Pub Date : 2017-10-24DOI: 10.6092/ISSN.1973-2201/7300
R. Sabre
Consider a symmetric α stable process having a spectral representation with an additive constant error. An estimator of that error and its rate of convergence are given. We study the rate of convergence when the spectral density have some behaviors at origin. Few long memory processes are taken here as example.
{"title":"Estimation of Additive Error in Mixed Spectra for Stable Processes","authors":"R. Sabre","doi":"10.6092/ISSN.1973-2201/7300","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/7300","url":null,"abstract":"Consider a symmetric α stable process having a spectral representation with an additive constant error. An estimator of that error and its rate of convergence are given. We study the rate of convergence when the spectral density have some behaviors at origin. Few long memory processes are taken here as example.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"77 1","pages":"75-90"},"PeriodicalIF":1.9,"publicationDate":"2017-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45987213","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}
Pub Date : 2017-10-24DOI: 10.6092/ISSN.1973-2201/6688
S. Kayal, S. S. Madhavan, R. Ganapathy
Generalized information measures play an important role in the measurement of uncertainty of certain random variables, where the standard practice of applying ordinary uncertainty measures fails to fit. Based on the Renyi entropy and its divergence, we propose a generalized measure of inaccuracy of order α(≠1)>0 between two residual and past lifetime distributions of a system. We study some important properties and characterizations of these measures. A numerical example is given to illustrate the usefulness of the proposed measure.
{"title":"On Dynamic Generalized Measures of Inaccuracy","authors":"S. Kayal, S. S. Madhavan, R. Ganapathy","doi":"10.6092/ISSN.1973-2201/6688","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6688","url":null,"abstract":"Generalized information measures play an important role in the measurement of uncertainty of certain random variables, where the standard practice of applying ordinary uncertainty measures fails to fit. Based on the Renyi entropy and its divergence, we propose a generalized measure of inaccuracy of order α(≠1)>0 between two residual and past lifetime distributions of a system. We study some important properties and characterizations of these measures. A numerical example is given to illustrate the usefulness of the proposed measure.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"77 1","pages":"133-148"},"PeriodicalIF":1.9,"publicationDate":"2017-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41573790","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}
Pub Date : 2017-10-24DOI: 10.6092/ISSN.1973-2201/6762
C. Withers, S. Nadarajah
Pitman efficiency is the oldest known efficiency. Most of the known results for computing the Pitman efficiency take the form of bounds. Based on some recent developments due to the authors and some calculus of variations, we develop tools for computing the Pitman efficiency exactly. Their use is illustrated numerically.
{"title":"Asymptotic Pitman's Relative Efficiency","authors":"C. Withers, S. Nadarajah","doi":"10.6092/ISSN.1973-2201/6762","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6762","url":null,"abstract":"Pitman efficiency is the oldest known efficiency. Most of the known results for computing the Pitman efficiency take the form of bounds. Based on some recent developments due to the authors and some calculus of variations, we develop tools for computing the Pitman efficiency exactly. Their use is illustrated numerically.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"77 1","pages":"91-108"},"PeriodicalIF":1.9,"publicationDate":"2017-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45019069","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}
Pub Date : 2017-04-07DOI: 10.6092/ISSN.1973-2201/6699
C. Bhupathi, Venakata HaraGopal Vajjha
There are clear guidelines and suggestions on the sample size and power calculation from health authorities (HA) for Bio equivalence (BE) studies in Healthy volunteers (HV). The suggested power is at least 80% and type 1 error is 5%. In real life situations, the clinical trials plan with more than 80%, giving rise to larger sample size. The increased power means more subjects, more wastage of time and more resources to complete the study, resulting in more money spent. This paper attempts to show how much reduction in the sample size can be achieved without affecting the scientific validity of the study and also the brief summary on the overall effect of reduced sample size on resources (subjects, time, blood and cost). We executed simulations in order to show the impact on the power and the 2 one sided confidence interval approach to show the study equivalence or otherwise. For illustration purpose, a couple of 2 period cross over studies were considered. 100 simulations were executed with different sample sizes to compare with the original results.
{"title":"Sample size recommendation for a bioequivalent study","authors":"C. Bhupathi, Venakata HaraGopal Vajjha","doi":"10.6092/ISSN.1973-2201/6699","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6699","url":null,"abstract":"There are clear guidelines and suggestions on the sample size and power calculation from health authorities (HA) for Bio equivalence (BE) studies in Healthy volunteers (HV). The suggested power is at least 80% and type 1 error is 5%. In real life situations, the clinical trials plan with more than 80%, giving rise to larger sample size. The increased power means more subjects, more wastage of time and more resources to complete the study, resulting in more money spent. This paper attempts to show how much reduction in the sample size can be achieved without affecting the scientific validity of the study and also the brief summary on the overall effect of reduced sample size on resources (subjects, time, blood and cost). We executed simulations in order to show the impact on the power and the 2 one sided confidence interval approach to show the study equivalence or otherwise. For illustration purpose, a couple of 2 period cross over studies were considered. 100 simulations were executed with different sample sizes to compare with the original results.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"77 1","pages":"65-71"},"PeriodicalIF":1.9,"publicationDate":"2017-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47616538","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}
Pub Date : 2017-04-07DOI: 10.6092/ISSN.1973-2201/6805
B. D. Finetti
This work was translated into English and published in the volume: Bruno De Finetti, Induction and Probability, Biblioteca di Statistica, eds. P. Monari, D. Cocchi, Clueb, Bologna, 1993. Bayesian statistical Inference is one of the last fundamental philosophical papers in which we can find the essential De Finetti's approach to the statistical inference.
这项工作被翻译成英文，并发表在以下卷中：Bruno De Finetti，《归纳与概率》，Biblioteca di Statistica，编辑：P.Monari，D.Cocchi，Clueb，Bologna，1993年。贝叶斯统计推断是最后一篇基础哲学论文之一，在这篇论文中，我们可以找到De Finetti的统计推断方法的精髓。
{"title":"Bayesian statistical inference","authors":"B. D. Finetti","doi":"10.6092/ISSN.1973-2201/6805","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6805","url":null,"abstract":"This work was translated into English and published in the volume: Bruno De Finetti, Induction and Probability, Biblioteca di Statistica, eds. P. Monari, D. Cocchi, Clueb, Bologna, 1993. Bayesian statistical Inference is one of the last fundamental philosophical papers in which we can find the essential De Finetti's approach to the statistical inference.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"77 1","pages":"3-11"},"PeriodicalIF":1.9,"publicationDate":"2017-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49519854","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}
Pub Date : 2017-04-07DOI: 10.6092/ISSN.1973-2201/6606
S. Nadarajah, I. Okorie
Mukhopadhyay and Cicconetti cite{mc2004} derived the Maximum Likelihood Estimator (MLE) and the Uniformly Minimum Variance Unbiased Estimator (UMVUE) of $theta$ in $N (theta, theta)$ and discussed their application to purely sequential and two-stage bounded risk estimation of $theta$. In this paper, a much simpler expression is derived for the UMVUE of $theta$. Using this expression, a comprehensive investigation is provided for comparing the performances of the sequential estimators based on the MLE and the UMVUE.
{"title":"On sequential estimation of a normal distribution having equal mean and variance","authors":"S. Nadarajah, I. Okorie","doi":"10.6092/ISSN.1973-2201/6606","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6606","url":null,"abstract":"Mukhopadhyay and Cicconetti cite{mc2004} derived the Maximum Likelihood Estimator (MLE) and the Uniformly Minimum Variance Unbiased Estimator (UMVUE) of $theta$ in $N (theta, theta)$ and discussed their application to purely sequential and two-stage bounded risk estimation of $theta$. In this paper, a much simpler expression is derived for the UMVUE of $theta$. Using this expression, a comprehensive investigation is provided for comparing the performances of the sequential estimators based on the MLE and the UMVUE.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"77 1","pages":"53-63"},"PeriodicalIF":1.9,"publicationDate":"2017-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48322199","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}
Pub Date : 2017-04-07DOI: 10.6092/ISSN.1973-2201/6347
Ajit Chaturvedi, Shantanu Vyas
Exponentiated distributions are considered. Two measures of reliability are considered, R(t)=P(X>t) and P=P(X>Y). Point estimation and testing procedures are developed for different parametric functions under Type II and Type I censoring. Uniformly minimum variance unbiased estimators (UMVUES) and maximum likelihood estimators (MLES) are derived. A new technique of obtaining these estimators is introduced.
{"title":"Estimation and Testing procedures for the Reliability functions of Exponentiated distributions under censorings","authors":"Ajit Chaturvedi, Shantanu Vyas","doi":"10.6092/ISSN.1973-2201/6347","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6347","url":null,"abstract":"Exponentiated distributions are considered. Two measures of reliability are considered, R(t)=P(X>t) and P=P(X>Y). Point estimation and testing procedures are developed for different parametric functions under Type II and Type I censoring. Uniformly minimum variance unbiased estimators (UMVUES) and maximum likelihood estimators (MLES) are derived. A new technique of obtaining these estimators is introduced.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"77 1","pages":"13-31"},"PeriodicalIF":1.9,"publicationDate":"2017-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49544020","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}
Pub Date : 2017-04-07DOI: 10.6092/ISSN.1973-2201/6808
M. Irshad
In this paper, we introduce a new extended generalized Lindley distribution ($NEGLD$). Some statistical properties of the proposed distribution are explicitly derived. These include conditional moments, vitality function, geometric vitality function, mean inactivity time and various entropy measures. Maximum likelihood estimation, moment estimation and asymptotic confidence interval are used for estimating the parameters. The distribution has been fitted to a data set to test its goodness of fit and it has been found that this distribution gives better fit than the some other well-known existing distributions.
{"title":"New Extended Generalized Lindley Distribution: Properties and Applications","authors":"M. Irshad","doi":"10.6092/ISSN.1973-2201/6808","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6808","url":null,"abstract":"In this paper, we introduce a new extended generalized Lindley distribution ($NEGLD$). Some statistical properties of the proposed distribution are explicitly derived. These include conditional moments, vitality function, geometric vitality function, mean inactivity time and various entropy measures. Maximum likelihood estimation, moment estimation and asymptotic confidence interval are used for estimating the parameters. The distribution has been fitted to a data set to test its goodness of fit and it has been found that this distribution gives better fit than the some other well-known existing distributions.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"77 1","pages":"33-52"},"PeriodicalIF":1.9,"publicationDate":"2017-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49578855","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}
Pub Date : 2017-01-01DOI: 10.6092/ISSN.1973-2201/7066
Valentina Sansivieri, M. Wiberg, M. Matteucci
The overall aim of this work is to review test equating methods with a particularly detailed description of item response theory (IRT) equating. Test score equating is used to compare different test scores from different test forms. Several methods have been developed to conduct equating: traditional methods, kernel method, and IRT equating. We synthetically explain the traditional equating methods which include mean equating, linear equating and equipercentile equating and which have been developed under all the possible data collection designs. We also briefly describe the idea of the kernel method: this is a unified approach to test equating for which recent interesting developments have been proposed. Then we focus on IRT equating, by describing old and new methods: in particular, we define IRT observed-score kernel equating and IRT observed-score equating using covariates, as well as other recent proposals in this field. We conclude the review by describing strengths and weaknesses of the different discussed approaches and by identifying future research topics.
{"title":"A Review of Test Equating Methods with a Special Focus on IRT-Based Approaches","authors":"Valentina Sansivieri, M. Wiberg, M. Matteucci","doi":"10.6092/ISSN.1973-2201/7066","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/7066","url":null,"abstract":"The overall aim of this work is to review test equating methods with a particularly detailed description of item response theory (IRT) equating. Test score equating is used to compare different test scores from different test forms. Several methods have been developed to conduct equating: traditional methods, kernel method, and IRT equating. We synthetically explain the traditional equating methods which include mean equating, linear equating and equipercentile equating and which have been developed under all the possible data collection designs. We also briefly describe the idea of the kernel method: this is a unified approach to test equating for which recent interesting developments have been proposed. Then we focus on IRT equating, by describing old and new methods: in particular, we define IRT observed-score kernel equating and IRT observed-score equating using covariates, as well as other recent proposals in this field. We conclude the review by describing strengths and weaknesses of the different discussed approaches and by identifying future research topics.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"77 1","pages":"329-352"},"PeriodicalIF":1.9,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71252569","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}
Pub Date : 2016-12-27DOI: 10.6092/ISSN.1973-2201/6682
M. Brizzi
In this paper a fuzzy version of three indices of risk (Diagonal Ratio, Rate ratio and Odds ratio), usually applied to exposure-affection studies, has been proposed and developed, considering the presence of a partial level of exposure and/or affection. These fuzzy indices are calculated after rescaling the cell frequencies according to fuzzy degrees of pertinence of partial modalities. A simulation study has then been performed, under the hypothesis of absence of effect of the risk factor, and some exploratory statistics have been reported, corresponding to different sample sizes; a transformed linear interpolation method has been described for extending simulation results. The rescaling method has been generalized, supposing that every observation has its proper level of exposure and affection. Finally, the fuzzy indices have been applied to an Italian survey, dealing with the relationship between physical activity and self-perceived health status of more than 4,500 people over 65, living in the province of Bologna.
{"title":"Fuzzy indices of risk for a deeper evaluation of exposure-affection studies","authors":"M. Brizzi","doi":"10.6092/ISSN.1973-2201/6682","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6682","url":null,"abstract":"In this paper a fuzzy version of three indices of risk (Diagonal Ratio, Rate ratio and Odds ratio), usually applied to exposure-affection studies, has been proposed and developed, considering the presence of a partial level of exposure and/or affection. These fuzzy indices are calculated after rescaling the cell frequencies according to fuzzy degrees of pertinence of partial modalities. A simulation study has then been performed, under the hypothesis of absence of effect of the risk factor, and some exploratory statistics have been reported, corresponding to different sample sizes; a transformed linear interpolation method has been described for extending simulation results. The rescaling method has been generalized, supposing that every observation has its proper level of exposure and affection. Finally, the fuzzy indices have been applied to an Italian survey, dealing with the relationship between physical activity and self-perceived health status of more than 4,500 people over 65, living in the province of Bologna.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"76 1","pages":"291-299"},"PeriodicalIF":1.9,"publicationDate":"2016-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251303","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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