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Estimation of Cumulative Incidence Function in the Presence of Middle Censoring Using Improper Gompertz Distribution 利用不适当Gompertz分布估计中间滤波存在下的累积关联函数
IF 1.9
Statistica Pub Date : 2021-10-26 DOI: 10.6092/ISSN.1973-2201/12309
H. Rehman, N. Chandra
{"title":"Estimation of Cumulative Incidence Function in the Presence of Middle Censoring Using Improper Gompertz Distribution","authors":"H. Rehman, N. Chandra","doi":"10.6092/ISSN.1973-2201/12309","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/12309","url":null,"abstract":"In this paper we deal with the modelling of cumulative incidence function using improper Gompertz distribution based on middle censored competing risks survival data. Together with the unknown parameters, cumulative incidence function also estimated. In classical set up, we derive the point estimates using maximum likelihood estimator and midpoint approximation methods. The asymptotic confidence interval are obtained based on asymptotic normality properties of maximum likelihood estimator. We also derive the Bayes estimates with associated credible intervals based on informative and non-informative types of priors under two loss functions such as squared error and LINEX loss functions. A simulation study is conducted for comprehensive comparison between various estimators proposed in this paper. A real life data set is also used for illustration.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48154934","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}
引用次数: 1
Polynomial Columns-Parameter Symmetry Model and its Decomposition for Square Contingency Tables 平方列联表的多项式列参数对称模型及其分解
IF 1.9
Statistica Pub Date : 2021-10-26 DOI: 10.6092/ISSN.1973-2201/12090
S. Ando
{"title":"Polynomial Columns-Parameter Symmetry Model and its Decomposition for Square Contingency Tables","authors":"S. Ando","doi":"10.6092/ISSN.1973-2201/12090","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/12090","url":null,"abstract":"This study proposes a polynomial columns-parameter symmetry model for square contingency tables with the same row and column ordinal classifications. In the proposed model, the odds for all i < j that an observation will fall in row category i and column category j instead of row category j and column category i depend on only the value of column category j . The proposed model is original because many asymmetry models in square contingency tables depend on the both values of row and column category. The proposed model constantly holds when the columns-parameter symmetry model holds; but the converse does not necessarily hold. This study shows that it is necessary to satisfy the polynomial columns-marginal symmetry model, in addition to the columns-parameter symmetry model, to satisfy the proposed model. This decomposition theorem is useful for explaining why the proposed model does not hold. Moreover, this study shows the value of likelihood ratio chi-square statistic for testing the proposed model is equal to the sum of that for testing the decomposed two models.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44026585","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}
引用次数: 0
The Marshall-Olkin Gompertz Distribution: Properties and Applications Marshall-Olkin-Gompertz分布：性质与应用
IF 1.9
Statistica Pub Date : 2021-10-26 DOI: 10.6092/ISSN.1973-2201/10993
J. T. Eghwerido, Joel Oruaoghene Ogbo, Adebola Evelyn Omotoye
{"title":"The Marshall-Olkin Gompertz Distribution: Properties and Applications","authors":"J. T. Eghwerido, Joel Oruaoghene Ogbo, Adebola Evelyn Omotoye","doi":"10.6092/ISSN.1973-2201/10993","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/10993","url":null,"abstract":"This article introduces three parameters class for lifetime Poisson processes in the Marshall-Olkin transformation family that are increasing, bathtub and skewed. Some structural mathematical properties of the Marshall-Olkin Gompertz (MO-G) model were derived. The MO-G model parameters were established by maximum likelihood approach. The flexibility, efficiency, and behavior of the MO-G model estimators were examined through simulation. The empirical applicability, flexibility and proficiency of the MO-G model was scrutinized by a real-life dataset. The proposed MO-G model provides a better fit when compared to existing models in statistical literature and can serve as an alternative model to those appearing in modeling Poisson processes.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47704331","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}
引用次数: 2
A Class of Univariate Non-Mesokurtic Distributions Using a Continuous Uniform Symmetrizer and Chi Generator 一类使用连续均匀对称器和Chi发生器的单变量非中丘分布
IF 1.9
Statistica Pub Date : 2021-10-26 DOI: 10.6092/ISSN.1973-2201/12336
Kamala Naganathan Radhalakshmi, M. L. William
{"title":"A Class of Univariate Non-Mesokurtic Distributions Using a Continuous Uniform Symmetrizer and Chi Generator","authors":"Kamala Naganathan Radhalakshmi, M. L. William","doi":"10.6092/ISSN.1973-2201/12336","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/12336","url":null,"abstract":"In a good number of real life situations, the observations on a random variable of interest tend to concentrate either too closely or too thinly around a central point but symmetrically like the normal distribution. The symmetric structure of the density function appears like that of a normal distribution but the concentration of the observations can be either thicker or thinner around the mean. This paper attempts to generate a family of densities that are symmetric like normal butwith different kurtosis. Drawing inspiration from a recent work on multivariate leptokurtic normal distribution, this paper seeks to consider the univariate case and adopt a different approach to generate a family to be called ’univariate non-mesokurtic normal’ family.The symmetricity of the densities is brought out by a uniform random variable while the kurtosis variation is brought about by a chi generator. Some of the properties of the resulting class of distributions and the pameter estimation are discussed.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45353938","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}
引用次数: 0
A New Discrete Distribution: Properties, Characterizations, Modeling Real Count Data, Bayesian and Non-Bayesian Estimations 一种新的离散分布:性质、表征、实数数据建模、贝叶斯和非贝叶斯估计
IF 1.9
Statistica Pub Date : 2021-10-26 DOI: 10.6092/ISSN.1973-2201/11635
H. Yousof, C. Chesneau, G. Hamedani, M. Ibrahim
{"title":"A New Discrete Distribution: Properties, Characterizations, Modeling Real Count Data, Bayesian and Non-Bayesian Estimations","authors":"H. Yousof, C. Chesneau, G. Hamedani, M. Ibrahim","doi":"10.6092/ISSN.1973-2201/11635","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/11635","url":null,"abstract":"In this work, a new discrete distribution which includes the discrete Burr-Hatke distribution is defined and studied. Relevant statistical properties are derived. The probability mass function of the new distribution can be \"right skewed\" with different shapes, bimodal and \"uniformed\". Also, the corresponding hazard rate function can be \"monotonically decreasing\", \"upside down\", \"monotonically increasing\", \"upside down increasing\", and \"upside down-constant-increasing\". A numerical analysis for the mean, variance, skewness, kurtosis and the index of dispersion is presented. The new distribution could be useful in the modeling of \"under-dispersed\" or \"overdispersed\" count data. Certain characterizations of the new distribution are presented. These characterizations are based on the conditional expectation of a certain function of the random variable and in terms of the hazard rate function. Bayesian and non-Bayesian estimation methods are considered. Numerical simulations for comparing Bayesian and non-Bayesian estimation methods are performed. The new model is applied for modeling carious teeth data and counts of cysts of kidneys data.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41761097","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}
引用次数: 11
The Zografos-Balakrishnan Lindley Distribution: Properties and Applications Zografos-Balakrishnan-Lindley分布的性质与应用
IF 1.9
Statistica Pub Date : 2021-09-03 DOI: 10.6092/ISSN.1973-2201/11101
M. Irshad, Veena D’cruz, R. Maya
{"title":"The Zografos-Balakrishnan Lindley Distribution: Properties and Applications","authors":"M. Irshad, Veena D’cruz, R. Maya","doi":"10.6092/ISSN.1973-2201/11101","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/11101","url":null,"abstract":"The Lindley distribution was proposed in the context of Bayesian statistics as a counter example of fiducial statistics. In this paper, we propose Zografos Balakrishnan Lindley (ZBL) distribution in which Lindley distribution is a special case. Some properties of the new distribution is obtained such as moments, hazard rate function, reliability function etc. The parameters are estimated using the method of maximum likelihood. Finally an application of the proposed distribution to a real data set is illustrated and it is concluded that Zogarfos Balakrishnan Lindley (ZBL) distribution provides better fit than other classical distributions.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43417314","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}
引用次数: 4
Robust Estimations of Survival Function for Weibull Distribution 威布尔分布生存函数的鲁棒估计
IF 1.9
Statistica Pub Date : 2021-09-03 DOI: 10.6092/ISSN.1973-2201/12433
D. Karagöz, N. A. Tutkun
{"title":"Robust Estimations of Survival Function for Weibull Distribution","authors":"D. Karagöz, N. A. Tutkun","doi":"10.6092/ISSN.1973-2201/12433","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/12433","url":null,"abstract":"The aim of this study is to estimate the robust survival function for the Weibull distribution. Since the survival function of Weibull distribution is based on the parameters, we consider two robust and explicit Weibull parameter estimators proposed by Boudt et al. (2011). The quantile and the quantile least squares which are all robust to censored data is used as an alternative to the maximum likelihood estimation of the Weibull parameters. The proposed estimators are applied to Hodgin’s disease data which produces smaller variances for the robust survival function. The advantage of new methods is that they are numerically explicit in applications. Monte Carlo simulation is performed to compare the behaviours of the proposed robust estimators in the presence of right, left and interval censored observations considering different censoring rates. The simulation results show that the proposed robust estimators are better than the maximum likelihood estimator.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45711778","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}
引用次数: 0
Muth Distribution and Estimation of a Parameter Using Order Statistics 用序统计量估计参数的分布和估计
IF 1.9
Statistica Pub Date : 2021-09-03 DOI: 10.6092/ISSN.1973-2201/9432
M. Irshad, R. Maya, Sasikumar Arun
{"title":"Muth Distribution and Estimation of a Parameter Using Order Statistics","authors":"M. Irshad, R. Maya, Sasikumar Arun","doi":"10.6092/ISSN.1973-2201/9432","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/9432","url":null,"abstract":"In this work, we have considered a lifetime distribution namely Muth distribution and pointed out instances where it appears as a good model to study the stochastic nature of the variable under consideration. We have derived the best linear unbiased estimator (BLUE) of the scale parameter of the Muth distribution based on order statistics for some known values of the shape parameter.We have further estimated the scale parameter of Muth distribution by U-statistics  based on best linear functions of order statistics as kernels. The efficiency of the BLUE relative to the usual unbiased estimator has been also evaluated. An illustration describing the performance of U-statistics estimation method when compared with the classical maximum likelihood method is also given.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41827213","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}
引用次数: 1
Characterization of Generalized Distribution by Doubly Truncated Moment 用双截矩刻画广义分布
IF 1.9
Statistica Pub Date : 2021-09-03 DOI: 10.6092/ISSN.1973-2201/10718
Haseeb Athar, Y. Abdel-Aty, M. A. Ali
{"title":"Characterization of Generalized Distribution by Doubly Truncated Moment","authors":"Haseeb Athar, Y. Abdel-Aty, M. A. Ali","doi":"10.6092/ISSN.1973-2201/10718","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/10718","url":null,"abstract":"In this paper characterization properties based on conditional expectation of a continuous function of random variable are studied when truncation is from both the sides, left and right. Then, these results are applied to obtain the k-th doubly truncated moment for a general class of distribution. Further, some examples and particular cases based on this general class of distributions are also demonstrated. The results are obtained in simple and explicit manner which also unifies the earlier results obtained by several authors. In the end, simulation study is performed to validate the correctness of theoretical characterization results and then two real life data sets are used to demonstrate the applications of these results.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45107827","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}
引用次数: 0
A Flexible Bathtub-Shaped Failure Time Model: Properties and Associated Inference 一个柔性浴盆形失效时间模型的性质及相关推断
IF 1.9
Statistica Pub Date : 2021-09-03 DOI: 10.6092/ISSN.1973-2201/10025
N. Choudhary, Abhishek Tyagi, B. Singh
{"title":"A Flexible Bathtub-Shaped Failure Time Model: Properties and Associated Inference","authors":"N. Choudhary, Abhishek Tyagi, B. Singh","doi":"10.6092/ISSN.1973-2201/10025","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/10025","url":null,"abstract":"In this study, we introduce an extended version of the modified Weibull distribution with an additional shape parameter, in order to provide more flexibility to its density and the hazard rate function. The distribution is capable of modeling the bathtub-shaped, decreasing, increasing and the constant hazard rate function. The proposed model contains sub-models that are widely used in lifetime data analysis such as the modified Weibull, Chen, extreme value, Weibull, Rayleigh, and exponential distributions. We study its statistical properties which include the hazard rate function, moments and distribution of the order statistics. The parameters involved in the model are estimated by using maximum likelihood and the Bayesian method of estimation. In Bayesian estimation, we assume independent Gamma priors for the parameters and MCMC technique such as the Metropolis-Hastings algorithm within Gibbs sampler has been implemented to obtain the sample-based estimators and the highest posterior density intervals of the parameters. Tierney and Kadane (1986) approximation is also used to obtain Bayes estimators of the parameters. In order to highlight the relative importance of various estimates obtained, a simulation study is carried out. The usefulness of the proposed model is illustrated using two real datasets.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49010290","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}
引用次数: 0
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