Statistica 2022-03-02T09:36:28+01:00 Simone Giannerini Open Journal Systems <strong>STATISTICA – ISSN 1973-2201</strong> is a quarterly journal, founded by Paolo Fortunati. Statistica accepts original papers dealing with methodological and technical aspects of statistics and statistical analyses in the various scientific fields. It publishes also book reviews and announcements. Full texts are available since 2002. On a Class of Time Series Model with Double Lindley Distribution as Marginals 2021-09-05T14:58:39+02:00 Kunnathully Unnikrishnan Nitha Sreekrishnanilayam Devakiamma Krishnarani <p>An autoregressive process of order one with double Lindley distribution as marginal is introduced. A mixture distribution is obtained for the innovation process. Analytical properties of the process are discussed. The parameters of the process are estimated and simulation studies are done. Practical application of the process is discussed with the help of a real data set.</p> 2022-03-02T00:00:00+01:00 Copyright (c) 2021 Statistica Entropy Methods for the Confidence Assessment of Probabilistic Classification Models 2021-08-09T15:30:52+02:00 Gabriele Nunzio Tornetta <p>Many classification models produce a probability distribution as the outcome of a prediction. This information is generally compressed down to the single class with the highest associated probability. In this paper we argue that part of the information that is discarded in this process can be in fact used to further evaluate the goodness of models, and in particular the confidence with which each prediction is made. As an application of the ideas presented in this paper, we provide a theoretical explanation of a confidence degradation phenomenon observed in the complement approach to the (Bernoulli) Naïve Bayes generative model.</p> 2022-03-02T00:00:00+01:00 Copyright (c) 2021 Statistica Asymptotic Properties of the Semi-Parametric Estimators of the Conditional Density for Functional Data in the Single Index Model with Missing Data at Random 2021-09-14T08:48:32+02:00 Abbes Rabhi Nadia Kadiri Sanaà Dounya Mekki <p>The main objective of this work is to estimate, semi-parametrically, the mode of a conditional density when the response is a real valued random variable subject to censored phenomenon and the predictor takes values in a semi-metric space. We assume that the explanatory and the response variables are linked through a single-index structure. First, we introduce a type of kernel estimator of the conditional density function when the data are supposed to be selected from an underlying stationary and ergodic process with missing at random (MAR). Under some general conditions, both the uniform almost-complete consistencies with convergence rates of the model are established. Further, the asymptotic normality of the considered model is given. As an application, the asymptotic (1−α) confidence interval of the conditional density function and the conditional mode are also presented for 0 &lt; α &lt; 1.</p> 2022-03-02T00:00:00+01:00 Copyright (c) 2021 Statistica On Zero-Inflated Alternative Hyper-Poisson Distribution 2021-09-29T19:42:38+02:00 Satheesh Kumar Rakhi Ramachandran <p>Here we develop a zero-inflated version of the alternative hyper-Poisson distribution and discuss its important statistical properties such as probability generating function, expressions for mean, variance, factorial moments, skewness, kurtosis, recursion formula for probabilities, raw moments and factorial moments. Then the maximum likelihood estimation of the parameters of the zero-inflated alternative hyper-Poisson distribution is discussed and certain test procedures are constructed for testing the significance of the inflation parameter. All the procedures are illustrated with the help of certain real life data sets. Moreover, a brief simulation study is carried out for assessing the performances</p> 2022-03-02T00:00:00+01:00 Copyright (c) 2021 Statistica Inference on P(Y < X) Based on Ranked Set Sample for Generalized Pareto Distribution 2021-08-24T10:08:09+02:00 Manoj Chacko Shiny Mathew <p>In this paper, the problem of estimation of R = P(Y &lt; X) based on ranked set sampling, when (X,Y) follows generalised Pareto distribution (GPD) is considered. The maximum likelihood (ML) estimators and Bayes estimators of R are obtained. A Monte Carlo simulation is also performed to study the behaviour of different estimators.</p> 2022-03-02T00:00:00+01:00 Copyright (c) 2021 Statistica