Statistica 2021-03-12T14:46:55+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. Revisiting the Canadian Lynx Time Series Analysis Through TARMA Models 2020-09-23T11:45:47+02:00 Greta Goracci <p>The class of threshold autoregressive models has been proven to be a powerful and appropriate tool to describe many dynamical phenomena in different fields. In this work, we deploy the threshold autoregressive moving-average framework to revisit the analysis of the benchmark Canadian lynx time series. This data set has attracted great attention among non-linear time series analysts due to its asymmetric cycle that makes the investigation very challenging. We compare some of the best threshold autoregressive models (TAR) proposed in literature with a selection of threshold<br />autoregressive moving-average models (TARMA). The models are compared under different prospectives: (i) goodness-of-fit through information criteria, (ii) their ability to reproduce characteristic cycles, (iv) their capability to capture multimodality and (iii) forecasting performance. We found TARMAmodels that perform better than TAR models with respect to all these aspects.</p> 2021-03-12T00:00:00+01:00 Copyright (c) 2021 Statistica Variance Inflation Due to Censoring in Survival Probability Estimates 2020-11-23T10:12:18+01:00 Szilard Nemes Andreas Gustavsson Ziad Taib <p>One of the most obvious features of time-to-event data is the occurrence of censoring. Rarely, if ever, studies are conducted until all participants experience the event of interest. Some participants survive beyond the end of follow-up time, some drop out from the studies for various non-study related reasons. During research planning it is paramount to consider the effect of censoring the follow-up times on the estimates. Herein, we look into the possibility of assessing<br />the loss of information, as measured by the variability of the survival probability estimates under right censoring. We provide the researchers with an easy to use formula to assess the magnitude of variance inflation due to censoring. Additionally, we conducted simulation studies assuming various survival distributions. We conclude that the provided variance inflation estimator can be an accurate practical tool for applied statisticians.</p> 2021-03-12T00:00:00+01:00 Copyright (c) 2021 Statistica Some Reliability Properties of Extropy and its Related Measures Using Quantile Function 2020-09-27T21:12:56+02:00 Aswathy Sree Krishnan Sreenarayanapurath Madhavan Sunoj Paduthol Godan Sankaran <p>Extropy is a recent addition to the family of information measures as a complementary dual of Shannon entropy, to measure the uncertainty contained in a probability distribution of a random variable. A probability distribution can be specified either in terms of the distribution function or by the quantile function. In many applied works, there do not have any tractable distribution function but the quantile function exists, where a study on the quantile-based extropy are of importance. The present paper thus focuses on deriving some properties of extropy and its related measures using quantile function. Some ordering relations of quantile-based residual extropy are presented. We also introduce the quantile-based extropy of order statistics and cumulative extropy and studied its properties. Some applications of empirical estimation of quantile-based extropy using simulation and real data analysis are investigated.</p> 2021-03-12T00:00:00+01:00 Copyright (c) 2021 Statistica On the Generalized Odd Transmuted Two-Sided Class of Distributions 2020-09-10T19:29:40+02:00 Omid Kharazmi Mansour Zargar Masoud Ajami <p>In this paper, a general class of two-sided lifetime distributions is introduced via odd ratio function, the well-known concept in survival analysis and reliability engineering. Some statistical and reliability properties including survival function, quantiles, moments function, asymptotic and maximum likelihood estimation are provided in a general setting. A special case of this new family is taken up by considering the exponential model as the parent distribution. Some characteristics of this specialized model and also a discussion associated with survival regression are provided.<br />A simulation study is presented to investigate the bias and mean square error of the maximum likelihood estimators. Moreover, two examples of real data sets are studied; point and interval estimations of all parameters are obtained by maximum likelihood and bootstrap (parametric and non-parametric) procedures. Finally, the superiority of the proposed model over some common statistical distributions is shown through the different criteria for model selection including loglikelihood values, Akaike information criterion and Kolmogorov-Smirnov test statistic values.</p> 2021-03-12T00:00:00+01:00 Copyright (c) 2021 Statistica An Expository Note on Unit - Gompertz Distribution with Applications 2020-09-20T09:42:32+02:00 Mohammed Zafar Anis Debsurya De <p>In a recent paper, Mazucheli et al. (2019) introduced the unit-Gompertz (UG) distribution and studied some of its properties. It is a continuous distribution with bounded support, and hence may be useful for modelling life-time phenomena. We present counter-examples to point out some subtle errors in their work, and subsequently correct them. We also look at some other interesting properties of this new distribution. Further, we also study some important reliability measures and consider some stochastic orderings associated with this new distribution.</p> 2021-03-12T00:00:00+01:00 Copyright (c) 2021 Statistica