{"title":"Generalized wordlength enumerator for asymmetrical designs","authors":"Kang Wang , Na Zou , Hong Qin","doi":"10.1016/j.spl.2024.110281","DOIUrl":"10.1016/j.spl.2024.110281","url":null,"abstract":"<div><div>In this paper, we extend the study of wordlength enumerator to asymmetrical designs, and unify the generalized <span><math><mi>α</mi></math></span>- and <span><math><mi>β</mi></math></span>-wordlength pattern with generalized wordlength enumerator. The generalized wordlength enumerator is easy and fast to compute, and can effectively compare and rank symmetrical and asymmetrical designs. A lower bound of generalized wordlength enumerator is provided, and can be used as a benchmark for searching and constructing optimal designs. Numerical results are also provided, which lend further support to our theoretical findings.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593992","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}
Jiang Cheng , Chao Deng , Shuyan Liu , Xudong Zeng
{"title":"An equilibrium model of reinsurance pricing","authors":"Jiang Cheng , Chao Deng , Shuyan Liu , Xudong Zeng","doi":"10.1016/j.spl.2024.110280","DOIUrl":"10.1016/j.spl.2024.110280","url":null,"abstract":"<div><div>Reinsurance is the insurance of insurance companies. We develop a dynamic equilibrium model for reinsurance pricing based on the supply and demand of reinsurance. In the model, an insurance company and a reinsurance company make decisions on the optimal reinsurance policy as a demander and a supplier of reinsurance, respectively. The reinsurance price is determined when the demand matches the supply. We incorporate the proportional reinsurance policy as well as investment opportunities into the framework. The high flexibility of this equilibrium pricing model paves a new way for studies of optimal reinsurance and reinsurance pricing.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417135","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}
{"title":"Stationary distribution of a stochastic generalized SIRI epidemic model with reinfection and relapse","authors":"Kai Wang , Hongjie Fan , Yanling Zhu","doi":"10.1016/j.spl.2024.110279","DOIUrl":"10.1016/j.spl.2024.110279","url":null,"abstract":"<div><div>In this paper, we propose and investigate the stochastic SIRI epidemic model with two generalized incidence rate functions. We firstly study the existence and uniqueness of the globally positive solution to the stochastic SIRI model with positive initial value. Then we obtain sufficient conditions for the extinction of the disease in the stochastic epidemic model, and find that the large noise can make the disease die out exponentially. Meanwhile, we obtain that the solution to the stochastic model has a unique stationary distribution when <span><math><mover><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>s</mi></mrow></msubsup></mrow><mrow><mo>˜</mo></mrow></mover></math></span> is greater than one. Our results show that the intensity of white noise can affect the dynamical behaviors of the model. Finally, we use numerical simulation to illustrate theoretical results, and apply both the stochastic and deterministic models to analyze the outbreak of COVID-19 epidemic in Serbia.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417136","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}
{"title":"Mean square error and variance estimation of the sample ratio under Lahiri ’s design","authors":"Hiroshi Saigo","doi":"10.1016/j.spl.2024.110277","DOIUrl":"10.1016/j.spl.2024.110277","url":null,"abstract":"<div><div>The mean square error of the sample ratio under Lahiri’s design is derived and is compared with that under simple random sampling without replacement. New variance estimators of the sample ratio under the design are proposed. A simulation study is conducted to confirm the main results.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322756","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}
Sambit Panda , Cencheng Shen , Ronan Perry , Jelle Zorn , Antoine Lutz , Carey E. Priebe , Joshua T. Vogelstein
{"title":"Universally consistent K-sample tests via dependence measures","authors":"Sambit Panda , Cencheng Shen , Ronan Perry , Jelle Zorn , Antoine Lutz , Carey E. Priebe , Joshua T. Vogelstein","doi":"10.1016/j.spl.2024.110278","DOIUrl":"10.1016/j.spl.2024.110278","url":null,"abstract":"<div><div>The K-sample testing problem involves determining whether K groups of data points are each drawn from the same distribution. Analysis of variance is arguably the most classical method to test mean differences, along with several recent methods to test distributional differences. In this paper, we demonstrate the existence of a transformation that allows K-sample testing to be carried out using any dependence measure. Consequently, universally consistent K-sample testing can be achieved using a universally consistent dependence measure, such as distance correlation and the Hilbert–Schmidt independence criterion. This enables a wide range of dependence measures to be easily applied to K-sample testing.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167715224002475/pdfft?md5=8319efb92609b489dc9c39c93ef72fa6&pid=1-s2.0-S0167715224002475-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142314508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"General mean-field reflected backward stochastic differential equations with locally monotone coefficients","authors":"Zongkui Fu , Dandan Fei","doi":"10.1016/j.spl.2024.110273","DOIUrl":"10.1016/j.spl.2024.110273","url":null,"abstract":"<div><p>In this paper, we study general mean-field reflected backward stochastic differential equations with locally monotone coefficients. With the help of choosing the suitable approximation sequence, we obtain the existence and uniqueness of solution to general mean-field reflected backward stochastic differential equations.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167715224002426/pdfft?md5=e746dc640796f25d5bc5e9e81624e7ec&pid=1-s2.0-S0167715224002426-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142273970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Extension of a strong form of the three-dimensional Gaussian product inequality","authors":"Bara Kim , Jeongsim Kim","doi":"10.1016/j.spl.2024.110276","DOIUrl":"10.1016/j.spl.2024.110276","url":null,"abstract":"<div><p>We generalize a strong form of the three-dimensional Gaussian product inequality studied by Herry et al. (2024), who resolved the case of any triple of even positive integers. We extend the result to any triple consisting of a pair of positive real numbers and an even positive integer. Our result includes all existing results on the three-dimensional Gaussian product inequality conjecture.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167715224002451/pdfft?md5=a8b31cd83eb2c899f4b3fa8fa028abdc&pid=1-s2.0-S0167715224002451-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142273971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Stein characterisation of the distribution of the product of correlated normal random variables","authors":"Robert E. Gaunt, Siqi Li, Heather L. Sutcliffe","doi":"10.1016/j.spl.2024.110269","DOIUrl":"10.1016/j.spl.2024.110269","url":null,"abstract":"<div><p>We obtain a Stein characterisation of the distribution of the product of two correlated normal random variables with non-zero means, and more generally the distribution of the sum of independent copies of such random variables. Our Stein characterisation is shown to naturally generalise a number of other Stein characterisations in the literature. From our Stein characterisation we derive recursive formulas for the moments of the product of two correlated normal random variables, and more generally the sum of independent copies of such random variables, which allows for efficient computation of higher order moments.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167715224002384/pdfft?md5=df7c086d07ad8089c037d05fa561ad0c&pid=1-s2.0-S0167715224002384-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142239584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Continuity of Gaussian extreme distributions","authors":"Lijian Yang","doi":"10.1016/j.spl.2024.110274","DOIUrl":"10.1016/j.spl.2024.110274","url":null,"abstract":"<div><p>Distribution continuity is established for extremes of Gaussian processes with bounded sample paths and positive variance or continuous sample paths over compact domain, and for multiparameter Brownian sheets. These results provide probabilistic support for global inference on unknown functions.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167715224002438/pdfft?md5=18580bb383254019118c8d7a0a3b75e0&pid=1-s2.0-S0167715224002438-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142239728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Multivariate Hawkes process allowing for common shocks","authors":"Zhehao Zhang, Ruina Xing","doi":"10.1016/j.spl.2024.110270","DOIUrl":"10.1016/j.spl.2024.110270","url":null,"abstract":"<div><p>Although the Hawkes process has been widely applied, their probability properties are difficult to obtain, depending on the model structure. This paper proposes a multivariate Hawkes process, which allows for common jumps from each marginal processes. The probability of this common jump is determined by another independent process, which represents the arrival intensity of external shocks to the system. The infinitesimal generator of the new multivariate jump process is derived. Based on that, moments and the Laplace transform are studied, which further demonstrate the advantages of this model structure.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167715224002396/pdfft?md5=af28dce83dfba4528a5b455d15773fb3&pid=1-s2.0-S0167715224002396-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142239740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}