Pub Date : 2020-08-28DOI: 10.1186/s40488-020-00108-7
Marianne Müller
To compare fit statistics for the Rasch model based on estimates of unconditional or conditional response probabilities. Using person estimates to calculate fit statistics can lead to problems because the person estimates are biased. Conditional response probabilities given the total person score could be used instead. Data sets are simulated which fit the Rasch model. Type I error rates are calculated and the distributions of the fit statistics are compared with the assumed normal or chi-square distribution. Parametric bootstrap is used to further study the distributions of the fit statistics. Type I error rates for unconditional chi-square statistics are larger than expected even for moderate sample sizes. The conditional chi-square statistics maintain the significance level. Unconditional outfit and infit statistics have asymmetric distributions with means slighly below 1. Conditional outfit and infit statistics have reduced Type I error rates. Conditional residuals should be used. If only unconditional residuals are available parametric bootstrapping is recommended to calculate valid p-values. Bootstrapping is also necessary for conditional outfit statistics. For conditional infit statistics the adjusted rule-of-thumb critical values look useful.
{"title":"Item fit statistics for Rasch analysis: can we trust them?","authors":"Marianne Müller","doi":"10.1186/s40488-020-00108-7","DOIUrl":"https://doi.org/10.1186/s40488-020-00108-7","url":null,"abstract":"To compare fit statistics for the Rasch model based on estimates of unconditional or conditional response probabilities. Using person estimates to calculate fit statistics can lead to problems because the person estimates are biased. Conditional response probabilities given the total person score could be used instead. Data sets are simulated which fit the Rasch model. Type I error rates are calculated and the distributions of the fit statistics are compared with the assumed normal or chi-square distribution. Parametric bootstrap is used to further study the distributions of the fit statistics. Type I error rates for unconditional chi-square statistics are larger than expected even for moderate sample sizes. The conditional chi-square statistics maintain the significance level. Unconditional outfit and infit statistics have asymmetric distributions with means slighly below 1. Conditional outfit and infit statistics have reduced Type I error rates. Conditional residuals should be used. If only unconditional residuals are available parametric bootstrapping is recommended to calculate valid p-values. Bootstrapping is also necessary for conditional outfit statistics. For conditional infit statistics the adjusted rule-of-thumb critical values look useful.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503837","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 : 2020-08-17DOI: 10.1186/s40488-020-00105-w
Samaradasa Weerahandi, Ching-Ray Yu
At this juncture when mixed models are heavily employed in applications ranging from clinical research to business analytics, the purpose of this article is to extend the exact distributional result of Wald (Ann. Math. Stat. 18: 586–589, 1947) to handle models involving a number of variance components.Due to the unavailability of exact distributional results for underlying statistics, currently available methods provide small group/sample inference only for balanced ANOVA models or simple regression models. The exact distributional results developed in this article should prove useful in making inferences by such methods as parametric bootstrap, fiducial, and generalized p-value approach, when there are a number of variance components to deal with.
{"title":"Exact distributions of statistics for making inferences on mixed models under the default covariance structure","authors":"Samaradasa Weerahandi, Ching-Ray Yu","doi":"10.1186/s40488-020-00105-w","DOIUrl":"https://doi.org/10.1186/s40488-020-00105-w","url":null,"abstract":"At this juncture when mixed models are heavily employed in applications ranging from clinical research to business analytics, the purpose of this article is to extend the exact distributional result of Wald (Ann. Math. Stat. 18: 586–589, 1947) to handle models involving a number of variance components.Due to the unavailability of exact distributional results for underlying statistics, currently available methods provide small group/sample inference only for balanced ANOVA models or simple regression models. The exact distributional results developed in this article should prove useful in making inferences by such methods as parametric bootstrap, fiducial, and generalized p-value approach, when there are a number of variance components to deal with.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503836","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 : 2020-08-01DOI: 10.1186/s40488-020-00104-x
I. Ghosh
{"title":"A new discrete pareto type (IV) model: theory, properties and applications","authors":"I. Ghosh","doi":"10.1186/s40488-020-00104-x","DOIUrl":"https://doi.org/10.1186/s40488-020-00104-x","url":null,"abstract":"","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s40488-020-00104-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65895775","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 : 2019-11-05DOI: 10.1186/s40488-019-0102-6
Oscar Alberto Quijano Xacur
We introduce a new distribution with support on (0,1) called unifed. It can be used as the response distribution for a GLM and it is suitable for data aggregation. We make a comparison to the beta regression. A link to an R package for working with the unifed is provided.
{"title":"The unifed distribution","authors":"Oscar Alberto Quijano Xacur","doi":"10.1186/s40488-019-0102-6","DOIUrl":"https://doi.org/10.1186/s40488-019-0102-6","url":null,"abstract":"We introduce a new distribution with support on (0,1) called unifed. It can be used as the response distribution for a GLM and it is suitable for data aggregation. We make a comparison to the beta regression. A link to an R package for working with the unifed is provided.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503835","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 : 2019-08-23DOI: 10.1186/s40488-019-0101-7
Fiaz Ahmad Bhatti, G. G. Hamedani, Mustafa C. Korkmaz, Gauss M. Cordeiro, Haitham M. Yousof, Munir Ahmad
In this paper, a flexible family of distributions with unimodel, bimodal, increasing, increasing and decreasing, inverted bathtub and modified bathtub hazard rate called Burr III-Marshal Olkin-G (BIIIMO-G) family is developed on the basis of the T-X family technique. The density function of the BIIIMO-G family is arc, exponential, left- skewed, right-skewed and symmetrical shaped. Descriptive measures such as quantiles, moments, incomplete moments, inequality measures and reliability measures are theoretically established. The BIIIMO-G family is characterized via different techniques. Parameters of the BIIIMO-G family are estimated using maximum likelihood method. A simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of BIIIMO-G family is demonstrated by its application to real data sets.
{"title":"On Burr III Marshal Olkin family: development, properties, characterizations and applications","authors":"Fiaz Ahmad Bhatti, G. G. Hamedani, Mustafa C. Korkmaz, Gauss M. Cordeiro, Haitham M. Yousof, Munir Ahmad","doi":"10.1186/s40488-019-0101-7","DOIUrl":"https://doi.org/10.1186/s40488-019-0101-7","url":null,"abstract":"In this paper, a flexible family of distributions with unimodel, bimodal, increasing, increasing and decreasing, inverted bathtub and modified bathtub hazard rate called Burr III-Marshal Olkin-G (BIIIMO-G) family is developed on the basis of the T-X family technique. The density function of the BIIIMO-G family is arc, exponential, left- skewed, right-skewed and symmetrical shaped. Descriptive measures such as quantiles, moments, incomplete moments, inequality measures and reliability measures are theoretically established. The BIIIMO-G family is characterized via different techniques. Parameters of the BIIIMO-G family are estimated using maximum likelihood method. A simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of BIIIMO-G family is demonstrated by its application to real data sets.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503834","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 : 2019-08-20DOI: 10.1186/s40488-019-0100-8
Roger W. Barnard, Chamila Perera, James G. Surles, A. Alexandre Trindade
Motivated by an engineering pullout test applied to a steel strip embedded in earth, we show how the resulting linearly decreasing force leads naturally to a new distribution, if the force under constant stress is modeled via a three-parameter Weibull. We term this the LDSWeibull distribution, and show that inference on the parameters of the underlying Weibull can be made upon collection of data from such pullout tests. Various classical finite-sample and asymptotic properties of the LDSWeibull are studied, including existence of moments, distribution of extremes, and maximum likelihood based inference under different regimes. The LDSWeibull is shown to have many similarities with the Weibull, but does not suffer from the problem of having an unbounded likelihood function under certain parameter configurations. We demonstrate that the quality of its fit can also be very competitive with that of the Weibull in certain applications.
{"title":"The linearly decreasing stress Weibull (LDSWeibull): a new Weibull-like distribution","authors":"Roger W. Barnard, Chamila Perera, James G. Surles, A. Alexandre Trindade","doi":"10.1186/s40488-019-0100-8","DOIUrl":"https://doi.org/10.1186/s40488-019-0100-8","url":null,"abstract":"Motivated by an engineering pullout test applied to a steel strip embedded in earth, we show how the resulting linearly decreasing force leads naturally to a new distribution, if the force under constant stress is modeled via a three-parameter Weibull. We term this the LDSWeibull distribution, and show that inference on the parameters of the underlying Weibull can be made upon collection of data from such pullout tests. Various classical finite-sample and asymptotic properties of the LDSWeibull are studied, including existence of moments, distribution of extremes, and maximum likelihood based inference under different regimes. The LDSWeibull is shown to have many similarities with the Weibull, but does not suffer from the problem of having an unbounded likelihood function under certain parameter configurations. We demonstrate that the quality of its fit can also be very competitive with that of the Weibull in certain applications.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503833","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 : 2019-07-24DOI: 10.1186/s40488-019-0099-x
S. Muthukumarana, David Martell, R. Tiwari
{"title":"Meta analysis of binary data with excessive zeros in two-arm trials","authors":"S. Muthukumarana, David Martell, R. Tiwari","doi":"10.1186/s40488-019-0099-x","DOIUrl":"https://doi.org/10.1186/s40488-019-0099-x","url":null,"abstract":"","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s40488-019-0099-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65895718","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 : 2019-06-12DOI: 10.1186/s40488-019-0097-z
Wolf-Dieter Richter
The class of (p1,…,pk)-spherical probability laws and a method of simulating random vectors following such distributions are introduced using a new stochastic vector representation. A dynamic geometric disintegration method and a corresponding geometric measure representation are used for generalizing the classical χ2-, t- and F-distributions. Comparing the principles of specialization and marginalization gives rise to an alternative method of dependence modeling.
{"title":"On (p1,…,pk)-spherical distributions","authors":"Wolf-Dieter Richter","doi":"10.1186/s40488-019-0097-z","DOIUrl":"https://doi.org/10.1186/s40488-019-0097-z","url":null,"abstract":"The class of (p1,…,pk)-spherical probability laws and a method of simulating random vectors following such distributions are introduced using a new stochastic vector representation. A dynamic geometric disintegration method and a corresponding geometric measure representation are used for generalizing the classical χ2-, t- and F-distributions. Comparing the principles of specialization and marginalization gives rise to an alternative method of dependence modeling.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503832","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 : 2019-06-11DOI: 10.1186/s40488-019-0095-1
M. Lee, G. A. Whitmore
{"title":"A new class of survival distribution for degradation processes subject to shocks","authors":"M. Lee, G. A. Whitmore","doi":"10.1186/s40488-019-0095-1","DOIUrl":"https://doi.org/10.1186/s40488-019-0095-1","url":null,"abstract":"","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s40488-019-0095-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65895667","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 : 2019-06-08DOI: 10.1186/s40488-019-0098-y
Maria C.S. Lima, Gauss M. Cordeiro, Edwin M.M. Ortega, Abraão D.C. Nascimento
Various applications in natural science require models more accurate than well-known distributions. In this context, several generators of distributions have been recently proposed. We introduce a new four-parameter extended normal (EN) distribution, which can provide better fits than the skew-normal and beta normal distributions as proved empirically in two applications to real data. We present Monte Carlo simulations to investigate the effectiveness of the EN distribution using the Kullback-Leibler divergence criterion. The classical regression model is not recommended for most practical applications because it oversimplifies real world problems. We propose an EN regression model and show its usefulness in practice by comparing with other regression models. We adopt maximum likelihood method for estimating the model parameters of both proposed distribution and regression model.
{"title":"A new extended normal regression model: simulations and applications","authors":"Maria C.S. Lima, Gauss M. Cordeiro, Edwin M.M. Ortega, Abraão D.C. Nascimento","doi":"10.1186/s40488-019-0098-y","DOIUrl":"https://doi.org/10.1186/s40488-019-0098-y","url":null,"abstract":"Various applications in natural science require models more accurate than well-known distributions. In this context, several generators of distributions have been recently proposed. We introduce a new four-parameter extended normal (EN) distribution, which can provide better fits than the skew-normal and beta normal distributions as proved empirically in two applications to real data. We present Monte Carlo simulations to investigate the effectiveness of the EN distribution using the Kullback-Leibler divergence criterion. The classical regression model is not recommended for most practical applications because it oversimplifies real world problems. We propose an EN regression model and show its usefulness in practice by comparing with other regression models. We adopt maximum likelihood method for estimating the model parameters of both proposed distribution and regression model.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503831","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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