Abstract In the present work, we investigate the applications of cumulative entropy as a tool in income analysis. The relationships the cumulative entropy has with income gap ratio, Lorenz curve, Gini index, Bonferroni curve and Zenga curve are provided. Applications of the results to real data are illustrated.
{"title":"Cumulative Entropy and Income Analysis","authors":"N. Nair, B. Vineshkumar","doi":"10.1515/eqc-2022-0012","DOIUrl":"https://doi.org/10.1515/eqc-2022-0012","url":null,"abstract":"Abstract In the present work, we investigate the applications of cumulative entropy as a tool in income analysis. The relationships the cumulative entropy has with income gap ratio, Lorenz curve, Gini index, Bonferroni curve and Zenga curve are provided. Applications of the results to real data are illustrated.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"24 1","pages":"165 - 179"},"PeriodicalIF":0.0,"publicationDate":"2022-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84539090","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}
Abstract This paper proves the existence and uniqueness theorem for generalized (reflected) backward stochastic differential equations under stochastic Lipschitz and monotone condition. The result is shown by using Picard’s iteration, the Snell envelope theory and the penalization method.
{"title":"On Generalized Reflected BSDEs with Rcll Obstacle","authors":"M. El Jamali, M. El Otmani","doi":"10.1515/eqc-2022-0001","DOIUrl":"https://doi.org/10.1515/eqc-2022-0001","url":null,"abstract":"Abstract This paper proves the existence and uniqueness theorem for generalized (reflected) backward stochastic differential equations under stochastic Lipschitz and monotone condition. The result is shown by using Picard’s iteration, the Snell envelope theory and the penalization method.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"29 1","pages":"1 - 19"},"PeriodicalIF":0.0,"publicationDate":"2022-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74747995","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}
Abstract We introduce a new test for exponentiality against decreasing (increasing) mean residual life alternatives based on a cumulative residual Renyi’s entropy of order α. The exact and asymptotic distributions of the test statistic are given. The performance of the proposed test statistic is compared with other constructed tests in the literature using a simulation study. Finally, some numerical examples illustrating the theory are given.
{"title":"Test for Decreasing Mean Residual Lifetimes Based on the Cumulative Residual Renyi’s Entropy","authors":"V. Zardasht","doi":"10.1515/eqc-2021-0051","DOIUrl":"https://doi.org/10.1515/eqc-2021-0051","url":null,"abstract":"Abstract We introduce a new test for exponentiality against decreasing (increasing) mean residual life alternatives based on a cumulative residual Renyi’s entropy of order α. The exact and asymptotic distributions of the test statistic are given. The performance of the proposed test statistic is compared with other constructed tests in the literature using a simulation study. Finally, some numerical examples illustrating the theory are given.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"91 1","pages":"75 - 84"},"PeriodicalIF":0.0,"publicationDate":"2022-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79520564","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}
Abstract In this paper, we develop a stochastic model to analyze how financial contagion may affect economic activity. In the deterministic case, we show that, according to specific parameter values, the economy may converge either to a stress-free equilibrium or to a stressed equilibrium: in the former situation, the level of economic growth is maximal, while in the latter, it is reduced by financial contagion. In the stochastic case, we compute a value around which the level of economic growth oscillates. Numerical simulations are performed to illustrate theoretical results obtained.
{"title":"Impact of Financial Crisis on Economic Growth: A Stochastic Model","authors":"C. Tadmon, Eric Rostand Njike Tchaptchet","doi":"10.1515/eqc-2021-0049","DOIUrl":"https://doi.org/10.1515/eqc-2021-0049","url":null,"abstract":"Abstract In this paper, we develop a stochastic model to analyze how financial contagion may affect economic activity. In the deterministic case, we show that, according to specific parameter values, the economy may converge either to a stress-free equilibrium or to a stressed equilibrium: in the former situation, the level of economic growth is maximal, while in the latter, it is reduced by financial contagion. In the stochastic case, we compute a value around which the level of economic growth oscillates. Numerical simulations are performed to illustrate theoretical results obtained.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"35 1","pages":"45 - 63"},"PeriodicalIF":0.0,"publicationDate":"2022-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80639891","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}
Abstract The main focus of this article is on the study of properties and characterizations of dynamic survival extropy and its scaled version. Its relation with other well-known measures is also discussed. A simple nonparametric estimator and a nonparametric estimator based on the kernel are proposed for survival extropy and scaled dynamic survival extropy respectively. These estimators could also be utilized to estimate the measures related to dynamic survival extropy, such as the Gini index. In addition, the performance of the suggested estimators is evaluated for the simulated data set.
{"title":"A Study on Some Properties of Dynamic Survival Extropy and Its Relation to Economic Measures","authors":"R. D. Nair, E. I. A. Sathar","doi":"10.1515/eqc-2021-0050","DOIUrl":"https://doi.org/10.1515/eqc-2021-0050","url":null,"abstract":"Abstract The main focus of this article is on the study of properties and characterizations of dynamic survival extropy and its scaled version. Its relation with other well-known measures is also discussed. A simple nonparametric estimator and a nonparametric estimator based on the kernel are proposed for survival extropy and scaled dynamic survival extropy respectively. These estimators could also be utilized to estimate the measures related to dynamic survival extropy, such as the Gini index. In addition, the performance of the suggested estimators is evaluated for the simulated data set.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"39 1","pages":"65 - 74"},"PeriodicalIF":0.0,"publicationDate":"2022-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87724584","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}
{"title":"5th International Workshop on Branching Processes and Their Applications (IWBPA 2021)","authors":"Miguel González, M. Molina, I. D. del Puerto","doi":"10.1515/eqc-2021-2001","DOIUrl":"https://doi.org/10.1515/eqc-2021-2001","url":null,"abstract":"","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"95 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87297820","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}
Abstract This article develops multiple dependent state (MDS) sampling inspection plans based on the mean of lifetime quality characteristic that follows non-normal distributions viz., exponential and Lindley distribution. In this plan, the lot quality is measured by the lot mean (𝜇). We have estimated the optimal plan parameters of the proposed technique by non-linear optimization approaches considering acceptable quality level and rejection quality level. We have compared the sample size between the MDS sampling inspection plan and the single sampling inspection plan for the variable. Finally, we have taken two examples to illustrate the proposed technique.
{"title":"Multiple Dependent State Sampling Inspection Plan for Lindley Distributed Quality Characteristic","authors":"Shovan Biswas, Sudhansu S. Maiti","doi":"10.1515/eqc-2021-0038","DOIUrl":"https://doi.org/10.1515/eqc-2021-0038","url":null,"abstract":"Abstract This article develops multiple dependent state (MDS) sampling inspection plans based on the mean of lifetime quality characteristic that follows non-normal distributions viz., exponential and Lindley distribution. In this plan, the lot quality is measured by the lot mean (𝜇). We have estimated the optimal plan parameters of the proposed technique by non-linear optimization approaches considering acceptable quality level and rejection quality level. We have compared the sample size between the MDS sampling inspection plan and the single sampling inspection plan for the variable. Finally, we have taken two examples to illustrate the proposed technique.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"1 1","pages":"85 - 99"},"PeriodicalIF":0.0,"publicationDate":"2022-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79928467","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}
Abstract We propose modeling COVID-19 infection dynamics using a class of two-type branching processes. These models require only observations on daily statistics to estimate the average number of secondary infections caused by a host and to predict the mean number of the non-observed infected individuals. The development of the epidemic process depends on the reproduction rate as well as on additional facets as immigration, adaptive immunity, and vaccination. Usually, in the existing deterministic and stochastic models, the officially reported and publicly available data are not sufficient for estimating model parameters. An important advantage of the proposed model, in addition to its simplicity, is the possibility of direct computation of its parameters estimates from the daily available data. We illustrate the proposed model and the corresponding data analysis with data from Bulgaria, however they are not limited to Bulgaria and can be applied to other countries subject to data availability.
{"title":"Branching Process Modelling of COVID-19 Pandemic Including Immunity and Vaccination","authors":"D. Atanasov, V. Stoimenova, N. Yanev","doi":"10.1515/eqc-2021-0040","DOIUrl":"https://doi.org/10.1515/eqc-2021-0040","url":null,"abstract":"Abstract We propose modeling COVID-19 infection dynamics using a class of two-type branching processes. These models require only observations on daily statistics to estimate the average number of secondary infections caused by a host and to predict the mean number of the non-observed infected individuals. The development of the epidemic process depends on the reproduction rate as well as on additional facets as immigration, adaptive immunity, and vaccination. Usually, in the existing deterministic and stochastic models, the officially reported and publicly available data are not sufficient for estimating model parameters. An important advantage of the proposed model, in addition to its simplicity, is the possibility of direct computation of its parameters estimates from the daily available data. We illustrate the proposed model and the corresponding data analysis with data from Bulgaria, however they are not limited to Bulgaria and can be applied to other countries subject to data availability.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"3 1","pages":"157 - 164"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80679963","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}
Abstract The stationary immigration has a limited effect over the asymptotic behavior of the underlying branching process. It affects mostly the limiting distribution and the life-period of the process. In contrast, if the immigration rate changes over time, then the asymptotic behavior of the process is significantly different and a variety of new phenomena are observed. In this review we discuss branching processes with time non-homogeneous immigration. Our goal is to help researchers interested in the topic to familiarize themselves with the current state of research.
{"title":"Homogeneous Branching Processes with Non-Homogeneous Immigration","authors":"I. Rahimov","doi":"10.1515/eqc-2021-0033","DOIUrl":"https://doi.org/10.1515/eqc-2021-0033","url":null,"abstract":"Abstract The stationary immigration has a limited effect over the asymptotic behavior of the underlying branching process. It affects mostly the limiting distribution and the life-period of the process. In contrast, if the immigration rate changes over time, then the asymptotic behavior of the process is significantly different and a variety of new phenomena are observed. In this review we discuss branching processes with time non-homogeneous immigration. Our goal is to help researchers interested in the topic to familiarize themselves with the current state of research.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"43 1","pages":"165 - 183"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90049690","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}
Abstract We consider a strongly supercritical branching process in random environment with immigration stopped at a distant time 𝑛. The offspring reproduction law in each generation is assumed to be geometric. The process is considered under the condition of its extinction after time 𝑛. Two limit theorems for this process are proved: the first one is for the time interval from 0 till 𝑛, and the second one is for the time interval from 𝑛 till + ∞ +infty .
{"title":"Limit Theorems for a Strongly Supercritical Branching Process with Immigration in Random Environment","authors":"V. Afanasyev","doi":"10.1515/eqc-2021-0036","DOIUrl":"https://doi.org/10.1515/eqc-2021-0036","url":null,"abstract":"Abstract We consider a strongly supercritical branching process in random environment with immigration stopped at a distant time 𝑛. The offspring reproduction law in each generation is assumed to be geometric. The process is considered under the condition of its extinction after time 𝑛. Two limit theorems for this process are proved: the first one is for the time interval from 0 till 𝑛, and the second one is for the time interval from 𝑛 till + ∞ +infty .","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"163 1","pages":"129 - 143"},"PeriodicalIF":0.0,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91300112","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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