Pub Date : 2020-10-14DOI: 10.1285/I20705948V13N2P413
M’barek Iaousse, Zouhair Elhadri, M. Hanafi, P. Dolce, Y. Elkettani
The present paper announces and demonstrates some useful properties of the impliedcorrelation matrix built by the Finite Iterative Method (Elhadri and Hanafi,2015, 2016; Elhadri et al., 2019) The most important property is that the impliedcorrelation matrix is affine for each of its parameters. In other words, the firstderivative with respect to each parameter does not depend on this parameter. Moreover,two properties affirm that the first and the second derivatives can be builtiteratively using the previous property. The final property shows that the secondderivatives with respect to every pair ofparameters in the same structural equationare null. These properties are very important in the sense that they can be used toconstruct a new computational approach to estimate recursive model parameters.These findings can be exploited in the estimation stage implementation, especiallyin the computation of the Newton Raphson algorithm to make the first and the secondderivatives of the discrepancy function more explicit and simplistic.
本文宣布并证明了有限迭代法建立的隐相关矩阵的一些有用性质（Elhadri和Hanafi，20152016；Elhadri et al.，2019）。最重要的性质是隐相关矩阵对其每个参数都是仿射的。换句话说，关于每个参数的一阶导数不取决于这个参数。此外，有两个性质证实了一阶导数和二阶导数可以使用前面的性质重复构建。最后的性质表明，对于同一结构方程中的每一对参数的二阶导数为零。这些性质非常重要，因为它们可以用来构建一种新的计算方法来估计递归模型参数。这些发现可以在估计阶段的实现中加以利用，特别是在Newton-Raphson算法的计算中，使差异函数的一阶和二阶导数更加明确和简单。
{"title":"Properties of the Correlation Matrix Implied by a Recursive Path Model using the Finite Iterative Method","authors":"M’barek Iaousse, Zouhair Elhadri, M. Hanafi, P. Dolce, Y. Elkettani","doi":"10.1285/I20705948V13N2P413","DOIUrl":"https://doi.org/10.1285/I20705948V13N2P413","url":null,"abstract":"The present paper announces and demonstrates some useful properties of the impliedcorrelation matrix built by the Finite Iterative Method (Elhadri and Hanafi,2015, 2016; Elhadri et al., 2019) The most important property is that the impliedcorrelation matrix is affine for each of its parameters. In other words, the firstderivative with respect to each parameter does not depend on this parameter. Moreover,two properties affirm that the first and the second derivatives can be builtiteratively using the previous property. The final property shows that the secondderivatives with respect to every pair ofparameters in the same structural equationare null. These properties are very important in the sense that they can be used toconstruct a new computational approach to estimate recursive model parameters.These findings can be exploited in the estimation stage implementation, especiallyin the computation of the Newton Raphson algorithm to make the first and the secondderivatives of the discrepancy function more explicit and simplistic.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":"24 9","pages":"413-435"},"PeriodicalIF":0.7,"publicationDate":"2020-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41267513","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 : 2020-10-14DOI: 10.1285/I20705948V13N2P375
Farideh Tavazoee, D. Buscaldi, F. Mola, C. Conversano
The role of Twitter as a platform to share opinions has been growing in the recent years especially since it has been widely used by public personae such as politicians, personalities of the show business, and other influencers to communicate with the public. For these reasons, the use of social bots to manipulate information and influence people's opinions is also growing. In this paper, we use a supervised classification model to distinguish bots from legitimate users on Twitter. More specifically, we show the importance of sentiment features in bot-human account detection. Moreover, we evaluate our detection model by testing on Russian bot accounts who are the most recent set of social bots that appeared on Twitter to show that these techniques may be easily adapted to work on new, unseen types of social bots.
{"title":"Empowering Detection of Malicious Social Bots and Content Spammers on Twitter by Sentiment Analysis","authors":"Farideh Tavazoee, D. Buscaldi, F. Mola, C. Conversano","doi":"10.1285/I20705948V13N2P375","DOIUrl":"https://doi.org/10.1285/I20705948V13N2P375","url":null,"abstract":"The role of Twitter as a platform to share opinions has been growing in the recent years especially since it has been widely used by public personae such as politicians, personalities of the show business, and other influencers to communicate with the public. For these reasons, the use of social bots to manipulate information and influence people's opinions is also growing. In this paper, we use a supervised classification model to distinguish bots from legitimate users on Twitter. More specifically, we show the importance of sentiment features in bot-human account detection. Moreover, we evaluate our detection model by testing on Russian bot accounts who are the most recent set of social bots that appeared on Twitter to show that these techniques may be easily adapted to work on new, unseen types of social bots.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":"13 1","pages":"375-389"},"PeriodicalIF":0.7,"publicationDate":"2020-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43287275","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 : 2020-10-14DOI: 10.1285/I20705948V13N2P284
A. Olosunde, A. T. Soyinkab
It is common to assume a normal distribution when discriminating and classifying a multivariate data based on some attributes. But when such data is lighter or heavier in both tails than the normal distribution, then the probability of misclassification becomes higher giving unreliable result. This study proposed multivariate exponential power distribution a family of elliptically contoured model as underlining model for discrimination and classification. The distribution has a shape parameter which regulate the tail of the symmetric distribution to mitigate the problem of both lighter and heavier tails data, this generalizes the normal distribution and thus will definitely gives a lower misclassification error in discrimination and classification. The resulting discriminant model was compared with fisher linear discriminant function when applying to real data.
{"title":"Discrimination and Classification model from Multivariate Exponential Power Distribution","authors":"A. Olosunde, A. T. Soyinkab","doi":"10.1285/I20705948V13N2P284","DOIUrl":"https://doi.org/10.1285/I20705948V13N2P284","url":null,"abstract":"It is common to assume a normal distribution when discriminating and classifying a multivariate data based on some attributes. But when such data is lighter or heavier in both tails than the normal distribution, then the probability of misclassification becomes higher giving unreliable result. This study proposed multivariate exponential power distribution a family of elliptically contoured model as underlining model for discrimination and classification. The distribution has a shape parameter which regulate the tail of the symmetric distribution to mitigate the problem of both lighter and heavier tails data, this generalizes the normal distribution and thus will definitely gives a lower misclassification error in discrimination and classification. The resulting discriminant model was compared with fisher linear discriminant function when applying to real data.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":"13 1","pages":"284-292"},"PeriodicalIF":0.7,"publicationDate":"2020-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45164898","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 : 2020-02-05DOI: 10.1285/I20705948V13N1P256
Giovanna Di Lorenzo, A. Orlando, Massimo Politano
The reverse mortgage market has been expanding rapidly in developed economies in recent years. Reverse mortgages provide an alternative source of funding for retirement income and health care costs. Increase in life expectancies and decrease in the real income at retirement continue to worry the those who are retired or close to retirement. Therefore, financial products that help to alleviate the “risk of living longer” continue to be attractive among the retirees. Reverse mortgage contracts involve a range of risks from the insurer’s perspective. When the outstanding balance exceeds the housing value before the loan is settled, the insurer suffers an exposure to crossover risk induced by three risk factors: interest rates, house prices and mortality rates. We analyse the combined impact of these risks on the pricing and the risk profile of reverse mortgage loans in a stochastic interest-mortality-house pricing model. Our results show shows that pricing of reverse mortgages loans does not accurately assess the risks underwritten by reverse mortgages lenders and that failing to take into account mortality improvements substantially underestimates the longevity risk involved in reverse mortgage loans.
{"title":"The security mortgage valuation in a stochastic perspective","authors":"Giovanna Di Lorenzo, A. Orlando, Massimo Politano","doi":"10.1285/I20705948V13N1P256","DOIUrl":"https://doi.org/10.1285/I20705948V13N1P256","url":null,"abstract":"The reverse mortgage market has been expanding rapidly in developed economies in recent years. Reverse mortgages provide an alternative source of funding for retirement income and health care costs. Increase in life expectancies and decrease in the real income at retirement continue to worry the those who are retired or close to retirement. Therefore, financial products that help to alleviate the “risk of living longer” continue to be attractive among the retirees. Reverse mortgage contracts involve a range of risks from the insurer’s perspective. When the outstanding balance exceeds the housing value before the loan is settled, the insurer suffers an exposure to crossover risk induced by three risk factors: interest rates, house prices and mortality rates. We analyse the combined impact of these risks on the pricing and the risk profile of reverse mortgage loans in a stochastic interest-mortality-house pricing model. Our results show shows that pricing of reverse mortgages loans does not accurately assess the risks underwritten by reverse mortgages lenders and that failing to take into account mortality improvements substantially underestimates the longevity risk involved in reverse mortgage loans.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":"13 1","pages":"256-267"},"PeriodicalIF":0.7,"publicationDate":"2020-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48259100","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 : 2020-02-05DOI: 10.1285/I20705948V13N1P146
P. N. Inverardi, E. Taufer
The paper investigates the use of a finite mixture model with an additional uniform density for outlier detection and robust estimation. The main contribution of this paper lies in the analysis of the properties of the improper component and the introduction of a modified EM algorithm which, beyond providing the maximum likelihood estimates of the mixture parameters, endogenously provides a numerical value for the density of the uniform distribution used for the improper component. The mixing proportion of outliers may be known or unknown. Applications to robust estimation and outlier detection will be discussed with particular attention to the normal mixture case.
{"title":"Outlier detection through mixtures with an improper component","authors":"P. N. Inverardi, E. Taufer","doi":"10.1285/I20705948V13N1P146","DOIUrl":"https://doi.org/10.1285/I20705948V13N1P146","url":null,"abstract":"The paper investigates the use of a finite mixture model with an additional uniform density for outlier detection and robust estimation. The main contribution of this paper lies in the analysis of the properties of the improper component and the introduction of a modified EM algorithm which, beyond providing the maximum likelihood estimates of the mixture parameters, endogenously provides a numerical value for the density of the uniform distribution used for the improper component. The mixing proportion of outliers may be known or unknown. Applications to robust estimation and outlier detection will be discussed with particular attention to the normal mixture case.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":"13 1","pages":"146-163"},"PeriodicalIF":0.7,"publicationDate":"2020-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44548209","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 : 2020-02-05DOI: 10.1285/I20705948V13N1P1
Norihiro Mita, H. Sasaki, K. Kani, A. Tabuchi, H. Hara
To establish the computer assisted system of the visual acuity test, we propose a statistical modelling of the visual acuity measurement and its multiple test procedure. The psychometric functions for individual patients are produced by the logistic regression combined with the guessing rate. We adopt test statistics based on (i) psychometric functions (the Cochran-Mantel-Haenszel method) and (ii) psychophysical thresholds (the delta method). The multiple comparisons are performed by the step-down procedure with Ryan-Einot-Gabriel-Welsch (REGW) significance levels. To show the practical effectiveness of our system, we present a numerical example of four patient groups.
为了建立计算机辅助视力测试系统，我们提出了一种视力测量的统计模型及其多重测试程序。个体患者的心理测量函数是通过逻辑回归与猜测率相结合产生的。我们采用基于（i）心理测量函数（Cochran-Mantel-Haenszel方法）和（ii）心理物理阈值（delta方法）的测试统计。多重比较通过降压程序与Ryan Einot Gabriel Welsch（REGW）显著性水平进行。为了显示我们的系统的实际有效性，我们给出了四个患者组的数值示例。
{"title":"A statistical modelling of the visual acuity measurement and its multiple test procedure","authors":"Norihiro Mita, H. Sasaki, K. Kani, A. Tabuchi, H. Hara","doi":"10.1285/I20705948V13N1P1","DOIUrl":"https://doi.org/10.1285/I20705948V13N1P1","url":null,"abstract":"To establish the computer assisted system of the visual acuity test, we propose a statistical modelling of the visual acuity measurement and its multiple test procedure. The psychometric functions for individual patients are produced by the logistic regression combined with the guessing rate. We adopt test statistics based on (i) psychometric functions (the Cochran-Mantel-Haenszel method) and (ii) psychophysical thresholds (the delta method). The multiple comparisons are performed by the step-down procedure with Ryan-Einot-Gabriel-Welsch (REGW) significance levels. To show the practical effectiveness of our system, we present a numerical example of four patient groups.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":"13 1","pages":"1-15"},"PeriodicalIF":0.7,"publicationDate":"2020-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1285/I20705948V13N1P1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43221644","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 : 2020-02-05DOI: 10.1285/I20705948V13N1P16
J. Divecha, Jigneshkumar Gondaliya
The assumption of carryover effects is unavoidable due to the very nature of crossover designs. Even in case of crossover design with washout period, the hypothesis of no carryover effect should be tested and established. On the other hand, this assumption makes the analysis difficult and potentially biased or inefficient in case of two treatment two period crossover design. For a reasonable estimation, experimenters are advocated to employ a two period three treatment crossover designs, or a three period two treatment crossover design. In this article, we present optional analyses of a uniform three period three treatment crossover design, consisting of a placebo and two active treatments. We develop a test for detecting presence of carryover effects which directs experimenter for a proper analysis of his crossover trial. We present ANOVA for each of the three possible carryover models, that both, single, or none of the active treatments has carryover effect, and illustrate through an example.
{"title":"Optional analyses of crossover trials having two treatments and a placebo","authors":"J. Divecha, Jigneshkumar Gondaliya","doi":"10.1285/I20705948V13N1P16","DOIUrl":"https://doi.org/10.1285/I20705948V13N1P16","url":null,"abstract":"The assumption of carryover effects is unavoidable due to the very nature of crossover designs. Even in case of crossover design with washout period, the hypothesis of no carryover effect should be tested and established. On the other hand, this assumption makes the analysis difficult and potentially biased or inefficient in case of two treatment two period crossover design. For a reasonable estimation, experimenters are advocated to employ a two period three treatment crossover designs, or a three period two treatment crossover design. In this article, we present optional analyses of a uniform three period three treatment crossover design, consisting of a placebo and two active treatments. We develop a test for detecting presence of carryover effects which directs experimenter for a proper analysis of his crossover trial. We present ANOVA for each of the three possible carryover models, that both, single, or none of the active treatments has carryover effect, and illustrate through an example.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":"13 1","pages":"16-30"},"PeriodicalIF":0.7,"publicationDate":"2020-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1285/I20705948V13N1P16","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43658692","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 : 2020-02-05DOI: 10.1285/I20705948V13N1P75
H. Kuswanto, Nesia Balqis, H. Ohwada, S.F. Toha
Colorectal cancer has become one of the cancer types with high incidence rate all over the world. Various eorts have been carried out to nd a way to decrease the risk of cancer. Chemotherapy using 5-Fluorouracil (5-FU) is one of the common cancer treatments that is expected to drive the white blood cell (WBC) level into the normal level. This research investigates the factors inuencing the change of WBC level in cancer patients treated with 5-FU combined with physical treatment in the form of footsteps. By focusing on the change of WBC level, i.e. decreasing or increasing the WBC level as the response, probit regression was applied to the data measured from 28 cancer patients who have undergone 14 days of treatment. The probit regression found that age of the patient, average number of daily footsteps and the dose of 5-FU signcantly inuence the change of WBC. The regression is able to classify the case with a satisfactory results, i.e. 85.71% classication accuracy. This nding can be a guideline to better treat the colorectal cancer patient to reach a normal WBC.
{"title":"Modelling the Change of White Blood Cell on Colorectal Cancer Treatment Using Probit Regression","authors":"H. Kuswanto, Nesia Balqis, H. Ohwada, S.F. Toha","doi":"10.1285/I20705948V13N1P75","DOIUrl":"https://doi.org/10.1285/I20705948V13N1P75","url":null,"abstract":"Colorectal cancer has become one of the cancer types with high incidence rate all over the world. Various eorts have been carried out to nd a way to decrease the risk of cancer. Chemotherapy using 5-Fluorouracil (5-FU) is one of the common cancer treatments that is expected to drive the white blood cell (WBC) level into the normal level. This research investigates the factors inuencing the change of WBC level in cancer patients treated with 5-FU combined with physical treatment in the form of footsteps. By focusing on the change of WBC level, i.e. decreasing or increasing the WBC level as the response, probit regression was applied to the data measured from 28 cancer patients who have undergone 14 days of treatment. The probit regression found that age of the patient, average number of daily footsteps and the dose of 5-FU signcantly inuence the change of WBC. The regression is able to classify the case with a satisfactory results, i.e. 85.71% classication accuracy. This nding can be a guideline to better treat the colorectal cancer patient to reach a normal WBC.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":"13 1","pages":"75-85"},"PeriodicalIF":0.7,"publicationDate":"2020-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47812476","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 : 2020-02-05DOI: 10.1285/I20705948V13N1P47
T. Ogura, H. Murakami
Canonical correlation analysis (CCA) is often used to analyze correlations between the variables of two random vectors. As an extension of CCA, multiple-set canonical correlation analysis (MCCA) was proposed to analyze correlations between multiple-set random vectors. However, sometimes interpreting MCCA results may not be as straightforward as interpreting CCA results. Principal CCA (PCCA), which uses CCA between two sets of principal component (PC) scores, was proposed to address these difficulties in CCA. We propose multiple-set PCCA (MPCCA) by applying the idea to multiple-set of PC scores. PCs are ranked in descending order according to the amount of information they contain. Therefore, it is enough to use only a few PC scores from the top instead of using all PC scores. Decreasing the number of PC makes it easy to interpret the result. We confirmed the effectiveness of MPCCA using simulation studies and a practical example.
{"title":"Canonical Correlation Analysis of Principal Component Scores for Multiple-set Random Vectors","authors":"T. Ogura, H. Murakami","doi":"10.1285/I20705948V13N1P47","DOIUrl":"https://doi.org/10.1285/I20705948V13N1P47","url":null,"abstract":"Canonical correlation analysis (CCA) is often used to analyze correlations between the variables of two random vectors. As an extension of CCA, multiple-set canonical correlation analysis (MCCA) was proposed to analyze correlations between multiple-set random vectors. However, sometimes interpreting MCCA results may not be as straightforward as interpreting CCA results. Principal CCA (PCCA), which uses CCA between two sets of principal component (PC) scores, was proposed to address these difficulties in CCA. We propose multiple-set PCCA (MPCCA) by applying the idea to multiple-set of PC scores. PCs are ranked in descending order according to the amount of information they contain. Therefore, it is enough to use only a few PC scores from the top instead of using all PC scores. Decreasing the number of PC makes it easy to interpret the result. We confirmed the effectiveness of MPCCA using simulation studies and a practical example.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":"13 1","pages":"47-74"},"PeriodicalIF":0.7,"publicationDate":"2020-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49330884","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 : 2020-02-05DOI: 10.1285/I20705948V13N1P229
M. Shakhatreh, Abedel-Qader Al-Masri
We take an in-depth look at the weighted Burr-XII distribution. This distribu-tion generalizes Burr-XII, Lomax, and log-logistic distributions. We discuss the dis-tributional characteristics of the probability density function, the failure rate function,and mean residual lifetime of this distribution. Moreover, we obtain various statisti-cal properties of this distribution such as moment generating function, entropies, meandeviations, order statistics and stochastic ordering. The estimation of the distributionparameters via maximum likelihood method and the observed Fisher information ma-trix are discussed. We further employ a simulation study to investigate the behavior ofthe maximum likelihood estimates (MLEs). A test concerning the existence of size-biasin the sample is provided. In the end, a real data is presented and is analyzed usingthis distribution along with some existing distributions for illustrative purposes.
{"title":"On The Weighted BurrXII Distribution: Theory and Practice","authors":"M. Shakhatreh, Abedel-Qader Al-Masri","doi":"10.1285/I20705948V13N1P229","DOIUrl":"https://doi.org/10.1285/I20705948V13N1P229","url":null,"abstract":"We take an in-depth look at the weighted Burr-XII distribution. This distribu-tion generalizes Burr-XII, Lomax, and log-logistic distributions. We discuss the dis-tributional characteristics of the probability density function, the failure rate function,and mean residual lifetime of this distribution. Moreover, we obtain various statisti-cal properties of this distribution such as moment generating function, entropies, meandeviations, order statistics and stochastic ordering. The estimation of the distributionparameters via maximum likelihood method and the observed Fisher information ma-trix are discussed. We further employ a simulation study to investigate the behavior ofthe maximum likelihood estimates (MLEs). A test concerning the existence of size-biasin the sample is provided. In the end, a real data is presented and is analyzed usingthis distribution along with some existing distributions for illustrative purposes.","PeriodicalId":44770,"journal":{"name":"Electronic Journal of Applied Statistical Analysis","volume":"13 1","pages":"229-255"},"PeriodicalIF":0.7,"publicationDate":"2020-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1285/I20705948V13N1P229","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45886040","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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