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An Extension of the Geometric Distribution with Properties and Applications 几何分布的一个推广及其性质和应用
IF 0.6
Austrian Journal of Statistics Pub Date : 2023-07-18 DOI: 10.17713/ajs.v52i3.1487
S. Chakraborty, S. Ong, Aniket Biswas
{"title":"An Extension of the Geometric Distribution with Properties and Applications","authors":"S. Chakraborty, S. Ong, Aniket Biswas","doi":"10.17713/ajs.v52i3.1487","DOIUrl":"https://doi.org/10.17713/ajs.v52i3.1487","url":null,"abstract":"A new parameter is introduced to extend the geometric distribution using Azzalini's method. Several important structural properties of the proposed two-parameter extended geometric distribution are investigated. Characterizations including for the geometric distribution, in terms of the proposed model, are established. Maximum likelihood estimation, method of moment estimation and relative frequency based estimation of the parameters are discussed in detail. The likelihood ratio test regarding relevance of the additional parameter is presented. Bayesian estimation of the parameters using STAN is also discussed. The proposed model is compared with some recently introduced two-parameter count models by analyzing two real-life datasets. The findings clearly indicate superiority of the proposed model over the rest.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"13 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87483828","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}
引用次数: 0
Prof. Rudolf Dutter (1946-2023): Ein Nachruf Rudolf Dutter教授:讣文
IF 0.6
Austrian Journal of Statistics Pub Date : 2023-07-18 DOI: 10.17713/ajs.v52i3.1736
Peter Filzmoser, Matthias Templ
{"title":"Prof. Rudolf Dutter (1946-2023): Ein Nachruf","authors":"Peter Filzmoser, Matthias Templ","doi":"10.17713/ajs.v52i3.1736","DOIUrl":"https://doi.org/10.17713/ajs.v52i3.1736","url":null,"abstract":"Der ehemalige TU Wien Professor Rudolf Dutter verstarb am 5. Mai 2023 an den Folgen seiner langjährigen Diabetes-Erkrankung. Prof.~Dutter war von 1997 bis 2003 Redakteur der Österreichischen Zeitschrift für Statistik (Austrian Journal of Statistics), und diese Tätigkeit hat er mit viel Engagement im Sinne der Österreichischen Statistischen Gesellschaft geleistet. Eine seiner Aktivitäten war die Einrichtung und der Betrieb einer Website für die Zeitschrift, die einen \"Open Access\" Zugriff auf die Artikel ermöglichte. Ein kurzer Nachruf in dieser Zeitschrift, auch als Information für die Mitglieder der Gesellschaft, scheint daher mehr als passend zu sein.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"39 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79102600","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}
引用次数: 0
Bootstrap Based Diagnostics for Survival Regression Model with Interval and Right-Censored Data 区间和右截尾数据生存回归模型的自举诊断
IF 0.6
Austrian Journal of Statistics Pub Date : 2023-03-12 DOI: 10.17713/ajs.v52i2.1393
J. Arasan, H. Midi
{"title":"Bootstrap Based Diagnostics for Survival Regression Model with Interval and Right-Censored Data","authors":"J. Arasan, H. Midi","doi":"10.17713/ajs.v52i2.1393","DOIUrl":"https://doi.org/10.17713/ajs.v52i2.1393","url":null,"abstract":"This research proposes a new approach based on the bias-corrected bootstrap harmonic mean and random imputation technique to obtain the adjusted residuals (Hboot) when a survival model is fit to right- and interval-censored data with covariates. Following that, the model adequacy and influence diagnostics based on these adjusted residuals, case deletion diagnostics, and the normal curvature are discussed. Simulation studies were conducted to assess the performance of the parameter estimate and compare the performances of the traditional Cox-Snell (CS), modified Cox-Snell (MCS) and Hboot at various censoring proportions (cp) and samples sizes ($n$) using the log-logistic and extreme minimum value regression models with right- and interval-censored data. The results clearly indicated that Hboot outperformed other residuals at all levels of cp and $n$, for both models. The proposed methods are then illustrated using real data set from the COM breast cancer data. The results indicate that the proposed methods work well to address model adequacy and identify potentially influential observations in the data set.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"77 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86233216","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}
引用次数: 0
A Flexible Probability Model for Proportion Data: Unit Gumbel Type-II Distribution, Development, Properties, Different Method of Estimations and Applications 比例数据的灵活概率模型:单位甘贝尔ii型分布，发展，性质，不同的估计方法和应用
IF 0.6
Austrian Journal of Statistics Pub Date : 2023-03-12 DOI: 10.17713/ajs.v52i2.1407
Anum Shafiq, T. Sindhu, Z. Hussain, J. Mazucheli, Bruna Alves
{"title":"A Flexible Probability Model for Proportion Data: Unit Gumbel Type-II Distribution, Development, Properties, Different Method of Estimations and Applications","authors":"Anum Shafiq, T. Sindhu, Z. Hussain, J. Mazucheli, Bruna Alves","doi":"10.17713/ajs.v52i2.1407","DOIUrl":"https://doi.org/10.17713/ajs.v52i2.1407","url":null,"abstract":"In explaining and forecasting real life scenarios, statistical distributions are very helpful. It is very important to select the best fitting statistical distribution for modelling data. In analysis of real world phenomena like in reliability and economics, we may finddistributions for bounded data observed as percentages, proportions or fractions (see, for example, Marshall and Olkin (2007)). In this context, in view of pertinent transformation on the Gumbel Type-II model, we suggest and study the unit Gumbel Type-II (UG-TII)model and explore few of its statistical characteristics. We also consider various methods of estimating the unknown parameters of UG-TII model from the frequentist perspective. Monte Carlo simulations are worked out in order to compare efficiency of suggestedestimation methods for small as well as large samples. The efficiency of estimators is measured using simulated samples in terms of their bias and mean square error. In the end, two datasets have been examined in attempt to validate the realistic possibilities ofnew model. In comparison to the six severe competitors.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"50 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79263401","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}
引用次数: 1
Properties and Applications of the Type I Half-logistic Nadarajah-Haghighi Distribution I型半物流Nadarajah-Haghighi分布的性质及应用
IF 0.6
Austrian Journal of Statistics Pub Date : 2023-03-12 DOI: 10.17713/ajs.v52i2.1363
M. Shrahili, Mustapha Muhammad, I. Elbatal, Isyaku Muhammad, Mouna Bouchane, B. Abba
{"title":"Properties and Applications of the Type I Half-logistic Nadarajah-Haghighi Distribution","authors":"M. Shrahili, Mustapha Muhammad, I. Elbatal, Isyaku Muhammad, Mouna Bouchane, B. Abba","doi":"10.17713/ajs.v52i2.1363","DOIUrl":"https://doi.org/10.17713/ajs.v52i2.1363","url":null,"abstract":"A new three-parameter distribution called the type I half-logistic Nadarajah-Haghighi (T IHL N H ) is proposed. We discussed some important mathematical and statistical properties of the new model such as an explicit form of its r th moment, mean deviations,quantile function, Bonferroni and Lorenz curves. The Shannon entropy and Renyi entropy are computed, the expression for the Kullback-Leibler divergence measure is provided. The model parameters estimation was approached by the maximum likelihoodestimation (MLE), and the information matrix is obtained. The finite sample properties of the MLEs are investigated numerically by simulation studies; by examining the bias and mean square error of the estimators, and the results was satisfactory. We used tworeal data applications to demonstrate the superior performance of the T IHL N H in terms of fit over some other existing lifetime models.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"31 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78081797","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}
引用次数: 3
Maximum Product Spacings Estimator for Fuzzy Data Using Inverse Lindley Distribution 基于逆Lindley分布的模糊数据最大积间距估计
IF 0.6
Austrian Journal of Statistics Pub Date : 2023-03-12 DOI: 10.17713/ajs.v52i2.1395
Ankita Chaturvedi, Dr. Sanjay Kumar Singh, Dr. Umesh Singh
{"title":"Maximum Product Spacings Estimator for Fuzzy Data Using Inverse Lindley Distribution","authors":"Ankita Chaturvedi, Dr. Sanjay Kumar Singh, Dr. Umesh Singh","doi":"10.17713/ajs.v52i2.1395","DOIUrl":"https://doi.org/10.17713/ajs.v52i2.1395","url":null,"abstract":"The article addresses the problem of parameter estimation of the inverse Lindley distribution when the observations are fuzzy. The estimation of the unknown model parameter was performed using both classical and Bayesian methods. In the classical approach, the estimation of the population parameter is performed using the maximum likelihood (ML) method and the maximum product of distances (MPS) method. In the Bayesian setup, the estimation is obtained using the squared error loss function (SELF) with the Markov Chain Monte Carlo (MCMC) technique. Asymptotic confidence intervals and highest posterior density (HPD) credible intervals for the unknown parameter are also obtained. The performances of the estimators are compared based on their MSEs. Finally, a real data set is analyzed for numerical illustration of the above estimation methods.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"18 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82277277","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}
引用次数: 2
High-order Coverage of Smoothed Bayesian Bootstrap Intervals for Population Quantiles 总体分位数平滑贝叶斯Bootstrap区间的高阶覆盖
IF 0.6
Austrian Journal of Statistics Pub Date : 2023-03-12 DOI: 10.17713/ajs.v52i2.1385
David M. Kaplan, Lonnie Hofmann
{"title":"High-order Coverage of Smoothed Bayesian Bootstrap Intervals for Population Quantiles","authors":"David M. Kaplan, Lonnie Hofmann","doi":"10.17713/ajs.v52i2.1385","DOIUrl":"https://doi.org/10.17713/ajs.v52i2.1385","url":null,"abstract":"We characterize the high-order coverage accuracy of smoothed and unsmoothed Bayesian bootstrap confidence intervals for population quantiles. Although the original (Rubin 1981) unsmoothed intervals have the same O(n−1/2) coverage error as the standard empirical bootstrap, the smoothed Bayesian bootstrap of Banks (1988) has much smaller O(n−3/2[log(n)]3) coverage error and is exact in special cases, without requiring any smoothing parameter. It automatically removes an error term of order 1/n that other approaches need to explicitly correct for. This motivates further study of the smoothed Bayesian bootstrap in more complex settings and models.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"25 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82991136","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}
引用次数: 0
On Fixed-Accuracy Confidence Intervals for the Parameters of Lindley Distribution and Its Extensions 林德利分布参数的定精度置信区间及其扩展
IF 0.6
Austrian Journal of Statistics Pub Date : 2023-03-12 DOI: 10.17713/ajs.v52i2.1406
Sudeep R. Bapat, Neeraj Joshi, Ashish Shukla
{"title":"On Fixed-Accuracy Confidence Intervals for the Parameters of Lindley Distribution and Its Extensions","authors":"Sudeep R. Bapat, Neeraj Joshi, Ashish Shukla","doi":"10.17713/ajs.v52i2.1406","DOIUrl":"https://doi.org/10.17713/ajs.v52i2.1406","url":null,"abstract":"The purpose of the present paper is to deal with sequential estimation of the parameter θ in a Lindley distribution. A fixed-accuracy confidence interval for θ with a preassigned confidence coefficient is developed. It is established that, no fixed sample size procedure can solve the estimation problem and hence a purely sequential methodology is proposed to deal with the situation. The first-order asymptotic efficiency and consistency properties associated with our purely sequential strategy are derived. Similar estimation strategies are also outlined for a few other extensions of the Lindley distribution. Extensive simulation analysis is carried out to validate the theoretical findings. We also provide a real data example, where we estimate the parameter related to the “initial mass function\" for a particular cluster of stars.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"60 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75940872","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}
引用次数: 0
A New Poisson Generalized Lindley Regression Model 一种新的Poisson广义Lindley回归模型
IF 0.6
Austrian Journal of Statistics Pub Date : 2023-03-07 DOI: 10.17713/ajs.v52i1.1344
Yupapin Atikankul
{"title":"A New Poisson Generalized Lindley Regression Model","authors":"Yupapin Atikankul","doi":"10.17713/ajs.v52i1.1344","DOIUrl":"https://doi.org/10.17713/ajs.v52i1.1344","url":null,"abstract":"In this paper, a new count distribution is introduced. It is a mixture of the Poisson and generalized Lindley distributions. Statistical properties of the proposed distribution including the factorial moments, probability generating function, moment generating function and moments are studies. Maximum likelihood estimators of unknown parameters are derived. Moreover, an alternative count regression model based on the proposed distribution is presented. Finally, the proposed model is applied for real data and compared with other well-known models.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"22 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79025633","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}
引用次数: 0
Anti-Sum-Asymmetry Models and Orthogonal Decomposition of Anti-Sum-Symmetry Model for Ordinal Square Contingency Tables 序方列联表的反和不对称模型及反和对称模型的正交分解
IF 0.6
Austrian Journal of Statistics Pub Date : 2023-03-07 DOI: 10.17713/ajs.v52i1.1390
S. Ando
{"title":"Anti-Sum-Asymmetry Models and Orthogonal Decomposition of Anti-Sum-Symmetry Model for Ordinal Square Contingency Tables","authors":"S. Ando","doi":"10.17713/ajs.v52i1.1390","DOIUrl":"https://doi.org/10.17713/ajs.v52i1.1390","url":null,"abstract":"For the analysis of C × C square contingency tables, we usually estimate using a statistical model an unknown probability distribution with high confidence from obtained observations. The statistical model that fits the data well and is easy to interpret is preferred. The anti-sum-symmetry (ASS) and anti-conditional sum-symmetry (ACSS) models have a structure that the ratio of the probability with which the sum of row and column levels is t, for t = 2, . . . , C, and the probability with which the sum of row and column levels is 2(C + 1) − t is always one and constant, respectively. This study proposes two kinds of models that the ratio of those changes exponentially depending on the sum of row and column levels. This study also gives the decomposition theorems of the ASS model using the proposed models. Moreover, we show that the value of the likelihood ratio chi-squared statistics for the ASS model is asymptotically equivalent to the sum of those for the decomposed models. We evaluate the advantage of the proposed models by applying they to a single data set of real-world grip strength data.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"76 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75996104","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}
引用次数: 0
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