Pub Date : 2019-06-06DOI: 10.1186/s40488-019-0096-0
Wolf-Dieter Richter
Stochastic representations of star-shaped distributed random vectors having heavy or light tail density generating function g are studied for increasing dimensions along with corresponding geometric measure representations. Intervals are considered where star radius variables take values with high probability, and the derivation of values of distribution functions of g-robust statistics is proved to be based upon considering random events whose probability is asymptotically negligible if the dimension of the sample vector is approaching infinity. Moreover, a principal component representation of p-generalized elliptically contoured p-generalized Gaussian distributions is discussed.
{"title":"High-dimensional star-shaped distributions","authors":"Wolf-Dieter Richter","doi":"10.1186/s40488-019-0096-0","DOIUrl":"https://doi.org/10.1186/s40488-019-0096-0","url":null,"abstract":"Stochastic representations of star-shaped distributed random vectors having heavy or light tail density generating function g are studied for increasing dimensions along with corresponding geometric measure representations. Intervals are considered where star radius variables take values with high probability, and the derivation of values of distribution functions of g-robust statistics is proved to be based upon considering random events whose probability is asymptotically negligible if the dimension of the sample vector is approaching infinity. Moreover, a principal component representation of p-generalized elliptically contoured p-generalized Gaussian distributions is discussed.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503830","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 : 2019-06-06DOI: 10.1186/s40488-019-0094-2
Li-Pang Chen, Grace Y. Yi, Qihuang Zhang, Wenqing He
Technological advances associated with data acquisition are leading to the production of complex structured data sets. The recent development on classification with multiclass responses makes it possible to incorporate the dependence structure of predictors. The available methods, however, are hindered by the restrictive requirements. Those methods basically assume a common network structure for predictors of all subjects without taking into account the heterogeneity existing in different classes. Furthermore, those methods mainly focus on the case where the distribution of predictors is normal. In this paper, we propose classification methods which address these limitations. Our methods are flexible in handling possibly class-dependent network structures of variables and allow the predictors to follow a distribution in the exponential family which includes normal distributions as a special case. Our methods are computationally easy to implement. Numerical studies are conducted to demonstrate the satisfactory performance of the proposed methods.
{"title":"Multiclass analysis and prediction with network structured covariates","authors":"Li-Pang Chen, Grace Y. Yi, Qihuang Zhang, Wenqing He","doi":"10.1186/s40488-019-0094-2","DOIUrl":"https://doi.org/10.1186/s40488-019-0094-2","url":null,"abstract":"Technological advances associated with data acquisition are leading to the production of complex structured data sets. The recent development on classification with multiclass responses makes it possible to incorporate the dependence structure of predictors. The available methods, however, are hindered by the restrictive requirements. Those methods basically assume a common network structure for predictors of all subjects without taking into account the heterogeneity existing in different classes. Furthermore, those methods mainly focus on the case where the distribution of predictors is normal. In this paper, we propose classification methods which address these limitations. Our methods are flexible in handling possibly class-dependent network structures of variables and allow the predictors to follow a distribution in the exponential family which includes normal distributions as a special case. Our methods are computationally easy to implement. Numerical studies are conducted to demonstrate the satisfactory performance of the proposed methods.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503828","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 : 2019-04-15DOI: 10.1186/s40488-019-0093-3
Johannes T. Ferreira, Andriëtte Bekker
The eigenvalue distributions from a complex noncentral Wishart matrix S=XHX has been the subject of interest in various real world applications, where X is assumed to be complex matrix variate normally distributed with nonzero mean M and covariance Σ. This paper focuses on a weighted analytical representation of S to alleviate the restriction of normality; thereby allowing the choice of X to be complex matrix variate elliptically distributed for the practitioner. New results for eigenvalue distributions of more generalised forms are derived under this elliptical assumption, and investigated for certain members of the complex elliptical class. The distribution of the minimum eigenvalue enjoys particular attention. This theoretical investigation has proposed impact in communications systems (where massive datasets can be conveniently formulated in matrix terms), in particular the case where the noncentral matrix has rank one which is useful in practice.
{"title":"A unified complex noncentral Wishart type distribution inspired by massive MIMO systems","authors":"Johannes T. Ferreira, Andriëtte Bekker","doi":"10.1186/s40488-019-0093-3","DOIUrl":"https://doi.org/10.1186/s40488-019-0093-3","url":null,"abstract":"The eigenvalue distributions from a complex noncentral Wishart matrix S=XHX has been the subject of interest in various real world applications, where X is assumed to be complex matrix variate normally distributed with nonzero mean M and covariance Σ. This paper focuses on a weighted analytical representation of S to alleviate the restriction of normality; thereby allowing the choice of X to be complex matrix variate elliptically distributed for the practitioner. New results for eigenvalue distributions of more generalised forms are derived under this elliptical assumption, and investigated for certain members of the complex elliptical class. The distribution of the minimum eigenvalue enjoys particular attention. This theoretical investigation has proposed impact in communications systems (where massive datasets can be conveniently formulated in matrix terms), in particular the case where the noncentral matrix has rank one which is useful in practice.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503829","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 : 2019-04-08DOI: 10.1186/s40488-019-0092-4
Yu Shi, Zizhao Zhang, W. Wong
{"title":"Particle swarm based algorithms for finding locally and Bayesian D-optimal designs","authors":"Yu Shi, Zizhao Zhang, W. Wong","doi":"10.1186/s40488-019-0092-4","DOIUrl":"https://doi.org/10.1186/s40488-019-0092-4","url":null,"abstract":"","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s40488-019-0092-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65895615","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 : 2019-03-08DOI: 10.1186/s40488-019-0091-5
Mark Huber, Nevena Marić
A multivariate symmetric Bernoulli distribution has marginals that are uniform over the pair {0,1}. Consider the problem of sampling from this distribution given a prescribed correlation between each pair of variables. Not all correlation structures can be attained. Here we completely characterize the admissible correlation vectors as those given by convex combinations of simpler distributions. This allows us to bijectively relate the correlations to the well-known CUTn polytope, as well as determine if the correlation is possible through a linear programming formulation.
{"title":"Admissible Bernoulli correlations","authors":"Mark Huber, Nevena Marić","doi":"10.1186/s40488-019-0091-5","DOIUrl":"https://doi.org/10.1186/s40488-019-0091-5","url":null,"abstract":"A multivariate symmetric Bernoulli distribution has marginals that are uniform over the pair {0,1}. Consider the problem of sampling from this distribution given a prescribed correlation between each pair of variables. Not all correlation structures can be attained. Here we completely characterize the admissible correlation vectors as those given by convex combinations of simpler distributions. This allows us to bijectively relate the correlations to the well-known CUTn polytope, as well as determine if the correlation is possible through a linear programming formulation.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503751","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 : 2019-03-07DOI: 10.1186/s40488-019-0090-6
K. Müller, W. Richter
{"title":"On p-generalized elliptical random processes","authors":"K. Müller, W. Richter","doi":"10.1186/s40488-019-0090-6","DOIUrl":"https://doi.org/10.1186/s40488-019-0090-6","url":null,"abstract":"","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s40488-019-0090-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65895548","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 : 2018-12-05DOI: 10.1186/s40488-018-0089-4
Emrah Altun, Haitham M. Yousof, G.G. Hamedani
In this paper, a new extension of the generalized half-normal distribution is introduced and studied. We assess the performance of the maximum likelihood estimators of the parameters of the new distribution via simulation study. The flexibility of the new model is illustrated by means of four real data sets. A new log-location regression model based on the new distribution is also introduced and studied. It is shown that the new log-location regression model can be useful in the analysis of survival data and provides more realistic fits than other competitive regression models.
{"title":"A new generalization of generalized half-normal distribution: properties and regression models","authors":"Emrah Altun, Haitham M. Yousof, G.G. Hamedani","doi":"10.1186/s40488-018-0089-4","DOIUrl":"https://doi.org/10.1186/s40488-018-0089-4","url":null,"abstract":"In this paper, a new extension of the generalized half-normal distribution is introduced and studied. We assess the performance of the maximum likelihood estimators of the parameters of the new distribution via simulation study. The flexibility of the new model is illustrated by means of four real data sets. A new log-location regression model based on the new distribution is also introduced and studied. It is shown that the new log-location regression model can be useful in the analysis of survival data and provides more realistic fits than other competitive regression models.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503750","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 : 2018-12-04DOI: 10.1186/s40488-018-0088-5
Alex Dytso, Ronit Bustin, H. Vincent Poor, Shlomo Shamai
The family of Generalized Gaussian (GG) distributions has received considerable attention from the engineering community, due to the flexible parametric form of its probability density function, in modeling many physical phenomena. However, very little is known about the analytical properties of this family of distributions, and the aim of this work is to fill this gap. Roughly, this work consists of four parts. The first part of the paper analyzes properties of moments, absolute moments, the Mellin transform, and the cumulative distribution function. For example, it is shown that the family of GG distributions has a natural order with respect to second-order stochastic dominance. The second part of the paper studies product decompositions of GG random variables. In particular, it is shown that a GG random variable can be decomposed into a product of a GG random variable (of a different order) and an independent positive random variable. The properties of this decomposition are carefully examined. The third part of the paper examines properties of the characteristic function of the GG distribution. For example, the distribution of the zeros of the characteristic function is analyzed. Moreover, asymptotically tight bounds on the characteristic function are derived that give an exact tail behavior of the characteristic function. Finally, a complete characterization of conditions under which GG random variables are infinitely divisible and self-decomposable is given. The fourth part of the paper concludes this work by summarizing a number of important open questions.
{"title":"Analytical properties of generalized Gaussian distributions","authors":"Alex Dytso, Ronit Bustin, H. Vincent Poor, Shlomo Shamai","doi":"10.1186/s40488-018-0088-5","DOIUrl":"https://doi.org/10.1186/s40488-018-0088-5","url":null,"abstract":"The family of Generalized Gaussian (GG) distributions has received considerable attention from the engineering community, due to the flexible parametric form of its probability density function, in modeling many physical phenomena. However, very little is known about the analytical properties of this family of distributions, and the aim of this work is to fill this gap. Roughly, this work consists of four parts. The first part of the paper analyzes properties of moments, absolute moments, the Mellin transform, and the cumulative distribution function. For example, it is shown that the family of GG distributions has a natural order with respect to second-order stochastic dominance. The second part of the paper studies product decompositions of GG random variables. In particular, it is shown that a GG random variable can be decomposed into a product of a GG random variable (of a different order) and an independent positive random variable. The properties of this decomposition are carefully examined. The third part of the paper examines properties of the characteristic function of the GG distribution. For example, the distribution of the zeros of the characteristic function is analyzed. Moreover, asymptotically tight bounds on the characteristic function are derived that give an exact tail behavior of the characteristic function. Finally, a complete characterization of conditions under which GG random variables are infinitely divisible and self-decomposable is given. The fourth part of the paper concludes this work by summarizing a number of important open questions.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503749","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 : 2018-11-03DOI: 10.1186/s40488-018-0087-6
Zubair Ahmad, M. Elgarhy, G. Hamedani
{"title":"A new Weibull-X family of distributions: properties, characterizations and applications","authors":"Zubair Ahmad, M. Elgarhy, G. Hamedani","doi":"10.1186/s40488-018-0087-6","DOIUrl":"https://doi.org/10.1186/s40488-018-0087-6","url":null,"abstract":"","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s40488-018-0087-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65895479","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 : 2018-08-13DOI: 10.1186/s40488-018-0085-8
Fiaz Ahmad Bhatti, G. G. Hamedani, Mustafa Ç. Korkmaz, Munir Ahmad
We propose a five parameter transmuted geometric quadratic hazard rate (TG-QHR) distribution derived from mixture of quadratic hazard rate (QHR), geometric and transmuted distributions via the application of transmuted geometric-G (TG-G) family of Afify et al.(Pak J Statist 32(2), 139-160, 2016). Some of its structural properties are studied. Moments, incomplete moments, inequality measures, residual life functions and some other properties are theoretically taken up. The TG-QHR distribution is characterized via different techniques. Estimates of the parameters for TG-QHR distribution are obtained using maximum likelihood method. The simulation studies are performed on the basis of graphical results to illustrate the performance of maximum likelihood estimates (MLEs) of the TG-QHR distribution. The significance and flexibility of TG-QHR distribution is tested through different measures by application to two real data sets.
我们通过应用Afify等人的transmeded geometric- g (TG-G)族，提出了由二次风险率(QHR)、几何和转化分布混合而成的五参数转化几何二次风险率(TG-QHR)分布(Pak J Statist 32(2)， 139-160, 2016)。研究了它的一些结构特性。从理论上讨论了矩、不完全矩、不等式测度、剩余生命函数和其他一些性质。TG-QHR分布是通过不同的技术表征的。利用极大似然法对TG-QHR分布参数进行估计。模拟研究是在图形结果的基础上进行的，以说明TG-QHR分布的最大似然估计(MLEs)的性能。通过对两个实际数据集的应用，通过不同的度量来检验TG-QHR分布的重要性和灵活性。
{"title":"The transmuted geometric-quadratic hazard rate distribution: development, properties, characterizations and applications","authors":"Fiaz Ahmad Bhatti, G. G. Hamedani, Mustafa Ç. Korkmaz, Munir Ahmad","doi":"10.1186/s40488-018-0085-8","DOIUrl":"https://doi.org/10.1186/s40488-018-0085-8","url":null,"abstract":"We propose a five parameter transmuted geometric quadratic hazard rate (TG-QHR) distribution derived from mixture of quadratic hazard rate (QHR), geometric and transmuted distributions via the application of transmuted geometric-G (TG-G) family of Afify et al.(Pak J Statist 32(2), 139-160, 2016). Some of its structural properties are studied. Moments, incomplete moments, inequality measures, residual life functions and some other properties are theoretically taken up. The TG-QHR distribution is characterized via different techniques. Estimates of the parameters for TG-QHR distribution are obtained using maximum likelihood method. The simulation studies are performed on the basis of graphical results to illustrate the performance of maximum likelihood estimates (MLEs) of the TG-QHR distribution. The significance and flexibility of TG-QHR distribution is tested through different measures by application to two real data sets.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503747","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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