Showing papers in "Statistica in 2020"
TL;DR: In this paper, an additional shape parameter is introduced which allows a wide range of coefficients of asymmetry and kurtosis, and the authors present a class of density functions that can be used to obtain a more general density function.
Abstract: The author’s 1986 paper with the same title is reprinted here alongside some comments and corrections. The original abstract, here translated in English, was as follows: "Some further results are presented concerning a class of density functions already examined in another work of the author (1985). Specifically, an additional shape parameter is introduced which allows a wide range of the coefficients of asymmetry and kurtosis."
52 citations
TL;DR: The canonical form of scale mixtures of multivariate skew-normal distributions was defined in this article, emphasizing its role in summarizing some key properties of this class of distributions, and it was also shown that the canonical form corresponds to an affine invariant coordinate system as defined in Tyler et al. (2009).
Abstract: The canonical form of scale mixtures of multivariate skew-normal distribution is defined, emphasizing its role in summarizing some key properties of this class of distributions. It is also shown that the canonical form corresponds to an affine invariant co-ordinate system as defined in Tyler et al. (2009), and a method for obtaining the linear transform that converts a scale mixture of multivariate skew-normal distribution into a canonical form is presented. Related results, where the particular case of the multivariate skew t distribution is considered in greater detail, are the general expression of the Mardia indices of multivariate skewness and kurtosis and the reduction of dimensionality in calculating the mode.
17 citations
TL;DR: In this article, the authors introduce the discrete analogue of the NH distribution, which is an alternative that always provides better fits than the gamma, Weibull, and the generalized exponential distributions whenever the data contains zero values.
Abstract: An extension of the exponential distribution due toNadarajah and Haghighi referred to as Nadarajah and Haghighi (NH) distribution is an alternative that always provides better fits than the gamma, Weibull, and the generalized exponential distributions whenever the data contains zero values. However, in practice, discrete data is easy to collect as compared to continuous data. Thus, keeping in mind the utility of discrete data, we introduce the discrete analogue of NH distribution.Our main focus is the estimation from the frequentist point of view of the unknown parameters along with deriving some mathematical properties of the new model. We briefly describe different frequentist approaches, namely, maximum likelihood, percentile based, least squares, weighted least squares, maximum product of spacings, Cramer-von-Mises, Anderson-Darling, and right-tail Anderson-Darling estimators, and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. The potentiality of the distribution is analyzed by means of two real data sets.
8 citations
TL;DR: In this paper, a new "odds generalized gamma-G" family of distributions, called the GG-G family, is introduced, with a special focus on the Frechet distribution as baseline distribution.
Abstract: In this article, a new "odds generalized gamma-G" family of distributions, called the GG-G family of distributions, is introduced We propose a complete mathematical and statistical study of this family, with a special focus on the Frechet distribution as baseline distribution In particular, we provide infinite mixture representations of its probability density function and its cumulative distribution function, the expressions for the Renyi entropy, the reliability parameter and the probability density function of ith order statistic Then, the statistical properties of the family are explored Model parameters are estimated by the maximum likelihood method A regression model is also investigated A simulation study is performed to check the validity of the obtained estimators Applications on real data sets are also included, with favorable comparisons to existing distributions in terms of goodness-of-fit
7 citations
TL;DR: The method of maximum likelihood estimation based on ranked set sampling (RSS) and some of its modifications is used to estimate the unknown parameters of the new Weibull-Pareto distribution as discussed by the authors.
Abstract: The method of maximum likelihood estimation based on ranked set sampling (RSS) and some of its modifications is used to estimate the unknown parameters of the new Weibull-Pareto distribution The estimators are compared with the conventional estimators based on simple random sampling (SRS) The biases, mean squared errors, and confidence intervals are used to the comparison The effect of the set size and number of cycles of the RSS schemes are addressed Monte Carlo simulation is carried out by using R The results showed that the RSS estimators are more efficient than their competitors using SRS
6 citations
TL;DR: In this article, the alpha-power transformed Lomax (APTL) distribution was proposed to provide better fits than the LOMax distribution and some of its known generalizations, including explicit expressions for quantiles, mode, moments, conditional moments, mean residual lifetime, stochastic ordering, Bonferroni and Lorenz curve, stress-strength reliability and order statistics.
Abstract: We introduce a new lifetime distribution, called the alpha-power transformed Lomax (APTL) distribution which generalizes the Lomax distribution to provide better fits than the Lomax distribution and some of its known generalizations. Various properties of the proposed distribution, including explicit expressions for the quantiles, mode, moments, conditional moments, mean residual lifetime, stochastic ordering, Bonferroni and Lorenz curve, stress-strength reliability and order statistics are derived. The new distribution can have a decreasing and upside-down bathtub failure rate function depending on its parameters. The maximum likelihood estimators of the three unknown parameters of APTL are obtained. A simulation study is carried out to examine the performances of the maximum likelihood estimates in terms of their mean squared error using simulated samples. Finally, the potentiality of the distribution is analyzed by means of two real data sets. For the real data sets, this distribution is found to be superior in its ability to sufficiently model both the data sets as compared to the Lomax (L) distribution, exponentiated-Lomax (EL) distribution, gamma-Lomax (GL) distribution, beta-Lomax (BL) distribution and Kumaraswamy-Lomax (KuL) distribution.
5 citations
TL;DR: This work deploys the threshold autoregressive moving-average framework to revisit the analysis of the benchmark Canadian lynx time series to find TARMA models that perform better than TAR models with respect to all aspects.
Abstract: 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 thresholdautoregressive 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.
4 citations
TL;DR: In this article, the authors present counter-examples to point out some subtle errors in their work, and subsequently correct them, and also look at some other interesting properties of the unit-Gompertz distribution.
Abstract: 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.
4 citations
TL;DR: In this article, a generalization of the Bilal distribution proposed by Abd-Elrahman (2017) by zeroing in on two measures of reliability, R(t) and P, based on type II censoring is considered.
Abstract: We consider here the generalization of the Bilal distribution proposed by Abd-Elrahman (2017) by zeroing in on two measures of reliability, R(t) and P, based on type II censoring. We obtain point estimators namely, λ and θ, of the above said distribution, when both parameters of the distribution are unknown. Maximum likelihood estimators (MLEs), Bayes estimators (BEs) and Lindley’s approximation for the Bayes estimators are proposed. By using independent noninformative type of priors for the unknown parameters Bayes estimators are derived. Although the proposed estimators cannot be expressed in closed forms, these can be easily obtained through the use of numerical procedures. The performance of these estimators is studied on the basis of their mean squared error (MSE), computed separately under LINEX loss function (LLF) and squared error loss function (SELF) through Monte-Carlo simulation technique.
3 citations
TL;DR: In this paper, the authors proposed an efficient estimation procedure for the population mean in the presence of non-response. And the proposed estimators of population mean provided an improvement over the corresponding conventional estimators proposed by Cochran (1977), Rao (1983, 1986), and Singh and Kumar (2008, 2010) under the deterministic non-answer in terms of efficiency.
Abstract: This paper introduces an efficient estimation procedure for the population mean in the presence of non-response. The proposed estimators of population mean provides an improvement over the corresponding conventional estimators proposed by Cochran (1977), Rao (1983, 1986) and Singh and Kumar (2008, 2010) under the deterministic non-response in terms of efficiency. A comparative study has been performed and it has been shown that the proposed estimators perform better in comparison to the conventional estimators. The theoretical findings are supported by an empirical study.
2 citations
TL;DR: In this paper, the authors exploit the connection between a popular construction of a well-known skew-normal distribution and an absolute autoregressive process, and show how the stochastic process approach can lead to other skew symmetric distributions, including a skew-Cauchy distribution and some singular distributions.
Abstract: By exploiting the connection between a popular construction of a well-known skew-normal distribution and an absolute autoregressive process, we show how the stochastic process approach can lead to other skew symmetric distributions, including a skew-Cauchy distribution and some singular distributions. In so doing, we also correct an erroneous skew-Cauchy-distribution in the literature. We discuss the estimation, for dependent data, of the key parameter relating to the skewness.
TL;DR: In this article, a zero-truncated form of the hyper-Poisson distribution is considered and its crucial properties through deriving its probability generating function, cumulative distribution function, expressions for factorial moments, mean, variance and recurrence relations for probabilities, raw moments and factorial moment.
Abstract: In this paper we consider a zero-truncated form of the hyper-Poisson distribution and investigate some of its crucial properties through deriving its probability generating function, cumulative distribution function, expressions for factorial moments, mean, variance and recurrence relations for probabilities, raw moments and factorial moments Further, the estimation of the parameters of the distribution is discussed The distribution has been fitted to certain real life data sets to test its goodness of fit The likelihood ratio test procedure is adopted for checking the significance of the parameters and a simulation study is performed for assessing the efficiency of the maximum likelihood estimators
TL;DR: The authors showed that the three-parameter Dagum distribution provides a good fit for shot lengths in Hollywood films due to its ability to model a wide range of skewness and kurtosis values and a variety of tail behaviours by virtue of its two shape parameters.
Abstract: This paper demonstrates the three-parameter Dagum distribution provides a good fit for shot lengths in Hollywood films due to its ability to model a wide range of skewness and kurtosis values and a variety of tail behaviours by virtue of its two shape parameters The fit of this distribution is better across films in the sample than the two-parameter lognormal distribution, though animated films are an important exception to this These results can be applied to more closely replicate the editing practice of film editors when generating film sequences using automated editing software
TL;DR: In this paper, the quantile-based residual extropy of order statistics and cumulative extropy is studied. But quantile functions do not have any tractable distribution function but quantile function exists, where a study on quantile based extropy are of importance.
Abstract: 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.
TL;DR: In this article, an improved class of estimators for estimating sensitive population mean at current occasion using an innocuous variable in two occasion successive sampling is proposed. But the proposed estimators have not been compared with recent modified estimators.
Abstract: Surveys related to sensitive issues are accompanied with social desirability response bias which flaw the validity of analysis. This problem became serious when sensitive issues are estimated on successive occasions. The scrambled response technique is an alternative solution as it preserve respondents anonymity. Therefore, the present article endeavours to propose an improved class of estimators for estimating sensitive population mean at current occasion using an innocuous variable in two occasion successive sampling. Detailed properties of the estimators are analysed. Optimum allocation to fresh and matched samples are obtained. Many existing estimators in successive sampling have been modified to work for sensitive population mean estimation under scrambled response technique. The proposed estimators has been compared with recent modified estimators. Theoretical considerations are integrated with empirical and simulation studies to ascertain the efficiency gain derived from the proposed improved class of estimators.
TL;DR: In this article, the authors studied the pattern of inclusion and exclusion of players from a team in any team sport and found that the inclusions and exclusions are related to the player's performance in the matches previously played.
Abstract: In this paper, we study the pattern of inclusion and exclusion of players from a team in any team sport. Usually these inclusions and exclusions are related to the player’s performance in the matches previously played. Also the inclusion and exclusion at any particular cycle depends on the player’s history as observed through the number of times he has been included or excluded previously. The focus of this paper is to study this pattern for cricketers who have represented their respective countries in One Day Internationals (ODIs). As observed in the study, there is a distinct difference in the inclusion and exclusion patterns of bowlers and batsmen, and hence the two groups have been studied separately. Respective survival functions over the cycles of inclusion and exclusion have been constructed for both groups. These reveal several interesting features regarding the chances of an ODI cricketer being retained or dropped from the team.
TL;DR: A new family of distributions called the extended odd Lomax family of distribution is introduced by adding two extra shape parameters and one scale parameter and the results show that the distributions adequately describe the datasets.
Abstract: The Lomax distribution has a wide range of applications. Due to this, it has had many extensions to render it more flexible and useful to model real world data. In this study, a new family of distributions called the extended odd Lomax family of distributions is introduced by adding two extra shape parameters and one scale parameter. We derived several statistical properties of the new family of distributions. The parameters of the family of distributions are estimated by the use of maximum likelihood method and the consistency of the estimators investigated via Monte Carlo simulations. The usefulness and flexibility of the new family of distributions are illustrated by the use of two real datasets. The results show that the distributions adequately describe the datasets.
TL;DR: In this article, a general class of two-sided lifetime distributions via odd ratio function, the well-known concept in survival analysis and reliability engineering, is introduced, and a simulation study is presented to investigate the bias and mean square error of the maximum likelihood estimators.
Abstract: 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.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.
TL;DR: A workshop to celebrate the life and works of Antonella Capitanio, one year after her premature death, and the inauguration of the academic year for the PhD program in Statistical Sciences.
Abstract: On November 6, 2017, the Department of Statistical Sciences of the University of Bologna organized a workshop to celebrate the life and works of Antonella Capitanio, one year after her premature death. The event also represented the inauguration of the academic year for the PhD program in Statistical Sciences. In this paper, the conversation that Angela Montanari had with Adelchi Azzalini and Narayanaswamy Balakrishnan on this occasion is reported.
TL;DR: In this paper, the authors look into the possibility of assessing the loss of information, as measured by the variability of the survival probability estimates under right censoring, and provide the researchers with an easy-to-use formula to assess the magnitude of variance inflation due to censoring.
Abstract: 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 assessingthe 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.
TL;DR: This paper extends the concept of the information volatility function to the residual random variable, a dynamic information volatilityfunction and studies its usefulness in reliability modelling.
Abstract: Liu (2007) discussed a new measure, known as the information volatility function to study the variability of the uncertainty contained in a probability distribution. In the present paper, we extend this concept to the residual random variable, a dynamic information volatility function and study its usefulness in reliability modelling. Different ageing and characterization properties of dynamic information volatility function are also derived.
TL;DR: In this paper, the authors discuss the relationship between skew symmetric distributions and threshold autoregressive models, and re-present the seminal 1986 Azzalini paper, together with corrections and comments from the author.
Abstract: This theme issue on the skew-Normal and related distributions is motivated by the workshop held on November 6th, 2017 in memory of Antonella Capitanio, one year after her premature loss. The issue contains the transcript of the conversation between Angela Montanari, Adelchi Azzalini and Narayanaswamy Balakrishnan regarding their scientific collaboration with Antonella. Moreover, the last unpublished work of Antonella Capitanio on mixtures of skew normal distributions is reproduced here with the kind permission of her family. We also take the opportunity to re-present the seminal 1986 Azzalini paper, together with corrections and comments from the author. The last contribution, by Howell Tong and Dong Li, concerns the interesting relationship between skew symmetric distributions and threshold autoregressive models.
TL;DR: In this paper, a generalization of positive exponential family of distributions developed by Liang (2008) is taken into consideration, and two measures of reliability are discussed Uniformly minimum variance unbiased estimators (UMVUES), maximum likelihood estimators, and method of moment estimators are developed for the reliability functions.
Abstract: A generalization of positive exponential family of distributions developed by Liang (2008) is taken into consideration Its properties are studied Two measures of reliability are discussed Uniformly minimum variance unbiased estimators (UMVUES), maximum likelihood estimators (MLES) and method of moment estimators (MMES) are developed for the reliability functions The performances of three types of estimators are compared through Monte Carlo simulation Real life data sets are also analyzed