Frantisek Duris, Juraj Gazdarica, Iveta Gazdaricova, Lucia Strieskova, Jaroslav Budis, Jan Turna, Tomas Szemes
{"title":"Mean and variance of ratios of proportions from categories of a multinomial distribution","authors":"Frantisek Duris, Juraj Gazdarica, Iveta Gazdaricova, Lucia Strieskova, Jaroslav Budis, Jan Turna, Tomas Szemes","doi":"10.1186/s40488-018-0083-x","DOIUrl":"https://doi.org/10.1186/s40488-018-0083-x","url":null,"abstract":"Ratio distribution is a probability distribution representing the ratio of two random variables, each usually having a known distribution. Currently, there are results when the random variables in the ratio follow (not necessarily the same) Gaussian, Cauchy, binomial or uniform distributions. In this paper we consider a case, where the random variables in the ratio are joint binomial components of a multinomial distribution. We derived formulae for mean and variance of this ratio distribution using a simple Taylor-series approach and also a more complex approach which uses a slight modification of the original ratio. We showed that the more complex approach yields better results with simulated data. The presented results can be directly applied in the computation of confidence intervals for ratios of multinomial proportions. AMS Subject Classification: 62E20","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":"13 9","pages":"1-20"},"PeriodicalIF":0.0,"publicationDate":"2018-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503745","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}
Muhammad Zubair, Muhammad H. Tahir, Gauss M. Cordeiro, Ayman Alzaatreh, Edwin M. M. Ortega
{"title":"The power-Cauchy negative-binomial: properties and regression","authors":"Muhammad Zubair, Muhammad H. Tahir, Gauss M. Cordeiro, Ayman Alzaatreh, Edwin M. M. Ortega","doi":"10.1186/s40488-017-0082-3","DOIUrl":"https://doi.org/10.1186/s40488-017-0082-3","url":null,"abstract":"We propose and study a new compounded model to extend the half-Cauchy and power-Cauchy distributions, which offers more flexibility in modeling lifetime data. The proposed model is analytically tractable and can be used effectively to analyze censored and uncensored data sets. Its density function can have various shapes such as reversed-J and right-skewed. It can accommodate different hazard shapes such as decreasing, upside-down bathtub and decreasing-increasing-decreasing. Some mathematical properties of the new distribution can be determined from a linear combination for its density function such as ordinary and incomplete moments. The performance of the maximum likelihood method to estimate the model parameters is investigated by a simulation study. Further, we introduce the new log-power-Cauchy negative-binomial regression model for censored data, which includes as sub-models some widely known regression models that can be applied to censored data. Four real life data sets, of which one is censored, have been analyzed and the new models provide adequate fits.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":"13 1‐2","pages":"1-17"},"PeriodicalIF":0.0,"publicationDate":"2018-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503748","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}
{"title":"A nonparametric approach for quantile regression.","authors":"Mei Ling Huang, Christine Nguyen","doi":"10.1186/s40488-018-0084-9","DOIUrl":"10.1186/s40488-018-0084-9","url":null,"abstract":"<p><p>Quantile regression estimates conditional quantiles and has wide applications in the real world. Estimating high conditional quantiles is an important problem. The regular quantile regression (QR) method often designs a linear or non-linear model, then estimates the coefficients to obtain the estimated conditional quantiles. This approach may be restricted by the linear model setting. To overcome this problem, this paper proposes a direct nonparametric quantile regression method with five-step algorithm. Monte Carlo simulations show good efficiency for the proposed direct QR estimator relative to the regular QR estimator. The paper also investigates two real-world examples of applications by using the proposed method. Studies of the simulations and the examples illustrate that the proposed direct nonparametric quantile regression model fits the data set better than the regular quantile regression method.</p>","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":"5 1","pages":"3"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s40488-018-0084-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37164735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Maria A Veretennikova, Alla Sikorskii, Michael J Boivin
{"title":"Parameters of stochastic models for electroencephalogram data as biomarkers for child's neurodevelopment after cerebral malaria.","authors":"Maria A Veretennikova, Alla Sikorskii, Michael J Boivin","doi":"10.1186/s40488-018-0086-7","DOIUrl":"https://doi.org/10.1186/s40488-018-0086-7","url":null,"abstract":"<p><p>The objective of this study was to test statistical features from the electroencephalogram (EEG) recordings as predictors of neurodevelopment and cognition of Ugandan children after coma due to cerebral malaria. The increments of the frequency bands of EEG time series were modeled as Student processes; the parameters of these Student processes were estimated and used along with clinical and demographic data in a machine-learning algorithm for the prediction of children's neurodevelopmental and cognitive scores 6 months after cerebral malaria illness. The key innovation of this work is in the identification of stochastic EEG features that can serve as language-independent markers of the impact of cerebral malaria on the developing brain. The results can enhance prognostic determination of which children are in most need of rehabilitative interventions, which is especially important in resource-constrained settings such as sub-Saharan Africa.</p>","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":"5 1","pages":"8"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s40488-018-0086-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36847539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Families of distributions arising from the quantile of generalized lambda distribution","authors":"Mahmoud Aldeni, Carl Lee, Felix Famoye","doi":"10.1186/s40488-017-0081-4","DOIUrl":"https://doi.org/10.1186/s40488-017-0081-4","url":null,"abstract":"In this paper, the class of T-R {generalized lambda} families of distributions based on the quantile of generalized lambda distribution has been proposed using the T-R{Y} framework. In the development of the T-R{Y} framework, the support of Y and T must be the same. It is typical that the random variable Y has one type of support and T is restricted to the same support. Taking Y to be a generalized lambda random variable leads to three different types of supports, thus, making the choice of the generator T to be much more broad and flexible. This is interesting and unique. By allowing T with different supports makes the T-R{generalized lambda} a desirable method for generating new versatile and broad families of generalized distributions for any given random variable R. Some general properties of these families of distributions are studied. Four members of the T-R{generalized lambda} families of distributions are derived. The shapes of these distributions can be symmetric, skewed to the left, skewed to the right, or bimodal. Two real life data sets are applied to illustrate the flexibility of the distributions.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":"13 8","pages":"1-18"},"PeriodicalIF":0.0,"publicationDate":"2017-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503746","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}
{"title":"Risk ratios and Scanlan’s HRX","authors":"H. Thomas, T. Hettmansperger","doi":"10.1186/s40488-017-0071-6","DOIUrl":"https://doi.org/10.1186/s40488-017-0071-6","url":null,"abstract":"","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s40488-017-0071-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65892958","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}
Anastasios N. Arapis, Frosso S. Makri, Zaharias M. Psillakis
{"title":"Joint distribution of k-tuple statistics in zero-one sequences of Markov-dependent trials","authors":"Anastasios N. Arapis, Frosso S. Makri, Zaharias M. Psillakis","doi":"10.1186/s40488-017-0080-5","DOIUrl":"https://doi.org/10.1186/s40488-017-0080-5","url":null,"abstract":"We consider a sequence of n, n≥3, zero (0) - one (1) Markov-dependent trials. We focus on k-tuples of 1s; i.e. runs of 1s of length at least equal to a fixed integer number k, 1≤k≤n. The statistics denoting the number of k-tuples of 1s, the number of 1s in them and the distance between the first and the last k-tuple of 1s in the sequence, are defined. The work provides, in a closed form, the exact conditional joint distribution of these statistics given that the number of k-tuples of 1s in the sequence is at least two. The case of independent and identical 0−1 trials is also covered in the study. A numerical example illustrates further the theoretical results.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":"14 1","pages":"1-13"},"PeriodicalIF":0.0,"publicationDate":"2017-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503744","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}
Gauss M. Cordeiro, Antonio E. Gomes, Cibele Q. da-Silva, Edwin M. M. Ortega
{"title":"A useful extension of the Burr III distribution","authors":"Gauss M. Cordeiro, Antonio E. Gomes, Cibele Q. da-Silva, Edwin M. M. Ortega","doi":"10.1186/s40488-017-0079-y","DOIUrl":"https://doi.org/10.1186/s40488-017-0079-y","url":null,"abstract":"For any continuous baseline G distribution, Zografos and Balakrishnan (Statistical Methodology 6:344–362, 2009) introduced the gamma-generated family of distributions with an extra shape parameter. Based on this family, we define a new four-parameter extension of the Burr III distribution. It can have decreasing, unimodal and decreasing-increasing-decreasing hazard rate function. We provide a comprehensive account of some of its structural properties. We propose a new log-gamma Burr III regression model, which is a feasible alternative for modeling the four existing types of failure rates. Two applications to real data sets and a simulation study illustrate the performance of the new models.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":"14 6‐7","pages":"1-15"},"PeriodicalIF":0.0,"publicationDate":"2017-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503741","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}
{"title":"Describing the Flexibility of the Generalized Gamma and Related Distributions","authors":"Matthew Matheson, Alvaro Muñoz, Christopher Cox","doi":"10.1186/s40488-017-0072-5","DOIUrl":"https://doi.org/10.1186/s40488-017-0072-5","url":null,"abstract":"The generalized gamma (GG) distribution is a widely used, flexible tool for parametric survival analysis. Many alternatives and extensions to this family have been proposed. This paper characterizes the flexibility of the GG by the quartile ratio relationship, log(Q2/Q1)/log(Q3/Q2), and compares the GG on this basis with two other three-parameter distributions and four parent distributions of four or five parameters. For most parameter combinations of other distributions, a very similar GG, as assessed by the Kullback-Liebler distance, can be found by matching the three quartiles; extreme cases where this fails are examined. Limited additional flexibility is observed, supporting the basic GG family as an ideal platform for parametric survival analysis.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":"14 2‐3","pages":"1-9"},"PeriodicalIF":0.0,"publicationDate":"2017-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503743","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}
{"title":"Quantile regression for overdispersed count data: a hierarchical method","authors":"Peter Congdon","doi":"10.1186/s40488-017-0073-4","DOIUrl":"https://doi.org/10.1186/s40488-017-0073-4","url":null,"abstract":"Generalized Poisson regression is commonly applied to overdispersed count data, and focused on modelling the conditional mean of the response. However, conditional mean regression models may be sensitive to response outliers and provide no information on other conditional distribution features of the response. We consider instead a hierarchical approach to quantile regression of overdispersed count data. This approach has the benefits of effective outlier detection and robust estimation in the presence of outliers, and in health applications, that quantile estimates can reflect risk factors. The technique is first illustrated with simulated overdispersed counts subject to contamination, such that estimates from conditional mean regression are adversely affected. A real application involves ambulatory care sensitive emergency admissions across 7518 English patient general practitioner (GP) practices. Predictors are GP practice deprivation, patient satisfaction with care and opening hours, and region. Impacts of deprivation are particularly important in policy terms as indicating effectiveness of efforts to reduce inequalities in care sensitive admissions. Hierarchical quantile count regression is used to develop profiles of central and extreme quantiles according to specified predictor combinations.","PeriodicalId":52216,"journal":{"name":"Journal of Statistical Distributions and Applications","volume":"14 4‐5","pages":"1-19"},"PeriodicalIF":0.0,"publicationDate":"2017-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503742","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}