Pub Date : 2020-10-01DOI: 10.6092/ISSN.1973-2201/10421
A. Azzalini
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."
{"title":"Further Results on a Class of Distributions which Includes the Normal Ones – Looking Back","authors":"A. Azzalini","doi":"10.6092/ISSN.1973-2201/10421","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/10421","url":null,"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.\"","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"80 1","pages":"161-175"},"PeriodicalIF":1.9,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43899816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-01DOI: 10.6092/ISSN.1973-2201/11589
A. Montanari
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.
{"title":"A Conversation with Adelchi Azzalini and Narayanaswamy Balakrishnan","authors":"A. Montanari","doi":"10.6092/ISSN.1973-2201/11589","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/11589","url":null,"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.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"80 1","pages":"131-143"},"PeriodicalIF":1.9,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46856796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-01DOI: 10.6092/ISSN.1973-2201/10420
Dong Li, H. Tong
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.
{"title":"On an Absolute Autoregressive Model and Skew Symmetric Distributions","authors":"Dong Li, H. Tong","doi":"10.6092/ISSN.1973-2201/10420","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/10420","url":null,"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.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"80 1","pages":"177-198"},"PeriodicalIF":1.9,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41604932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-01DOI: 10.6092/ISSN.1973-2201/11588
S. Giannerini, A. Montanari
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.
{"title":"Introduction to the Theme Issue: The Skew-Normal and Related Distributions","authors":"S. Giannerini, A. Montanari","doi":"10.6092/ISSN.1973-2201/11588","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/11588","url":null,"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.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"80 1","pages":"127-130"},"PeriodicalIF":1.9,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48970171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-25DOI: 10.6092/ISSN.1973-2201/8638
Surinder Kumar, A. Chaturvedi
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.
{"title":"On a Generalization of the Positive Exponential Family of Distributions and the Estimation of Reliability Characteristics","authors":"Surinder Kumar, A. Chaturvedi","doi":"10.6092/ISSN.1973-2201/8638","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/8638","url":null,"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.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"80 1","pages":"57-77"},"PeriodicalIF":1.9,"publicationDate":"2020-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46054458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-25DOI: 10.6092/ISSN.1973-2201/8665
M. A. Nasir, M. H. Tahir, C. Chesneau, Farrukh Jamal, M. A. A. Shah
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.
{"title":"The Odds Generalized Gamma-G Family of Distributions: Properties, Regressions and Applications","authors":"M. A. Nasir, M. H. Tahir, C. Chesneau, Farrukh Jamal, M. A. A. Shah","doi":"10.6092/ISSN.1973-2201/8665","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/8665","url":null,"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.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"80 1","pages":"3-38"},"PeriodicalIF":1.9,"publicationDate":"2020-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47728549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-25DOI: 10.6092/ISSN.1973-2201/8658
C. Kumar, Emil Ninan Abraham
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.
{"title":"Some Properties of the Positive Hyper-Poisson Distribution and its Applications","authors":"C. Kumar, Emil Ninan Abraham","doi":"10.6092/ISSN.1973-2201/8658","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/8658","url":null,"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.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"80 1","pages":"41-53"},"PeriodicalIF":1.9,"publicationDate":"2020-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44098223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-25DOI: 10.6092/ISSN.1973-2201/9910
Nick Redfern
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.
{"title":"Modelling Shot Lengths of Hollywood Motion Pictures with the Dagum Distribution","authors":"Nick Redfern","doi":"10.6092/ISSN.1973-2201/9910","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/9910","url":null,"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.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"80 1","pages":"81-99"},"PeriodicalIF":1.9,"publicationDate":"2020-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42301912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-25DOI: 10.6092/ISSN.1973-2201/9368
M. Samuh, A. Al-Omari, N. Koyuncu
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.
{"title":"Estimation of the Parameters of the New Weibull-Pareto Distribution Using Ranked Set Sampling","authors":"M. Samuh, A. Al-Omari, N. Koyuncu","doi":"10.6092/ISSN.1973-2201/9368","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/9368","url":null,"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.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"80 1","pages":"103-123"},"PeriodicalIF":1.9,"publicationDate":"2020-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48252870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-12DOI: 10.6092/ISSN.1973-2201/8561
K. Priyanka, Pidugu Trisandhya
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.
{"title":"Advances in Estimation of Sensitive Issues on Successive Occasions","authors":"K. Priyanka, Pidugu Trisandhya","doi":"10.6092/ISSN.1973-2201/8561","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/8561","url":null,"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.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"79 1","pages":"379-398"},"PeriodicalIF":1.9,"publicationDate":"2020-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48294901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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