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Statistical Properties and Applications of the Exponentiated Chen-G Family of Distributions: Exponential Distribution as a Baseline Distribution 指数陈- g族分布的统计性质及应用:指数分布作为基线分布
IF 0.6
Austrian Journal of Statistics Pub Date : 2022-01-25 DOI: 10.17713/ajs.v51i2.1245
P. Awodutire
{"title":"Statistical Properties and Applications of the Exponentiated Chen-G Family of Distributions: Exponential Distribution as a Baseline Distribution","authors":"P. Awodutire","doi":"10.17713/ajs.v51i2.1245","DOIUrl":"https://doi.org/10.17713/ajs.v51i2.1245","url":null,"abstract":"In this work, the Exponentiated Chen-G family of distributions is studied by generalizing the Chen-G family of distributions through the introduction of an additional shape parameter. The mixture properties of the derived family are studied. Some statistical properties of the family were considered, including moments, entropies, moment generating function, order statistics, quantile function. The estimation of the parameters of the family of distributions was done using the maximum likelihood estimation method, considering complete and censored situations. Using the Exponential distribution as a baseline, the Exponentiated Chen Exponential distribution was obtained and its statistical properties were studied. The Exponentiated Chen Exponential distribution has the Exponentiated Exponential, Exponential, Chen Exponential distributions as submodels. Lastly, the Exponentiated Chen Exponential distribution was applied to two real data sets and the results were compared with its submodels and relative distributions.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89240769","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
A Comparative Study of Goodness-of-Fit Tests for the Laplace Distribution 拉普拉斯分布拟合优度检验的比较研究
IF 0.6
Austrian Journal of Statistics Pub Date : 2022-01-25 DOI: 10.17713/ajs.v51i2.1251
A. Batsidis, P. Economou, S. Bar-Lev
{"title":"A Comparative Study of Goodness-of-Fit Tests for the Laplace Distribution","authors":"A. Batsidis, P. Economou, S. Bar-Lev","doi":"10.17713/ajs.v51i2.1251","DOIUrl":"https://doi.org/10.17713/ajs.v51i2.1251","url":null,"abstract":"The Laplace distribution is one of the earliest distributions in probability theory and is a frequently used distribution in many fields. Consequently, various goodness-of-fit tests for the Laplace distribution have been thoroughly derived in theliterature. The purpose of this paper is to carry out a comparative study of these tests as well as a new one we develop. Power comparisons of all such tests are performed via Monte Carlo simulations of sample data generatedfrom twenty seven alternatives distributions. Despite the fact that no single test was found to be most powerful in all situations, several useful recommendations however are made.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"39 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79194064","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
A Hill Climbing Algorithm for Maximum Likelihood Estimation of the Gamma Distributed-lag Model with Multiple Explanatory Variables 多解释变量分布滞后模型的最大似然估计爬坡算法
IF 0.6
Austrian Journal of Statistics Pub Date : 2022-01-25 DOI: 10.17713/ajs.v51i2.1244
Alessandro Magrini
{"title":"A Hill Climbing Algorithm for Maximum Likelihood Estimation of the Gamma Distributed-lag Model with Multiple Explanatory Variables","authors":"Alessandro Magrini","doi":"10.17713/ajs.v51i2.1244","DOIUrl":"https://doi.org/10.17713/ajs.v51i2.1244","url":null,"abstract":"Linear regression with distributed-lags is a consolidated methodology in time series analysis to assess the impact of several explanatory variables on an outcome that may persist over several periods.Finite polynomial distributed-lags have a long tradition due to a good flexibility accompanied by the advantage of a linear representation, which allows parameter estimation through Ordinary Least Squares (OLS).However, they require to specify polynomial degree and lag length, and entail the loss of some initial observations.Gamma distributed-lags overcome these problems and represents a good compromise between flexibility and number of parameters, however they have not a linear representation in the parameters and currently available estimation methods, like OLS-based grid search and non-linear least squares, are unsatisfactory in the case of multiple explanatory variables.For these reasons, the Gamma lag distribution has not been able to replace finite polynomial lags in applied time series analysis, and it has been mostly employed in the case of a single explanatory variable.In this paper, we propose a hill climbing algorithm for maximum likelihood estimation of multiple linear regression with Gamma distributed-lags.The proposed algorithm is applied to assess the dynamic relationship between Bitcoin's price and three composite indices of the US stock market.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"14 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81939367","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
Harmonic Mixture-G Family of Distributions: Survival Regression, Simulation by Likelihood, Bootstrap and Bayesian Discussion with MCMC Algorithm 调和混合- g族分布:生存回归、似然模拟、Bootstrap和贝叶斯与MCMC算法的讨论
IF 0.6
Austrian Journal of Statistics Pub Date : 2022-01-25 DOI: 10.17713/ajs.v51i2.1225
O. Kharazmi, A. S. Nik, G. Hamedani, E. Altun
{"title":"Harmonic Mixture-G Family of Distributions: Survival Regression, Simulation by Likelihood, Bootstrap and Bayesian Discussion with MCMC Algorithm","authors":"O. Kharazmi, A. S. Nik, G. Hamedani, E. Altun","doi":"10.17713/ajs.v51i2.1225","DOIUrl":"https://doi.org/10.17713/ajs.v51i2.1225","url":null,"abstract":"To study the heterogeneous nature of lifetimes of certain mechanical or engineering processes, a mixture model of some suitable lifetime distributions may be more appropriate and appealing than simpler models. In this paper, a new mixture family of the lifetime distributions is introduced via harmonic weighted mean of an underlying distribution and the distribution of the proportional hazard model corresponding to the baseline model.The proposed class of distributions includes the general Marshall-Olkin family of distributions as a special case. Some important properties of the proposed model such as survival function, hazard function, order statistics and some results on stochastic ordering are obtained in a general setting. A special case of this new family is considered by employingWeibull distribution as the parent distribution. We derive several properties of the special distribution such as moments,hazard function survival regression and certain characterizations results. Moreover, we estimate the parameters of the model by using frequentist and Bayesian approaches. For Bayesian analysis, five loss functions, namely the squared error loss function (SELF), weighted squared error loss function (WSELF), modified squared error loss function (MSELF), precautionary loss function (PLF), and K-loss function (KLF) are considered. The beta prior as well as the gamma prior are used to obtain the Bayes estimators and posterior risk of the unknown parameters of the model. Furthermore, credible intervals (CIs) and highest posterior density (HPD) intervals are also obtained. A simulation study is presented via Monte Carlo to investigate the bias and mean square error of the maximum likelihood estimators. For illustrative purposes, two real-life applications of the proposed distribution to  Kidney and cancer patients are provided.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"90 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88518328","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: 4
Applications of HLMOL-X Family of Distributions to Time Series, Acceptance Sampling and Stress-strength Parameter HLMOL-X族分布在时间序列、验收抽样和应力-强度参数中的应用
IF 0.6
Austrian Journal of Statistics Pub Date : 2022-01-25 DOI: 10.17713/ajs.v51i2.1253
Lishamol Tomy, Meenu Jose
{"title":"Applications of HLMOL-X Family of Distributions to Time Series, Acceptance Sampling and Stress-strength Parameter","authors":"Lishamol Tomy, Meenu Jose","doi":"10.17713/ajs.v51i2.1253","DOIUrl":"https://doi.org/10.17713/ajs.v51i2.1253","url":null,"abstract":"In this paper, the applications of the half logistic-Marshall Olkin X family of distributions are investigated with special emphasis to the half logistic-Marshall Olkin Lomax distribution. The specific areas we concentrated are time series modeling, acceptance sampling plan and stress-strength analysis. Different autoregressive minification structures of order one are introduced. The acceptance sampling plan is detailed by considering life time of products following the half logistic-Marshall Olkin Lomax distribution. The stress-strength reliability of the half logistic-Marshall Olkin Lomax distribution is derived and estimated. A simulation study is carried out to examine the bias, mean square error, average confidence length and coverage probability of the maximum likelihood estimator of thestress-strength reliability. Finally a real-life data analysis has also been presented.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"12 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82910429","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
Zero-inflated Modified Borel-Tanner Regression Model for Count Data 计数数据的零膨胀修正Borel-Tanner回归模型
IF 0.6
Austrian Journal of Statistics Pub Date : 2022-01-25 DOI: 10.17713/ajs.v51i2.1227
Anwar Hassan, Ishfaq S. Ahmad, Peer Bilal Ahmad
{"title":"Zero-inflated Modified Borel-Tanner Regression Model for Count Data","authors":"Anwar Hassan, Ishfaq S. Ahmad, Peer Bilal Ahmad","doi":"10.17713/ajs.v51i2.1227","DOIUrl":"https://doi.org/10.17713/ajs.v51i2.1227","url":null,"abstract":"By starting from the one-parameter Modified Borel-Tanner distribution proposed recently in the statistic literature, we introduce the zero-inflated Modified Borel-Tanner distribution. Additionally, on the basis of the proposed zero-inflated distribution, a novel zero-inflated regression model is proposed, which is quite simple and may be an interesting alternative to usual zero-inflated regression models for count data. The parameters of the proposed model are estimated by Maximum Likelihood Estimation technique. To check the potentiality of the zero inflated Modified Borel-Tanner regression, an application to the count of infected blood cells is taken. The results suggest that the new zero inflated Modified Borel-Tanner regression is more appropriate to model these count data than other familiar zero-inflated (or not) regression models commonly used in practice.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"29 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85003543","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
Asymmetry Model Using Marginal Ridits for Ordinal Square Contingency Tables 序方列联表的边缘不对称模型
IF 0.6
Austrian Journal of Statistics Pub Date : 2022-01-24 DOI: 10.17713/ajs.v51i1.1210
S. Ando
{"title":"Asymmetry Model Using Marginal Ridits for Ordinal Square Contingency Tables","authors":"S. Ando","doi":"10.17713/ajs.v51i1.1210","DOIUrl":"https://doi.org/10.17713/ajs.v51i1.1210","url":null,"abstract":"This study proposes a new marginal asymmetry model which can infer the relation between marginal ridits of row and column variables for ordinal square contingency tables. When the marginal homogeneity model does not hold, we will apply marginal asymmetry models (e.g., the marginal cumulative logistic and extended marginal homogeneity models). On the other hand, we may measure the degree of departure from the marginal homogeneity model. To measure the degree of that, multiple indexes were proposed. Some of them correspond to the marginal cumulative logistic and extended marginal homogeneity models. The proposed model corresponds to the index, which represents the degree of departure from the MH model, using marginal ridits. We compare the proposed model with the existing marginal asymmetry models and show that the proposed model provides better fit performance than them for real data.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"127 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75812719","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
Bayes Prediction on Optimum SS-PALT in Generalized Inverted Exponential Distribution: A Two-Sample Approach 广义倒指数分布中最优SS-PALT的贝叶斯预测:双样本方法
IF 0.6
Austrian Journal of Statistics Pub Date : 2022-01-24 DOI: 10.17713/ajs.v51i1.1003
G. Prakash
{"title":"Bayes Prediction on Optimum SS-PALT in Generalized Inverted Exponential Distribution: A Two-Sample Approach","authors":"G. Prakash","doi":"10.17713/ajs.v51i1.1003","DOIUrl":"https://doi.org/10.17713/ajs.v51i1.1003","url":null,"abstract":"The generalized Inverted Exponential distribution is considered for the study on Optimum Step Stress Partially Accelerated Life Test (SS-PALT) based on different censoring patterns. The first-failure progressive censoring (FFPC) scheme and their special cases are used in the present study. A two-sample Bayes Prediction Bound Length (TS-BPBL) under SS-PALT on FFPC have been obtained and studied their properties by using different special cases of FFPC. Based on simulated and real data set, the properties of the ML estimates and the approximate confidence length under the normal approximation, also have been studied.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"18 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79829486","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
Test for Linearity in Non-Parametric Regression Models 非参数回归模型的线性检验
IF 0.6
Austrian Journal of Statistics Pub Date : 2022-01-24 DOI: 10.17713/ajs.v51i1.1047
Khedidja Djaballah-Djeddour, Moussa Tazerouti
{"title":"Test for Linearity in Non-Parametric Regression Models","authors":"Khedidja Djaballah-Djeddour, Moussa Tazerouti","doi":"10.17713/ajs.v51i1.1047","DOIUrl":"https://doi.org/10.17713/ajs.v51i1.1047","url":null,"abstract":"The problem of checking the linearity of a regression relationship is addressed. The test uses nonparametric estimation techniques. The null hypothesis is that the regression function is linear; it is tested against the non-specic alternatives hypotheses. This test is based on a Hermite transform characterization of conditional expectations. A statistical test is derived, the distribution of this statisticunder the null hypothesis of linearity is determined. A power study using simulation shows the new statistic to be more sensitive to non-linearity.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"54 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90324250","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 Retrospective Study on Skellam and Related Distributions 骨裂体及其相关分布的回顾性研究
IF 0.6
Austrian Journal of Statistics Pub Date : 2022-01-24 DOI: 10.17713/ajs.v51i1.1224
Lishamol Tomy, Veena G
{"title":"A Retrospective Study on Skellam and Related Distributions","authors":"Lishamol Tomy, Veena G","doi":"10.17713/ajs.v51i1.1224","DOIUrl":"https://doi.org/10.17713/ajs.v51i1.1224","url":null,"abstract":"This paper reviews works on Skellam distribution, its extensions and areas of applications. Available literature shows that this distribution is flexible for modelling integer data where they appear as count data or paired count data in the field of finance, medicine, sports, and science. Bivariate Skellam distribution, dynamic Skellam model and other extensions are also discussed and additional literature are provided.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"161 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77625028","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
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