Pub Date : 2023-07-12DOI: 10.15446/rce.v46n2.103163
B. Oluyede, Morongwa Gabanakgosi
A new generalized family of distributions called the type II exponentiated half logistic-Marshall-Olkin-G distribution is developed. Some special cases of the new model are presented. We explore some statistical properties of the new family of distributions. The statistical properties studied include expansion of the density function, hazard rate and quantile functions, moments, moment generating functions, probability weighted moments, stochastic ordering, distribution of order statistics and Rényi entropy. The maximum likelihood, ordinary and weighted least-squares techniques for the estimation of model parameters are presented, and Monte Carlo simulations for the new family of distributions are conducted. The importance of the new family of distributions is examined by means of applications to two real data sets.
本文提出了一个新的广义分布系列，称为 II 型指数化半对数-Marshall-Olkin-G 分布。介绍了新模型的一些特例。我们探讨了新分布族的一些统计特性。研究的统计性质包括密度函数的扩展、危险率和量子函数、矩、矩产生函数、概率加权矩、随机排序、阶次统计分布和雷尼熵。介绍了估计模型参数的最大似然法、普通法和加权最小二乘法技术，并对新的分布族进行了蒙特卡罗模拟。通过对两个真实数据集的应用，考察了新分布族的重要性。
{"title":"The Type II Exponentiated Half Logistic-Marshall-Olkin-G Family of Distributions with Applications","authors":"B. Oluyede, Morongwa Gabanakgosi","doi":"10.15446/rce.v46n2.103163","DOIUrl":"https://doi.org/10.15446/rce.v46n2.103163","url":null,"abstract":"A new generalized family of distributions called the type II exponentiated half logistic-Marshall-Olkin-G distribution is developed. Some special cases of the new model are presented. We explore some statistical properties of the new family of distributions. The statistical properties studied include expansion of the density function, hazard rate and quantile functions, moments, moment generating functions, probability weighted moments, stochastic ordering, distribution of order statistics and Rényi entropy. The maximum likelihood, ordinary and weighted least-squares techniques for the estimation of model parameters are presented, and Monte Carlo simulations for the new family of distributions are conducted. The importance of the new family of distributions is examined by means of applications to two real data sets.","PeriodicalId":117214,"journal":{"name":"Revista Colombiana de Estadística","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139360125","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 : 2023-07-12DOI: 10.15446/rce.v46n2.104591
Rajesh Singh, Anamika Kumari
This paper presents improved population mean estimators using auxiliary variables in Stratified Ranked Set Sampling. We have derived the expressions for bias and mean square errors up to the first order of approximation and shown that the proposed estimators under optimum conditions are more efficient than other estimators taken in this paper. In an attempt to verify the efficiencies of proposed estimators, theoretical results are supported by numerical illustrations and simulation study for which we have considered two populations.
{"title":"Some Improved Combined Estimators of Population Mean in Stratified Ranked Set Sampling","authors":"Rajesh Singh, Anamika Kumari","doi":"10.15446/rce.v46n2.104591","DOIUrl":"https://doi.org/10.15446/rce.v46n2.104591","url":null,"abstract":"This paper presents improved population mean estimators using auxiliary variables in Stratified Ranked Set Sampling. We have derived the expressions for bias and mean square errors up to the first order of approximation and shown that the proposed estimators under optimum conditions are more efficient than other estimators taken in this paper. In an attempt to verify the efficiencies of proposed estimators, theoretical results are supported by numerical illustrations and simulation study for which we have considered two populations.","PeriodicalId":117214,"journal":{"name":"Revista Colombiana de Estadística","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139360138","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 : 2023-07-12DOI: 10.15446/rce.v46n2.103412
Fernando Arturo Peña Ramírez, R. Guerra, G. Cordeiro
We introduce a four-parameter model called the Weibull Nadarajah-Haghighi distribution. It is obtained by inserting the Nadarajah-Haghighi distribution in the Weibull-G family. The proposed distribution can produce constant, increasing, decreasing, bathtub, and upside down-bathtub hazard rate shapes, which are the most important in lifetime analysis. We explore some structural properties, including the quantile function, ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, and Rényi entropy. The maximum likelihood method is used to estimate the model parameters. A simulation study is formed to examine the precision of the estimates. The usefulness of the new distribution is illustrated through two applications to real data. The new model provides better fits than some widely known lifetime distributions.
{"title":"A New Nadarajah-Haghighi Generalization with Five Different Shapes for the Hazard Function","authors":"Fernando Arturo Peña Ramírez, R. Guerra, G. Cordeiro","doi":"10.15446/rce.v46n2.103412","DOIUrl":"https://doi.org/10.15446/rce.v46n2.103412","url":null,"abstract":"We introduce a four-parameter model called the Weibull Nadarajah-Haghighi distribution. It is obtained by inserting the Nadarajah-Haghighi distribution in the Weibull-G family. The proposed distribution can produce constant, increasing, decreasing, bathtub, and upside down-bathtub hazard rate shapes, which are the most important in lifetime analysis. We explore some structural properties, including the quantile function, ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, and Rényi entropy. The maximum likelihood method is used to estimate the model parameters. A simulation study is formed to examine the precision of the estimates. The usefulness of the new distribution is illustrated through two applications to real data. The new model provides better fits than some widely known lifetime distributions.","PeriodicalId":117214,"journal":{"name":"Revista Colombiana de Estadística","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139360254","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 : 2023-07-12DOI: 10.15446/rce.v46n2.105209
Neo Dingalo, B. Oluyede, Fastel Chipepa
This paper introduces and investigates a new family of distributions called the Topp-Leone-Gompertz-exponentiated half logistic-G (TL-Gom-EHL-G) distribution. Some mathematical and statistical properties of this family of distributions are derived. To estimate and evaluate the model parameters, the maximum likelihood estimation technique is used, and the consistency of maximum likelihood estimators is examined using Monte Carlo simulation. Applications to three real data sets from different areas were used to demonstrates the usefulness and versatility of the TL-Gom-EHL-G family of distributions.
{"title":"The Topp-Leone-Gompertz-Exponentiated Half Logistic-G Family of Distributions with Applications","authors":"Neo Dingalo, B. Oluyede, Fastel Chipepa","doi":"10.15446/rce.v46n2.105209","DOIUrl":"https://doi.org/10.15446/rce.v46n2.105209","url":null,"abstract":"This paper introduces and investigates a new family of distributions called the Topp-Leone-Gompertz-exponentiated half logistic-G (TL-Gom-EHL-G) distribution. Some mathematical and statistical properties of this family of distributions are derived. To estimate and evaluate the model parameters, the maximum likelihood estimation technique is used, and the consistency of maximum likelihood estimators is examined using Monte Carlo simulation. Applications to three real data sets from different areas were used to demonstrates the usefulness and versatility of the TL-Gom-EHL-G family of distributions.","PeriodicalId":117214,"journal":{"name":"Revista Colombiana de Estadística","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139360222","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 : 2023-07-12DOI: 10.15446/rce.v46n2.104019
Juan Carlos Salazar Uribe, Mauricio A Mazo Lopera, Juan Carlos Correa Morales
Linear mixed effects models are highly flexible in handling correlated data by considering covariance matrices that explain variation patterns between and within clusters. For these covariance matrices, there exist a wide list of possible structures proposed by researchers in multiple scientific areas. Maximum likelihood is the most common estimation method in linear mixed models and it depends on the structured covariance matrices for random effects and errors. Classical methods used to optimize the likelihood function, such as Newton-Raphson or Fisher's scoring, require analytical procedures to obtain parametrical restrictions to guarantee positive definiteness for the structured matrices and it is not, in general, an easy task. To avoid dealing with complex restrictions, we propose an adaptive method that incorporates the so-called Hybrid Genetic Algorithms with a penalization technique based on minimum eigenvalues to guarantee positive definiteness in an evolutionary process which discards non-viable cases. The proposed method is evaluated through simulations and its performance is compared with that of Newton-Raphson algorithm implemented in SAS® PROC MIXED V9.4.
{"title":"An Adaptive Method for Likelihood Optimization in Linear Mixed Models Under Constrained Search Spaces","authors":"Juan Carlos Salazar Uribe, Mauricio A Mazo Lopera, Juan Carlos Correa Morales","doi":"10.15446/rce.v46n2.104019","DOIUrl":"https://doi.org/10.15446/rce.v46n2.104019","url":null,"abstract":"Linear mixed effects models are highly flexible in handling correlated data by considering covariance matrices that explain variation patterns between and within clusters. For these covariance matrices, there exist a wide list of possible structures proposed by researchers in multiple scientific areas. Maximum likelihood is the most common estimation method in linear mixed models and it depends on the structured covariance matrices for random effects and errors. Classical methods used to optimize the likelihood function, such as Newton-Raphson or Fisher's scoring, require analytical procedures to obtain parametrical restrictions to guarantee positive definiteness for the structured matrices and it is not, in general, an easy task. To avoid dealing with complex restrictions, we propose an adaptive method that incorporates the so-called Hybrid Genetic Algorithms with a penalization technique based on minimum eigenvalues to guarantee positive definiteness in an evolutionary process which discards non-viable cases. The proposed method is evaluated through simulations and its performance is compared with that of Newton-Raphson algorithm implemented in SAS® PROC MIXED V9.4.","PeriodicalId":117214,"journal":{"name":"Revista Colombiana de Estadística","volume":"198 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139360176","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 : 2023-07-12DOI: 10.15446/rce.v46n2.98005
Adriana Marcela Salazar, Jaime Abel Huertas
The survival competing risks model in discrete time based on multinomial logistic regression, proposed by Luo et al. (2016), models the non-linear and irregular shape of hazard functions by incorporating a time-dependent spline into the multinomial logistic regression. This model also directly includes longitudinal variables in the regression. Due to the issues arising from including both baseline and longitudinal covariates in the extended form as proposed, and considering that the latter may be subject to error, this article suggests an extension of the existing model. The proposed extension utilizes the concept of joint models for longitudinal and survival data, which is an effective approach for integrating simultaneousness both baseline and time-dependent covariates into the survival model.,
{"title":"A Joint Model of Competing Risks in Discrete Time with Longitudinal Information","authors":"Adriana Marcela Salazar, Jaime Abel Huertas","doi":"10.15446/rce.v46n2.98005","DOIUrl":"https://doi.org/10.15446/rce.v46n2.98005","url":null,"abstract":"The survival competing risks model in discrete time based on multinomial logistic regression, proposed by Luo et al. (2016), models the non-linear and irregular shape of hazard functions by incorporating a time-dependent spline into the multinomial logistic regression. This model also directly includes longitudinal variables in the regression. Due to the issues arising from including both baseline and longitudinal covariates in the extended form as proposed, and considering that the latter may be subject to error, this article suggests an extension of the existing model. The proposed extension utilizes the concept of joint models for longitudinal and survival data, which is an effective approach for integrating simultaneousness both baseline and time-dependent covariates into the survival model.,","PeriodicalId":117214,"journal":{"name":"Revista Colombiana de Estadística","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139360201","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 : 2021-07-12DOI: 10.15446/rce.v44n2.89661
Karen Rosana Cordoba Perozo, Alvaro Mauricio Montenegro Díaz
Evaluations of professor performance are based on the assumption that students learn more from highly qualified professors and the fact that students observe professor performance in the classroom. However, many studies question the methodologies used for such measurements, in general, because the averages of categorical responses make little statistical sense. In this paper, we propose Bayesian multi-faceted item response theory models to measure teaching performance. The basic model takes into account effects associated with the severity of the students responding to the survey, and the courses that are evaluated. The basic model proposed in this work is applied to a data set obtained from a survey of perception of professor performance conducted by Science Faculty of the Universidad Nacional de Colombia to its students. professor scores that are obtained as model outputs are real numerical values that can be used to calculate common statistics in professor evaluation. In this case, the statistics are mathematically consistent. Some of them are shown to illustrate the usefulness of the model.
{"title":"Bayesian Multi-Faceted TRI Models for Measuring Professor's Performance in the Classroom","authors":"Karen Rosana Cordoba Perozo, Alvaro Mauricio Montenegro Díaz","doi":"10.15446/rce.v44n2.89661","DOIUrl":"https://doi.org/10.15446/rce.v44n2.89661","url":null,"abstract":"Evaluations of professor performance are based on the assumption that students learn more from highly qualified professors and the fact that students observe professor performance in the classroom. However, many studies question the methodologies used for such measurements, in general, because the averages of categorical responses make little statistical sense. In this paper, we propose Bayesian multi-faceted item response theory models to measure teaching performance. The basic model takes into account effects associated with the severity of the students responding to the survey, and the courses that are evaluated. The basic model proposed in this work is applied to a data set obtained from a survey of perception of professor performance conducted by Science Faculty of the Universidad Nacional de Colombia to its students. professor scores that are obtained as model outputs are real numerical values that can be used to calculate common statistics in professor evaluation. In this case, the statistics are mathematically consistent. Some of them are shown to illustrate the usefulness of the model.","PeriodicalId":117214,"journal":{"name":"Revista Colombiana de Estadística","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123898387","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 : 2018-07-01DOI: 10.15446/rce.v41n2.65654
M. Bolbolian Ghalibaf
Determining the extent of a disparity, if any, between groups of people, for example, race or gender, is of interest in many fields, including public health for medical treatment and prevention of disease or in discrimination cases concerning equal pay to estimate the pay disparities between minority and majority employees. An observed difference in the mean outcome between a majority/advantaged group (AG) and minority/disadvantaged group (DG) can be due to differences in the distribution of relevant covariates. The Peters Belson (PB) method fits a regression model with covariates to the AG to predict, for each DG member, their outcome measure as if they had been from the AG. The difference between the mean predicted and the mean observed outcomes of DG members is the (unexplained) disparity of interest. PB regression is a form of statistical matching, akin in spirit to Bhattacharya's band-width matching. In this paper we review the use of PB regression in legal cases from Hikawa et al. (2010b) Parametric and nonparametric approaches to PB regression are described and we show that in nonparametric PB regression choose a kernel function can be better resulted, i.e. by selecting the appropriate kernel function we can reduce bias and variance of estimators, also increase power of test.
{"title":"Kernel Function in Local Linear Peters-Belson Regression","authors":"M. Bolbolian Ghalibaf","doi":"10.15446/rce.v41n2.65654","DOIUrl":"https://doi.org/10.15446/rce.v41n2.65654","url":null,"abstract":"Determining the extent of a disparity, if any, between groups of people, for example, race or gender, is of interest in many fields, including public health for medical treatment and prevention of disease or in discrimination cases concerning equal pay to estimate the pay disparities between minority and majority employees. An observed difference in the mean outcome between a majority/advantaged group (AG) and minority/disadvantaged group (DG) can be due to differences in the distribution of relevant covariates. The Peters Belson (PB) method fits a regression model with covariates to the AG to predict, for each DG member, their outcome measure as if they had been from the AG. The difference between the mean predicted and the mean observed outcomes of DG members is the (unexplained) disparity of interest. PB regression is a form of statistical matching, akin in spirit to Bhattacharya's band-width matching. In this paper we review the use of PB regression in legal cases from Hikawa et al. (2010b) Parametric and nonparametric approaches to PB regression are described and we show that in nonparametric PB regression choose a kernel function can be better resulted, i.e. by selecting the appropriate kernel function we can reduce bias and variance of estimators, also increase power of test.","PeriodicalId":117214,"journal":{"name":"Revista Colombiana de Estadística","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127772688","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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