Journal of Probability and Statistics最新文献

{"title":"D-Optimal Design for a Causal Structure for Completely Randomized and Random Blocked Experiments","authors":"Zaher Kmail, K. Eskridge","doi":"10.1155/2022/7299086","DOIUrl":"https://doi.org/10.1155/2022/7299086","url":null,"abstract":"Most experimental design literature on causal inference focuses on establishing a causal relationship between variables, but there is no literature on how to identify a design that results in the optimal parameter estimates for a structural equation model (SEM). In this research, search algorithms are used to produce a D-optimal design for a SEM for three-stage least squares and full information maximum likelihood estimators. Then, a D-optimal design for the estimate of the model parameters of a mixed-effects SEM is obtained. The efficiency of each of the D-optimal designs for SEMs is compared with univariate optimal and uniform designs. In each case, the causal relationship changed the optimal designs dramatically and the new D-optimal designs were more efficient.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42005429","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":"On Hierarchical Bayesian Spatial Small Area Model for Binary Data under Spatial Misalignment","authors":"Kindie Fentahun Muchie, A. Wanjoya, S. Mwalili","doi":"10.1155/2022/3865626","DOIUrl":"https://doi.org/10.1155/2022/3865626","url":null,"abstract":"Small area models have become popular methods for producing reliable estimates for sub-populations (small geographic areas in this study). Small area modeling may be carried out via model-assisted approaches within the model-based approaches or design-based paradigm. When there are medium or large samples, a model-assisted approach may be reliable. However, when data are scarce, a model-based technique may be required. Model-based Bayesian analysis is popular for its ability to combine information from several sources as well as taking account uncertainties in the analysis and spatial prediction of spatial data. Nevertheless, things become more complex when the geographic boundaries of interest are misaligned. Some authors have addressed the problem of misalignment under hierarchical Bayesian approach. In this study, we developed non-trivial extension of existing hierarchical Bayesian model for a binary outcome variable under spatial misalignment with three contributions. First, the model uses unit-level survey data and area-level auxiliary data to predict the posterior mean proportion spatially at the second geographic area level. Second, the linking model is changed to logit-normal model in the proposed model. Lastly, the mean process was considered to overcome the multicollinearity between the true predictors and the spatial random effect. Sensitivity analysis was also done via simulation.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47651594","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":"Nonstationary Generalised Autoregressive Conditional Heteroskedasticity Modelling for Fitting Higher Order Moments of Financial Series within Moving Time Windows","authors":"Luke De Clerk, Sergey Savel’ev","doi":"10.1155/2022/4170866","DOIUrl":"https://doi.org/10.1155/2022/4170866","url":null,"abstract":"Here, we present a method for a simple GARCH (1,1) model to fit higher order moments for different companies’ stock prices. When we assume a Gaussian conditional distribution, we fail to capture any empirical data when fitting the first three even moments of financial time series. We show instead that a mixture of normal distributions is needed to better capture the higher order moments of the data. To demonstrate this point, we construct regions (parameter diagrams), in the fourth- and sixth-order standardised moment space, where a GARCH (1,1) model can be used to fit moment values and compare them with the corresponding moments from empirical data for different sectors of the economy. We found that the ability of the GARCH model with a double normal conditional distribution to fit higher order moments is dictated by the time window our data spans. We can only fit data collected within specific time window lengths and only with certain parameters of the conditional double Gaussian distribution. In order to incorporate the nonstationarity of financial series, we assume that the parameters of the GARCH model can have time dependence. Furthermore, using the method developed here, we investigate the effect of the COVID-19 pandemic has upon stock’s stability and how this compares with the 2008 financial crash.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48217396","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":"Mean Estimation of a Sensitive Variable under Nonresponse Using Three-Stage RRT Model in Stratified Two-Phase Sampling","authors":"Rodney Onyango, Brian Oduor, F. Odundo","doi":"10.1155/2022/4530120","DOIUrl":"https://doi.org/10.1155/2022/4530120","url":null,"abstract":"The present study addresses the problems of mean estimation and nonresponse under the three-stage RRT model. Auxiliary information on an attribute and variable is used to propose a generalized class of exponential ratio-type estimators. Expressions for the bias, mean squared error, and minimum mean squared error for the proposed estimator are derived up to the first degree of approximation. The efficiency of the proposed estimator is studied theoretically and numerically using two real datasets. From the numerical analysis, the proposed generalized class of exponential ratio-type estimators outperforms ordinary mean estimators, usual ratio estimators, and exponential ratio-type estimators. Furthermore, the efficiencies of the mean estimators are observed to decrease with an increase in the sensitivity level of the survey question. As the inverse sampling rate and nonresponse rate go up, so does the efficiency of the mean estimators, which makes them more accurate.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46260515","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":"Gompertz Ampadu Class of Distributions: Properties and Applications","authors":"A. Alhassan","doi":"10.1155/2022/1104330","DOIUrl":"https://doi.org/10.1155/2022/1104330","url":null,"abstract":"This paper introduces a new generator family of distributions called the Gompertz Ampadu-G family. Based on the generator, the Lomax distribution was modified into Gompertz Ampadu Lomax. The new distribution has a flexible hazard rate function that has upside-down and bathtub shapes, including increasing and decreasing hazard rate functions. The distribution comes with some desirable statistical properties. The distribution is applied to real-life data. Parameter estimates and test statistics show a better fit for the competitive models.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41837596","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":"Tweedie Model for Predicting Factors Associated with Distance Traveled to Access Inpatient Services in Kenya","authors":"Ngugi Mwenda, M. Kosgei, G. Kerich, R. Nduati","doi":"10.1155/2022/2706504","DOIUrl":"https://doi.org/10.1155/2022/2706504","url":null,"abstract":"Aim. This study aims to examine which factors influence the distance traveled by patients for inpatient care in Kenya. Methods. We used data from the fourth round of the Kenya Household Health Expenditure and Utilization survey. Our dependent variable was the self-reported distance traveled by patients to access inpatient care at public health facilities. As the clustered data were correlated, we used the generalized estimating equations approach with an exchangeable correlation under a Tweedie distribution. To select the best-fit covariates for predicting distance, we adopted a variable selection technique using the \u0000 \u0000 Q\u0000 I\u0000 \u0000 \u0000 C\u0000 \u0000 \u0000 u\u0000 \u0000 \u0000 \u0000 and \u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 2\u0000 \u0000 \u0000 \u0000 criteria, wherein the lowest (highest) value for the former (latter) is preferred. Results. Using data for 451 participants from 47 counties, we found that three-fifths were admitted between 1 and 5 days, two-thirds resided in rural areas, and 90% were satisfied with the facilities’ service. Wealth quintiles were evenly distributed across respondents. Most admissions (81%) comprised \u0000 \u0000 <\u0000 \u0000 15, \u0000 \u0000 >\u0000 \u0000 65, and 25–54 years. Many households were of medium size (4–6 members) and had low education level (48%), and nine-tenths had no access to insurance. While two-thirds reported employment-based income, the same number reported not having cash to pay for inpatient services; 6 out of 10 paid over 3000 KES. Thus, differences in employment, ability to pay, and household size influence the distance traveled to access government healthcare facilities in Kenya. Interpretation. Low-income individuals more likely have large households and live in rural areas and, thus, are forced to travel farther to access inpatient care. Unlike the unemployed, the employed may have better socioeconomic status and possibly live near inpatient healthcare facilities, thereby explaining their short distances to access these services. Policymakers must support equal access to inpatient services, prioritize rural areas, open job opportunities, and encourage smaller families.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45199139","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":"A Mixture of Clayton, Gumbel, and Frank Copulas: A Complete Dependence Model","authors":"M. A. Boateng, A. Y. Omari-Sasu, R. Avuglah, N. K. Frempong","doi":"10.1155/2022/1422394","DOIUrl":"https://doi.org/10.1155/2022/1422394","url":null,"abstract":"Knowledge of the dependence between random variables is necessary in the area of risk assessment and evaluation. Some of the existing Archimedean copulas, namely the Clayton and the Gumbel copulas, allow for higher correlations on the extreme left and right, respectively. In this study, we use the idea of convex combinations to build a hybrid Clayton–Gumbel–Frank copula that provides all dependence scenarios from existing Archimedean copulas. The corresponding density and conditional distribution functions of the derived models for two random variables, as well as an estimator for the proportion parameter associated with the proposed model, are also derived. The results show that the proposed model is able to show any case of dependence by providing coefficients for the upper tail and lower tail dependence.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64771533","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":"Trend Analysis of Temperature and Rainfall of Rajasthan, India","authors":"S. Sharma, D. Sharma, M. K. Sharma, K. Gaur, Pratibha Manohar","doi":"10.1155/2021/6296709","DOIUrl":"https://doi.org/10.1155/2021/6296709","url":null,"abstract":"Increasing temperature and declining and erratic rainfall is one of the greatest global challenges. This study presents the trend analysis of temperature and rainfall in five divisional headquarters of Rajasthan, namely, Bikaner, Jaipur, Jodhpur, Kota, and Udaipur. The historic data of minimum and maximum temperature and rainfall for a period of 49 years from 1971 to 2019 were collected from Climate Research and Services, India Meteorological Department, Pune. Detection of trends and change in magnitude was done using the Mann–Kendall (MK) test and Sen’s slope, respectively. The results of the study indicated a significant increase in both minimum and maximum temperature over time for all the five stations. However, rainfall showed a nonsignificant increasing trend for Kota and Udaipur district, whereas Bikaner, Jaipur, and Jodhpur detected a negative trend.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42164374","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":"Reliability Estimation for the Remained Stress-Strength Model under the Generalized Exponential Lifetime Distribution","authors":"M. M. Saber, Marwa M. Mohie El-Din, H. Yousof","doi":"10.1155/2021/7363449","DOIUrl":"https://doi.org/10.1155/2021/7363449","url":null,"abstract":"A stress-strength reliability model compares the strength and stresses on a certain system; it is used not only primarily in reliability engineering and quality control but also in economics, psychology, and medicine. In this paper, a novel extension of stress-strength models is presented. The mew model is applied under the generalized exponential distribution. The maximum likelihood estimator, asymptotic distribution, and Bayesian estimation are obtained. A comprehensive simulation study along with real data analysis is performed for illustrating the importance of the new stress-strength model.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49454774","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":"Explicit Solutions of the Extended Skorokhod Problems in Affine Transformations of Time-Dependent Strata","authors":"M. Slaby","doi":"10.1155/2021/9992546","DOIUrl":"https://doi.org/10.1155/2021/9992546","url":null,"abstract":"The goal of this paper is to expand the explicit formula for the solutions of the Extended Skorokhod Problem developed earlier for a special class of constraining domains in \u0000 \u0000 \u0000 \u0000 ℝ\u0000 \u0000 \u0000 n\u0000 \u0000 \u0000 \u0000 with orthogonal reflection fields. We examine how affine transformations convert solutions of the Extended Skorokhod Problem into solutions of the new problem for the transformed constraining system. We obtain an explicit formula for the solutions of the Extended Skorokhod Problem for any \u0000 \u0000 \u0000 \u0000 ℝ\u0000 \u0000 \u0000 n\u0000 \u0000 \u0000 \u0000 - valued càdlàg function with the constraining set that changes in time and the reflection field naturally defined by any basis. The evolving constraining set is a region sandwiched between two graphs in the coordinate system generating the reflection field. We discuss the Lipschitz properties of the extended Skorokhod map and derive Lipschitz constants in special cases of constraining sets of this type.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42763211","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}