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On a limit structure of the Galton–Watson branching processes with regularly varying generating functions 关于具有正则变生成函数的Galton–Watson分支过程的一个极限结构
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2019-06-10 DOI: 10.19195/0208-4147.39.1.4
A. Imomov
{"title":"On a limit structure of the Galton–Watson branching processes with regularly varying generating functions","authors":"A. Imomov","doi":"10.19195/0208-4147.39.1.4","DOIUrl":"https://doi.org/10.19195/0208-4147.39.1.4","url":null,"abstract":"We investigate limit properties of discrete time branching processes with application of the theory of regularly varying functions in the sense of Karamata. In the critical situation we suppose that the offspring probability generating function has an infinite second moment but its tail regularly varies. In the noncritical case, the finite moment of type Ε[x ln x] is required. The lemma on the asymptotic representation of the generating function of the process and its differential analogue will underlie our conclusions.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49614751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Large deviations for generalized conditioned Gaussian processes and their bridges 广义条件高斯过程的大偏差及其桥接
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2019-06-10 DOI: 10.19195/0208-4147.39.1.11
B. Pacchiarotti
{"title":"Large deviations for generalized conditioned Gaussian processes and their bridges","authors":"B. Pacchiarotti","doi":"10.19195/0208-4147.39.1.11","DOIUrl":"https://doi.org/10.19195/0208-4147.39.1.11","url":null,"abstract":"We study the asymptotic behavior of a Gaussian process conditioned to n linear functionals of its paths and of the bridge of such a process. In particular, functional large deviation results are stated for small time. Two examples are considered.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45839002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
On a conjecture about the comparability of parallel systems with respect to the convex transform order 关于平行系统关于凸变换阶的可比性的一个猜想
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2019-01-10 DOI: 10.37190/0208-4147.41.2.8
Idir Arab, M. Hadjikyriakou, P. E. Oliveira
{"title":"On a conjecture about the comparability of parallel systems with respect to the convex transform order","authors":"Idir Arab, M. Hadjikyriakou, P. E. Oliveira","doi":"10.37190/0208-4147.41.2.8","DOIUrl":"https://doi.org/10.37190/0208-4147.41.2.8","url":null,"abstract":"In this paper we prove that two heterogeneous parallel systems with independent exponentially distributed components are comparable via the star transform order while the comparison via the convex transform fails. The latter conclusion provides a partial answer to a problem that remained open for a decade.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43122660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Entropic upper bound for Bayes risk in the quantum case 量子情形下Bayes风险的熵上界
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-12-28 DOI: 10.19195/0208-4147.38.2.9
Rafał M. Wieczorek, H. Podsędkowska
{"title":"Entropic upper bound for Bayes risk in the quantum case","authors":"Rafał M. Wieczorek, H. Podsędkowska","doi":"10.19195/0208-4147.38.2.9","DOIUrl":"https://doi.org/10.19195/0208-4147.38.2.9","url":null,"abstract":"The entropic upper bound for Bayes risk in a general quantum case is presented. We obtained generalization of the entropic lower bound for probability of detection. Our result indicates upper bound for Bayes risk in a particular case of loss function – for probability of detection in a pretty general setting of an arbitrary finite von Neumann algebra. It is also shown under which condition the indicated upper bound is achieved.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2018-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48461076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the longest runs in Markov chains 在马尔可夫链的最长运行中
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-12-28 DOI: 10.19195/0208-4147.38.2.8
Zhenxia Liu, Xiangfeng Yang
{"title":"On the longest runs in Markov chains","authors":"Zhenxia Liu, Xiangfeng Yang","doi":"10.19195/0208-4147.38.2.8","DOIUrl":"https://doi.org/10.19195/0208-4147.38.2.8","url":null,"abstract":"In the first n steps of a two-state success and failure Markov chain, the longest success run Ln has been attracting considerable attention due to its various applications. In this paper, we study Ln in terms of its two closely connected properties: moment generating function and large deviations. This study generalizes several existing results in the literature, and also finds an application in statistical inference. Our method on the moment generating function is based on a global estimate of the cumulative distribution function of Ln proposed in this paper, and the proofs of the large deviations include the Gärtner–Ellis theorem and the moment generating function.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2018-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42368931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Supermodular ordering of Poisson and binomial random vectors by tree-based correlations 基于树相关的泊松和二项随机向量的超模排序
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-12-28 DOI: 10.19195/0208-4147.38.2.7
Bünyamin Kızıldemir, Nicolas Privault
{"title":"Supermodular ordering of Poisson and binomial random vectors by tree-based correlations","authors":"Bünyamin Kızıldemir, Nicolas Privault","doi":"10.19195/0208-4147.38.2.7","DOIUrl":"https://doi.org/10.19195/0208-4147.38.2.7","url":null,"abstract":"We construct a dependence structure for binomial, Poisson and Gaussian random vectors, based on partially ordered binary trees and sums of independent random variables. Using this construction, we characterize the supermodular ordering of such random vectors via the componentwise ordering of their covariance matrices. For this, we apply Möbius inversion techniques on partially ordered trees, which allow us to connect the Lévy measures of Poisson random vectors on the discrete d-dimensional hypercube to their covariance matrices.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2018-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45368088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Preservation properties of stochastic orders by transformation to Harris family Harris族变换下随机阶的保存性质
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-12-28 DOI: 10.19195/0208-4147.38.2.10
S. Abbasi, M. H. Alamatsaz
{"title":"Preservation properties of stochastic orders by transformation to Harris family","authors":"S. Abbasi, M. H. Alamatsaz","doi":"10.19195/0208-4147.38.2.10","DOIUrl":"https://doi.org/10.19195/0208-4147.38.2.10","url":null,"abstract":"Stochastic comparisons of lifetime characteristics of reliability systems and their components are of common use in lifetime analysis. In this paper, using Harris family distributions, we compare lifetimes of two series systems with random number of components, with respect to several types of stochastic orders. Our results happen to enfold several previous findings in this connection. We shall also show that several stochastic orders and ageing characteristics, such as IHRA, DHRA, NBU, and NWU, are inherited by transformation to Harris family. Finally, some refinements are made concerning related existing results in the literature.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2018-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43021728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
M-estimation of the mixed-type generalized linear model 混合型广义线性模型的m估计
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-07-30 DOI: 10.19195/0208-4147.38.1.11
Ying Dong, Lixin Song, Mingqiu Wang, Muhammad Amin
{"title":"M-estimation of the mixed-type generalized linear model","authors":"Ying Dong, Lixin Song, Mingqiu Wang, Muhammad Amin","doi":"10.19195/0208-4147.38.1.11","DOIUrl":"https://doi.org/10.19195/0208-4147.38.1.11","url":null,"abstract":"To investigate the features of the individual from the mixedtype model, a novel model, named the mixed-type generalized linear model, is proposed firstly in this work, which is verified to be realistic and useful. We consider the robustness of M-estimation to estimate the unknown parameters of the mixed-type generalized linear model. By applying the law of large numbers and the central limit theorem, the consistency and asymptotic normality of the M-estimation for the mixed-type generalized linear model are proved with regularity assumptions. At last, in order to evaluate the finite sample performance of the estimator for the new model, several applied instances are presented, which show the good performance of the estimator.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44144023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On exact strong laws of large numbers under general dependence conditions 关于一般依赖条件下的精确强大数定律
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-07-30 DOI: 10.19195/0208-4147.38.1.6
A. Adler, P. Matuła
{"title":"On exact strong laws of large numbers under general dependence conditions","authors":"A. Adler, P. Matuła","doi":"10.19195/0208-4147.38.1.6","DOIUrl":"https://doi.org/10.19195/0208-4147.38.1.6","url":null,"abstract":"We study the almost sure convergence of weighted sums of dependent random variables to a positive and finite constant, in the case when the random variables have either mean zero or no mean at all. These are not typical strong laws and they are called exact strong laws of large numbers. We do not assume any particular type of dependence and furthermore consider sequences which are not necessarily identically distributed. The obtained results may be applied to sequences of negatively associated random variables.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49506051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 14
Extremes of order statistics of stationary Gaussian processes 平稳高斯过程阶统计量的极值
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-07-30 DOI: 10.19195/0208-4147.38.1.4
Chunming Zhao
{"title":"Extremes of order statistics of stationary Gaussian processes","authors":"Chunming Zhao","doi":"10.19195/0208-4147.38.1.4","DOIUrl":"https://doi.org/10.19195/0208-4147.38.1.4","url":null,"abstract":"Tu wpisz tekst","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46051840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
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