Pub Date : 2019-10-14DOI: 10.1285/I20705948V12N2P392
David Han, T. Bai
In order to gather the information about the lifetime distribution of a product, a standard life testing method at normal operating conditions is not practical when the product has an extremely long lifespan. Accelerated life testing solves this difficult issue by subjecting the test units at higher stress levels than normal for quicker and more failure data. The lifetime at the design stress is then estimated through extrapolation using an appropriate regression model. Estimation of the regression parameters based on exponentially distributed lifetimes from accelerated life tests has been considered by a number of authors using numerical methods but without systematic or analytical validation. In this article, we propose an alternative approach based on a simple and easy-to-apply graphical method, which also establishes the existence and uniqueness of the maximum likelihood estimates for constant-stress and step-stress accelerated life tests under progressive censorings.
{"title":"On the maximum likelihood estimation for progressively censored lifetimes from constant-stress and step-stress accelerated tests","authors":"David Han, T. Bai","doi":"10.1285/I20705948V12N2P392","DOIUrl":"https://doi.org/10.1285/I20705948V12N2P392","url":null,"abstract":"In order to gather the information about the lifetime distribution of a product, a standard life testing method at normal operating conditions is not practical when the product has an extremely long lifespan. Accelerated life testing solves this difficult issue by subjecting the test units at higher stress levels than normal for quicker and more failure data. The lifetime at the design stress is then estimated through extrapolation using an appropriate regression model. Estimation of the regression parameters based on exponentially distributed lifetimes from accelerated life tests has been considered by a number of authors using numerical methods but without systematic or analytical validation. In this article, we propose an alternative approach based on a simple and easy-to-apply graphical method, which also establishes the existence and uniqueness of the maximum likelihood estimates for constant-stress and step-stress accelerated life tests under progressive censorings.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":"12 1","pages":"392-404"},"PeriodicalIF":0.7,"publicationDate":"2019-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1285/I20705948V12N2P392","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46820219","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 : 2019-10-14DOI: 10.1285/I20705948V12N2P380
Meghlaoui Dakhmouche, Oussama Bahi
In this work, we are interested in a hypothesis testing problem within the framework of a GPD model with interval censoring. For this purpose, we rst develop the calculation of the likelihood function using conditional probabilities to achieve the same expression proposed by Klein and Moeschberger. Next, we show that the properties of the maximum pseudo-likelihood estimates of the model parameters, and essentially the asymptotic normality, are preserved. Finally, we built a hypothesis testing to compare two types of breast cancer treatment as part of the model mentioned above.
{"title":"Analysis of breast cancer data in framework of a GPD model with interval censoring","authors":"Meghlaoui Dakhmouche, Oussama Bahi","doi":"10.1285/I20705948V12N2P380","DOIUrl":"https://doi.org/10.1285/I20705948V12N2P380","url":null,"abstract":"In this work, we are interested in a hypothesis testing problem within the framework of a GPD model with interval censoring. For this purpose, we rst develop the calculation of the likelihood function using conditional probabilities to achieve the same expression proposed by Klein and Moeschberger. Next, we show that the properties of the maximum pseudo-likelihood estimates of the model parameters, and essentially the asymptotic normality, are preserved. Finally, we built a hypothesis testing to compare two types of breast cancer treatment as part of the model mentioned above.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":"12 1","pages":"380-391"},"PeriodicalIF":0.7,"publicationDate":"2019-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1285/I20705948V12N2P380","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45149841","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 : 2019-10-14DOI: 10.1285/I20705948V12N2P542
Laura Antonucci, M. Bolzan, E. Carrozzo, C. Crocetta, L. Gioia, M. Manacorda, F. Mastrangelo, M. Russo, L. Salmaso
In 2012, a comprehensive historical and genealogical discussion of correspondence analysis was published in Australian and New Zealand Journal of Statistics. That genealogy consisted of more than 270 key books and articles and focused on an historical development of the correspondence analysis, a statistical tool which provides the analyst with a visual inspection of the association between two or more categorical variables. In this new genealogy, we provide a brief overview of over 30 variants of correspondence analysis that now exist outside of the traditional approaches used to analyse the association between two or more categorical variables. It comprises of a bibliography of a more than 300 books and articles that were not included in the 2012 bibliography and highlights the growth in the development of correspondence analysis across all areas of research.
{"title":"Accuracy of computer guided implant dentistry: a permutation testing approach","authors":"Laura Antonucci, M. Bolzan, E. Carrozzo, C. Crocetta, L. Gioia, M. Manacorda, F. Mastrangelo, M. Russo, L. Salmaso","doi":"10.1285/I20705948V12N2P542","DOIUrl":"https://doi.org/10.1285/I20705948V12N2P542","url":null,"abstract":"In 2012, a comprehensive historical and genealogical discussion of correspondence analysis was published in Australian and New Zealand Journal of Statistics. That genealogy consisted of more than 270 key books and articles and focused on an historical development of the correspondence analysis, a statistical tool which provides the analyst with a visual inspection of the association between two or more categorical variables. In this new genealogy, we provide a brief overview of over 30 variants of correspondence analysis that now exist outside of the traditional approaches used to analyse the association between two or more categorical variables. It comprises of a bibliography of a more than 300 books and articles that were not included in the 2012 bibliography and highlights the growth in the development of correspondence analysis across all areas of research.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":"12 1","pages":"542-551"},"PeriodicalIF":0.7,"publicationDate":"2019-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1285/I20705948V12N2P542","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45655415","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 : 2019-10-14DOI: 10.1285/I20705948V12N2P520
A. Al-Omari, Doaa Shraa
In this paper, Darna distribution (DD) is suggested as a new continuousprobability density function. The statistical properties of the DD as the moments,shapes of the distribution, measures of skewness, kurtosis, coefficientof variation are presented as well as some calculations are provided. Also,the maximum likelihood estimators, the Bonferroni and Lorenz curves, andGini Index are obtained. The Stress - Strength Reliability, R´enyi entropy,mean and median deviations are derived and proved. The distribution oforder statistics are presented. The reliability analysis including hazard, reliability,odds, and reverse hazard functions are presented. An application ofWheaton River data is considered.
{"title":"Darna Distribution: Properties and Application","authors":"A. Al-Omari, Doaa Shraa","doi":"10.1285/I20705948V12N2P520","DOIUrl":"https://doi.org/10.1285/I20705948V12N2P520","url":null,"abstract":"In this paper, Darna distribution (DD) is suggested as a new continuousprobability density function. The statistical properties of the DD as the moments,shapes of the distribution, measures of skewness, kurtosis, coefficientof variation are presented as well as some calculations are provided. Also,the maximum likelihood estimators, the Bonferroni and Lorenz curves, andGini Index are obtained. The Stress - Strength Reliability, R´enyi entropy,mean and median deviations are derived and proved. The distribution oforder statistics are presented. The reliability analysis including hazard, reliability,odds, and reverse hazard functions are presented. An application ofWheaton River data is considered.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":"12 1","pages":"520-541"},"PeriodicalIF":0.7,"publicationDate":"2019-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1285/I20705948V12N2P520","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46041363","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 : 2019-10-14DOI: 10.1285/I20705948V12N2P491
L. Amusa, T. Zewotir, D. North
In observational studies, propensity score weighting methods are regarded as the conventional standard for estimating the effects of treatments on outcomes. We introduce entropy balancing, which despite its excellent conceptual properties, has been under-utilized in the applied studies. Using an extensive series of Monte Carlo simulations, we evaluated the performance of entropy balancing, in estimating difference in means, marginal odds ratios, rate ratios and hazard ratios. The performance of entropy balancing was relatively compared with that of inverse probability of treatment weighting using the propensity score. We found that entropy balancing outperformed the IPW method in estimating difference in means, marginal odds ratios, and hazard ratios, but when estimating marginal rate ratios, IPW performed better. Entropy balancing produced more biased estimates in many cases. However, the entropy balancing algorithm is capable of controlling bias by loosening the tightening of the pre-specified tolerance on covariate balance. We report findings as to when one technique is better than the other with no proclamation on whether one method is in every case superior to the other. Entropy balancing merits more widespread adoption in applied studies.
{"title":"Examination of Entropy balancing technique for estimating some standard measures of treatment effects: A simulation study","authors":"L. Amusa, T. Zewotir, D. North","doi":"10.1285/I20705948V12N2P491","DOIUrl":"https://doi.org/10.1285/I20705948V12N2P491","url":null,"abstract":"In observational studies, propensity score weighting methods are regarded as the conventional standard for estimating the effects of treatments on outcomes. We introduce entropy balancing, which despite its excellent conceptual properties, has been under-utilized in the applied studies. Using an extensive series of Monte Carlo simulations, we evaluated the performance of entropy balancing, in estimating difference in means, marginal odds ratios, rate ratios and hazard ratios. The performance of entropy balancing was relatively compared with that of inverse probability of treatment weighting using the propensity score. We found that entropy balancing outperformed the IPW method in estimating difference in means, marginal odds ratios, and hazard ratios, but when estimating marginal rate ratios, IPW performed better. Entropy balancing produced more biased estimates in many cases. However, the entropy balancing algorithm is capable of controlling bias by loosening the tightening of the pre-specified tolerance on covariate balance. We report findings as to when one technique is better than the other with no proclamation on whether one method is in every case superior to the other. Entropy balancing merits more widespread adoption in applied studies.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":"12 1","pages":"491-507"},"PeriodicalIF":0.7,"publicationDate":"2019-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42462081","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 : 2019-04-26DOI: 10.1285/I20705948V12N1P1
T. Zoubeidi, M. Y. El-Bassiouni
We develop fixed size confidence regions for estimating the fixed and random effects parameters of the mixed effects logistic regression model. This model applies to, among others, the study of the effects of covariates on a dichotomous response variable when subjects are sampled in clusters. Two sequential procedures are developed to estimate with a prescribed accuracy (confidence level) and fixed precision the set of fixed and random effects parameters and linear transformations of these parameters, respectively. We show that the two procedures are asymptotically consistent (i.e., the coverage probability converges to the nominal confidence level) and asymptotically efficient (i.e., the ratio of the expected random sample size to the unknown best fixed sample size converges to 1) as the width of the confidence region converges to 0. Suggestions to improve the performance of the procedures are provided based on Monte Carlo simulation and illustrated through a longitudinal clinical trial data.
{"title":"Fixed Size Confidence Regions for the Parameters of the Mixed Effects Logistic Regression Model","authors":"T. Zoubeidi, M. Y. El-Bassiouni","doi":"10.1285/I20705948V12N1P1","DOIUrl":"https://doi.org/10.1285/I20705948V12N1P1","url":null,"abstract":"We develop fixed size confidence regions for estimating the fixed and random effects parameters of the mixed effects logistic regression model. This model applies to, among others, the study of the effects of covariates on a dichotomous response variable when subjects are sampled in clusters. Two sequential procedures are developed to estimate with a prescribed accuracy (confidence level) and fixed precision the set of fixed and random effects parameters and linear transformations of these parameters, respectively. We show that the two procedures are asymptotically consistent (i.e., the coverage probability converges to the nominal confidence level) and asymptotically efficient (i.e., the ratio of the expected random sample size to the unknown best fixed sample size converges to 1) as the width of the confidence region converges to 0. Suggestions to improve the performance of the procedures are provided based on Monte Carlo simulation and illustrated through a longitudinal clinical trial data.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":"12 1","pages":"1-13"},"PeriodicalIF":0.7,"publicationDate":"2019-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1285/I20705948V12N1P1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49164989","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 : 2019-04-26DOI: 10.1285/I20705948V12N1P190
M. A. Kadiri, Mohammad Migdadi
This paper develops estimating parameters for Morgenstern type bivariatedistribution by using bivariate ranked set sampling procedure as an alterna-tive method to simple random sampling. This proposed procedure gives anopportunity to estimate all distribution's parameters simultaneously whichis not investigated in previous studies, yet. In the last part of this paper,simulation studies show properties of the new estimators and compare themwith some other existed estimators.
{"title":"Estimating parameters of Morgenstern type bivariate distribution using bivariate ranked set sampling","authors":"M. A. Kadiri, Mohammad Migdadi","doi":"10.1285/I20705948V12N1P190","DOIUrl":"https://doi.org/10.1285/I20705948V12N1P190","url":null,"abstract":"This paper develops estimating parameters for Morgenstern type bivariatedistribution by using bivariate ranked set sampling procedure as an alterna-tive method to simple random sampling. This proposed procedure gives anopportunity to estimate all distribution's parameters simultaneously whichis not investigated in previous studies, yet. In the last part of this paper,simulation studies show properties of the new estimators and compare themwith some other existed estimators.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":"38 1","pages":"190-208"},"PeriodicalIF":0.7,"publicationDate":"2019-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66340457","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 : 2019-04-26DOI: 10.1285/I20705948V12N1P44
Amber Asghar, A. Sanaullah, M. Hanif
This paper considers a class of generalized estimators for estimating the unknown population variance using two auxiliary variables when mean of one auxiliary variable may not be available. The expressions for bias and mean square error of the proposed estimators are obtained up to the first order of approximation. Conditions for which the proposed generalized estimator is more efficient than the existing estimators have been derived. Both empirical and simulation studies have also been carried out to analyze the efficiency of the proposed estimators with some existing estimators.
{"title":"Generalized Class of Variance Estimators under Two-Phase Sampling for Partial Information Case","authors":"Amber Asghar, A. Sanaullah, M. Hanif","doi":"10.1285/I20705948V12N1P44","DOIUrl":"https://doi.org/10.1285/I20705948V12N1P44","url":null,"abstract":"This paper considers a class of generalized estimators for estimating the unknown population variance using two auxiliary variables when mean of one auxiliary variable may not be available. The expressions for bias and mean square error of the proposed estimators are obtained up to the first order of approximation. Conditions for which the proposed generalized estimator is more efficient than the existing estimators have been derived. Both empirical and simulation studies have also been carried out to analyze the efficiency of the proposed estimators with some existing estimators.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1285/I20705948V12N1P44","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49016632","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 : 2019-04-26DOI: 10.1285/I20705948V12N1P176
M. A. Kadiri, Mohammad Migdadi
This paper investigates estimating the association parameter of Morgenstern type bivariate distribution using a modified maximum likelihood method where the regular maximum likelihood methods failed to achieve estimation. The simple random sampling, concomitant of ordered statistics and bivariate ranked set sampling methods are used and compared. Efficiency and bias of the produced estimators are compared for two specific examples, Morgenstern type bivariate uniform and exponential distributions.
{"title":"Estimating Morgenstern Type Bivariate Association Parameter Using a Modified Maximum Likelihood Method","authors":"M. A. Kadiri, Mohammad Migdadi","doi":"10.1285/I20705948V12N1P176","DOIUrl":"https://doi.org/10.1285/I20705948V12N1P176","url":null,"abstract":"This paper investigates estimating the association parameter of Morgenstern type bivariate distribution using a modified maximum likelihood method where the regular maximum likelihood methods failed to achieve estimation. The simple random sampling, concomitant of ordered statistics and bivariate ranked set sampling methods are used and compared. Efficiency and bias of the produced estimators are compared for two specific examples, Morgenstern type bivariate uniform and exponential distributions.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":"12 1","pages":"176-189"},"PeriodicalIF":0.7,"publicationDate":"2019-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1285/I20705948V12N1P176","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44232224","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 : 2019-04-26DOI: 10.1285/I20705948V12N1P140
A. Al-Zou'bi, A. Smadi
The process capability indices give a measure of how a process suits within the specification limits. Traditionally, the main assumptions are used in calculating these indices that the measurements for the specified characteristic are independent and normally distributed. In this paper we investigated the distributional properties in terms of Bias, MSE and empirical distribution for the sample version of the most common three process capability measures namely; when the process data are autocorrelated following seasonal or non-seasonal first-order autoregressive process. We have found that the characteristics of those estimators are negatively affected by the autocorrelation data, especially for the multiplicative seasonal AR model. Besides, we found that the empirical distributions of the three sample capability measures are positively skewed and leptokurtic, a fact which is true when the data are independent and normal.
{"title":"A comparison of Process Capability Measures for Seasonal and Non-Seasonal Autoregressive Auto-Correlated Data","authors":"A. Al-Zou'bi, A. Smadi","doi":"10.1285/I20705948V12N1P140","DOIUrl":"https://doi.org/10.1285/I20705948V12N1P140","url":null,"abstract":"The process capability indices give a measure of how a process suits within the specification limits. Traditionally, the main assumptions are used in calculating these indices that the measurements for the specified characteristic are independent and normally distributed. In this paper we investigated the distributional properties in terms of Bias, MSE and empirical distribution for the sample version of the most common three process capability measures namely; when the process data are autocorrelated following seasonal or non-seasonal first-order autoregressive process. We have found that the characteristics of those estimators are negatively affected by the autocorrelation data, especially for the multiplicative seasonal AR model. Besides, we found that the empirical distributions of the three sample capability measures are positively skewed and leptokurtic, a fact which is true when the data are independent and normal.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":"12 1","pages":"140-152"},"PeriodicalIF":0.7,"publicationDate":"2019-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43550873","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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