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Unusual limit theorems for the two tailed Pareto distribution 双尾帕累托分布的异常极限定理
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2020-01-01 DOI: 10.37190/0208-4147.41.2.4
A. Adler, P. Matuła
{"title":"Unusual limit theorems for the two tailed Pareto distribution","authors":"A. Adler, P. Matuła","doi":"10.37190/0208-4147.41.2.4","DOIUrl":"https://doi.org/10.37190/0208-4147.41.2.4","url":null,"abstract":"We examine order statistics from a two sided Pareto distribution. It turns out that the smallest two order statistics and the two largest order statistics have very unusual limits. We obtain strong and weak exact laws for the smallest and the largest order statistics. For such statistics we also study the generalized law of the iterated logarithm. For the second smallest and second largest order statistics we prove the central limit theorem even though their second moment is infinite. 2010 AMS Mathematics Subject Classification: Primary: 60F05; Secondary: 60F15.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69997131","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
A class of weighted rank correlation measures 一类加权秩相关测度
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2020-01-01 DOI: 10.37190/0208-4147.41.1.4
M. Sanatgar, A. Dolati, M. Amini
{"title":"A class of weighted rank correlation measures","authors":"M. Sanatgar, A. Dolati, M. Amini","doi":"10.37190/0208-4147.41.1.4","DOIUrl":"https://doi.org/10.37190/0208-4147.41.1.4","url":null,"abstract":"We propose a class of weighted rank correlation measures extending Spearman’s rho. This class consists of two types of measures. The first type that extends Blest’s rank correlation, places more emphasis on the agreement on top ranks. The second one places more emphasis on the agreement on the bottom ranks. The asymptotic distribution of the proposed measures and some of their properties are studied. A simulation study is performed to compare the performance of the proposed statistics for testing independence by using asymptotic relative efficiency calculations. 2010 AMS Mathematics Subject Classification: Primary: 01A23; Secondary: 45B67.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69996960","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
Complete f-moment convergence of moving average process and its application to nonparametric regression models 移动平均过程的完全f矩收敛及其在非参数回归模型中的应用
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2020-01-01 DOI: 10.37190/0208-4147.41.2.10
Chi Yao, Rui Wang, Ling Chen, Xuejun Wang
{"title":"Complete f-moment convergence of moving average process and its application to nonparametric regression models","authors":"Chi Yao, Rui Wang, Ling Chen, Xuejun Wang","doi":"10.37190/0208-4147.41.2.10","DOIUrl":"https://doi.org/10.37190/0208-4147.41.2.10","url":null,"abstract":"","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"107 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69997108","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
Wick calculus for vector-valued Gaussian white noise unctionals 向量值高斯白噪声泛函的芯演算
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2020-01-01 DOI: 10.37190/0208-4147.41.2.5
Un Cig Ji, Peng Cheng Ma
{"title":"Wick calculus for vector-valued Gaussian white noise unctionals","authors":"Un Cig Ji, Peng Cheng Ma","doi":"10.37190/0208-4147.41.2.5","DOIUrl":"https://doi.org/10.37190/0208-4147.41.2.5","url":null,"abstract":"","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69997176","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
Weighted Laws of Large Numbers for a class of independent summands 一类独立和的加权大数定律
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2020-01-01 DOI: 10.37190/0208-4147.41.1.5
A. Pakes
{"title":"Weighted Laws of Large Numbers for a class of independent summands","authors":"A. Pakes","doi":"10.37190/0208-4147.41.1.5","DOIUrl":"https://doi.org/10.37190/0208-4147.41.1.5","url":null,"abstract":"This paper obtains a necessary and sufficient condition for a weak law of large numbers for weighted averages of positive-valued independent random variables whose distributions belong to a class which includes the F-scheme of record theory. Additional general conditions are found under which the weak law extends to a strong law with the same norming. Examples show these conditions can be fulfilled, and that if they are not, then the weighted averages exhibit multiple growth rates. 2020 Mathematics Subject Classification: Primary 60F05, 60F15; Secondary 60E10.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69996991","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
Scaled Fisher consistency of partial likelihood estimator in the Cox model with arbitrary frailty 具有任意脆弱性的Cox模型中部分似然估计量的缩放Fisher一致性
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2020-01-01 DOI: 10.37190/0208-4147.41.1.6
T. Bednarski, P. Nowak
{"title":"Scaled Fisher consistency of partial likelihood estimator in the Cox model with arbitrary frailty","authors":"T. Bednarski, P. Nowak","doi":"10.37190/0208-4147.41.1.6","DOIUrl":"https://doi.org/10.37190/0208-4147.41.1.6","url":null,"abstract":"It is argued that inference based on the Cox regression model and the partial likelihood estimator is possible for various extensions of the model, which in particular include an arbitrary frailty variable. We demonstrate that the estimator in such a general setup is Fisher consistent up to a scaling factor under symmetry type distributional assumptions on explanatory variables. A simulation experiment shows exemplary behaviour of the estimator and also of a test of fit based on the Anderson–Darling statistic for different Cox model extensions. 2020 Mathematics Subject Classification: Primary 62N01; Secondary 62F12.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69997003","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
JH-singularity and JH-regularity of multivariate stationary processes over LCA groups LCA群上多元平稳过程的jh -奇异性和jh -正则性
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2020-01-01 DOI: 10.37190/0208-4147.41.1.11
L. Klotz, J. M. Medina
{"title":"JH-singularity and JH-regularity of multivariate stationary processes over LCA groups","authors":"L. Klotz, J. M. Medina","doi":"10.37190/0208-4147.41.1.11","DOIUrl":"https://doi.org/10.37190/0208-4147.41.1.11","url":null,"abstract":"","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"168 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69996902","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
Link functions for parameters of sequential order statistics and curved exponential families 序列统计量和曲线指数族参数的链接函数
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2020-01-01 DOI: 10.37190/0208-4147.41.1.8
G. Volovskiy, S. Bedbur, U. Kamps
{"title":"Link functions for parameters of sequential order statistics and curved exponential families","authors":"G. Volovskiy, S. Bedbur, U. Kamps","doi":"10.37190/0208-4147.41.1.8","DOIUrl":"https://doi.org/10.37190/0208-4147.41.1.8","url":null,"abstract":"Estimation of model parameters of sequential order statistics under linear and nonlinear link function assumptions is considered. Utilizing the arising curved exponential family structure, conditions for existence and uniqueness as well as the validity of asymptotic properties of maximum likelihood estimators are stated. Minimal sufficiency and completeness of the associated canonical statistics are discussed. 2020 Mathematics Subject Classification: Primary 62F10; Secondary 62N05, 62N02.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69997059","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
Stochastic complex integrals associated with homogeneous independently scattered random measures on the line 线性上齐次独立分散随机测度的随机复积分
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2019-06-10 DOI: 10.19195/0208-4147.39.1.14
Kouji Yamamuro
{"title":"Stochastic complex integrals associated with homogeneous independently scattered random measures on the line","authors":"Kouji Yamamuro","doi":"10.19195/0208-4147.39.1.14","DOIUrl":"https://doi.org/10.19195/0208-4147.39.1.14","url":null,"abstract":"Complex integrals associated with homogeneous independently scattered random measures on the line are discussed. Theorems corresponding to Cauchy’s theorem and the residue theorem are given. Furthermore, the converse of Cauchy’s theorem is discussed.","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":"49436528","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
Dynamic reliability estimation in a rank-based design 基于秩的动态可靠性估计
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2019-06-10 DOI: 10.19195/0208-4147.39.1.1
M. Mahdizadeh, Ehsan Zamanzade
{"title":"Dynamic reliability estimation in a rank-based design","authors":"M. Mahdizadeh, Ehsan Zamanzade","doi":"10.19195/0208-4147.39.1.1","DOIUrl":"https://doi.org/10.19195/0208-4147.39.1.1","url":null,"abstract":"Ranked set sampling RSS is a data collection method that allows us to direct attention toward measurements of more representative sample units. This article deals with estimating a time-dependent reliability measure under a generalization of the RSS. Some results concerning optimal properties of the proposed estimator are presented. Monte Carlo simulation is employed to assess performance of the estimator. A sport data set is finally analyzed.","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":"47547779","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: 11
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