Stress-Strength Model Reliability

In many statistical applications, it is often necessary to obtain an interval estimate for an unknown proportion or probability or, more generally, for a parameter whose natural space is the unit interval. The customary approximate two-sided confidence interval for such a parameter, based on some version of the central limit theorem, is known to be unsatisfactory when its true value is close to zero or one or when the sample size is small. A possible way to tackle this issue is the transformation of the data through a proper function that is able to make the approximation to the normal distribution less coarse. In this paper, we study the application of several of these transformations to the context of the estimation of the reliability parameter for stress-strength models, with a special focus on Poisson distribution. From this work, some practical hints emerge on which transformation may more efficiently improve standard confidence intervals in which scenarios.

Inference on Reliability of Stress-Strength Models for Poisson Data

Researchers in reliability engineering regularly encounter variables that are discrete in nature, such as the number of events (e.g., failures) occurring in a certain spatial or temporal interval. The methods for analyzing and interpreting such data are often based on asymptotic theory, so that when the sample size is not large, their accuracy is suspect. This paper discusses statistical inference for the reliability of stress-strength models when stress and strength are independent Poisson random variables. The maximum likelihood estimator and the uniformly minimum variance unbiased estimator are here presented and empirically compared in terms of their mean square error; recalling the delta method, confidence intervals based on these point estimators are proposed, and their reliance is investigated through a simulation study, which assesses their performance in terms of coverage rate and average length under several scenarios and for various sample sizes. The study indicates that the two estimators possess similar properties, and the accuracy of these estimators is still satisfactory even when the sample size is small. An application to an engineering experiment is also provided to elucidate the use of the proposed methods.

Parameter Estimation for Type III Discrete Weibull Distribution: A Comparative Study

The type III discrete Weibull distribution can be used in reliability analysis for modeling failure data such as the number of shocks, cycles, or runs a component or a structure can overcome before failing. This paper describes three methods for estimating its parameters: two customary techniques and a technique particularly suitable for discrete distributions, which, in contrast to the two other techniques, provides analytical estimates, whose derivation is detailed here. The techniques’ peculiarities and practical limits are outlined. A Monte Carlo simulation study has been performed to assess the statistical performance of these methods for different parameter combinations and sample sizes and then give some indication for their mindful use. Two applications of real data are provided with the aim of showing how the type III discrete Weibull distribution can fit real data, even better than other popular discrete models, and how the inferential procedures work. A software implementation of the model is also provided.

Algorithmic-Type Imputation Techniques with Different Data Structures: Alternative Approaches in Comparison

In recent years, with the spread availability of large datasets from multiple sources, increasing attention has been devoted to the treatment of missing information. Recent approaches have paved the way to the development of new powerful algorithmic techniques, in which imputation is performed through computer-intensive procedures. Although most of these approaches are attractive for many reasons, less attention has been paid to the problem of which method should be preferred according to the data structure at hand. This work addresses the problem by comparing the two methods missForest and IPCA with a new method we developed within the forward imputation approach. We carried out comparisons by considering different data patterns with varying skewness and correlation of variables, in order to ascertain in which situations a given method produces more satisfying results.