Pub Date : 2020-06-14DOI: 10.19139/soic-2310-5070-557
Luiz Paulo Fávero, P. Belfiore, Marco Aurélio dos Santos, R. F. Souza
Stata has several procedures that can be used in analyzing count-data regression models and, more specifically, in studying the behavior of the dependent variable, conditional on explanatory variables. Identifying overdispersion in countdata models is one of the most important procedures that allow researchers to correctly choose estimations such as Poisson or negative binomial, given the distribution of the dependent variable. The main purpose of this paper is to present a new command for the identification of overdispersion in the data as an alternative to the procedure presented by Cameron and Trivedi [5], since it directly identifies overdispersion in the data, without the need to previously estimate a specific type of count-data model. When estimating Poisson or negative binomial regression models in which the dependent variable is quantitative, with discrete and non-negative values, the new Stata package overdisp helps researchers to directly propose more consistent and adequate models. As a second contribution, we also present a simulation to show the consistency of the overdispersion test using the overdisp command. Findings show that, if the test indicates equidispersion in the data, there are consistent evidence that the distribution of the dependent variable is, in fact, Poisson. If, on the other hand, the test indicates overdispersion in the data, researchers should investigate more deeply whether the dependent variable actually exhibits better adherence to the Poisson-Gamma distribution or not.
{"title":"Overdisp: A Stata (and Mata) Package for Direct Detection of Overdispersion in Poisson and Negative Binomial Regression Models","authors":"Luiz Paulo Fávero, P. Belfiore, Marco Aurélio dos Santos, R. F. Souza","doi":"10.19139/soic-2310-5070-557","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-557","url":null,"abstract":"Stata has several procedures that can be used in analyzing count-data regression models and, more specifically, in studying the behavior of the dependent variable, conditional on explanatory variables. Identifying overdispersion in countdata models is one of the most important procedures that allow researchers to correctly choose estimations such as Poisson or negative binomial, given the distribution of the dependent variable. The main purpose of this paper is to present a new command for the identification of overdispersion in the data as an alternative to the procedure presented by Cameron and Trivedi [5], since it directly identifies overdispersion in the data, without the need to previously estimate a specific type of count-data model. When estimating Poisson or negative binomial regression models in which the dependent variable is quantitative, with discrete and non-negative values, the new Stata package overdisp helps researchers to directly propose more consistent and adequate models. As a second contribution, we also present a simulation to show the consistency of the overdispersion test using the overdisp command. Findings show that, if the test indicates equidispersion in the data, there are consistent evidence that the distribution of the dependent variable is, in fact, Poisson. If, on the other hand, the test indicates overdispersion in the data, researchers should investigate more deeply whether the dependent variable actually exhibits better adherence to the Poisson-Gamma distribution or not.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"773-789"},"PeriodicalIF":0.0,"publicationDate":"2020-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42759716","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 : 2020-06-10DOI: 10.19139/soic-2310-5070-976
A. Verster, Lizanne Raubenheimer Department of Mathematical Statistics, Actuarial Science, U. State, Bloemfontein, S. Africa, School of Mathematical, Statistical Sciences, North-West University, Potchefstroom
In Extreme Value methodology the choice of threshold plays an important role in efficient modelling of observations exceeding the threshold. The threshold must be chosen high enough to ensure an unbiased extreme value index but choosing the threshold too high results in uncontrolled variances. This paper investigates a generalized model that can assist in the choice of optimal threshold values in the γ positive domain. A Bayesian approach is considered by deriving a posterior distribution for the unknown generalized parameter. Using the properties of the posterior distribution allows for a method to choose an optimal threshold without visual inspection.
{"title":"A Different Approach for Choosing a Threshold in Peaks over Threshold","authors":"A. Verster, Lizanne Raubenheimer Department of Mathematical Statistics, Actuarial Science, U. State, Bloemfontein, S. Africa, School of Mathematical, Statistical Sciences, North-West University, Potchefstroom","doi":"10.19139/soic-2310-5070-976","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-976","url":null,"abstract":"In Extreme Value methodology the choice of threshold plays an important role in efficient modelling of observations exceeding the threshold. The threshold must be chosen high enough to ensure an unbiased extreme value index but choosing the threshold too high results in uncontrolled variances. This paper investigates a generalized model that can assist in the choice of optimal threshold values in the γ positive domain. A Bayesian approach is considered by deriving a posterior distribution for the unknown generalized parameter. Using the properties of the posterior distribution allows for a method to choose an optimal threshold without visual inspection.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84410200","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 : 2020-05-29DOI: 10.19139/soic-2310-5070-614
Haseeb Athar, Zubdahe Noor, S. Zarrin, H. Almutairi
The Poisson Lomax distribution was proposed by [3], as a useful model for analyzing lifetime data. In this paper,we have derived recurrence relations for single and product moments of generalized order statistics for this distribution. Further, characterization of the distribution is carried out. Some deductions and particular cases are also discussed.
{"title":"Expectation Properties of Generalized Order Statistics from Poisson Lomax Distribution","authors":"Haseeb Athar, Zubdahe Noor, S. Zarrin, H. Almutairi","doi":"10.19139/soic-2310-5070-614","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-614","url":null,"abstract":"The Poisson Lomax distribution was proposed by [3], as a useful model for analyzing lifetime data. In this paper,we have derived recurrence relations for single and product moments of generalized order statistics for this distribution. Further, characterization of the distribution is carried out. Some deductions and particular cases are also discussed.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84195253","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 : 2020-05-28DOI: 10.19139/soic-2310-5070-648
V. Sivaramaraju, Nilambar Sethi, R. Rajender
Cricket is popularly known as the game of gentlemen. The game of cricket has been introduced to the World by England. Since the introduction till date, it has become the second most ever popular game. In this context, few a data mining and analytical techniques have been proposed for the same. In this work, two different scenario have been considered for the prediction of winning team based on several parameters. These scenario are taken for two different standard formats for the game namely, one day international (ODI) cricket and twenty-twenty cricket (T-20). The prediction approaches differ from each other based on the types of parameters considered and the corresponding functional strategies. The strategies proposed here adopts two different approaches. One approach is for the winner prediction for one-day matches and the other is for predicting the winner for a T-20 match. The approaches have been proposed separately for both the versions of the game pertaining to the intra-variability in the strategies adopted by a team and individuals for each. The proposed strategies for each of the two scenarios have been individually evaluated against existing benchmark works, and for each of the cases the duo of approaches have outperformed the rest in terms of the prediction accuracy. The novel heuristics proposed herewith reflects efficiency and accuracy with respect to prediction of cricket data.
{"title":"Heuristics for Winner Prediction in International Cricket Matches","authors":"V. Sivaramaraju, Nilambar Sethi, R. Rajender","doi":"10.19139/soic-2310-5070-648","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-648","url":null,"abstract":"Cricket is popularly known as the game of gentlemen. The game of cricket has been introduced to the World by England. Since the introduction till date, it has become the second most ever popular game. In this context, few a data mining and analytical techniques have been proposed for the same. In this work, two different scenario have been considered for the prediction of winning team based on several parameters. These scenario are taken for two different standard formats for the game namely, one day international (ODI) cricket and twenty-twenty cricket (T-20). The prediction approaches differ from each other based on the types of parameters considered and the corresponding functional strategies. The strategies proposed here adopts two different approaches. One approach is for the winner prediction for one-day matches and the other is for predicting the winner for a T-20 match. The approaches have been proposed separately for both the versions of the game pertaining to the intra-variability in the strategies adopted by a team and individuals for each. The proposed strategies for each of the two scenarios have been individually evaluated against existing benchmark works, and for each of the cases the duo of approaches have outperformed the rest in terms of the prediction accuracy. The novel heuristics proposed herewith reflects efficiency and accuracy with respect to prediction of cricket data.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"602-609"},"PeriodicalIF":0.0,"publicationDate":"2020-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45722682","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 : 2020-05-28DOI: 10.19139/soic-2310-5070-678
M. Ibrahim, E. Ea, H. Yousof
In this paper and after introducing a new model along with its properties, we estimate the unknown parameter of the new model using the maximum likelihood method, Cramér-Von-Mises method, bootstrapping method, least square method and weighted least square method. We assess the performance of all estimation method employing simulations. All methods perform well but bootstrapping method is the best in modeling relief times whereas the maximum likelihood method is the best in modeling survival times. Censored data modeling with covariates is addressed along with the index plot of the modified deviance residuals and its Q-Q plot.
{"title":"A New Distribution for Modeling Lifetime Data with Different Methods of Estimation and Censored Regression Modeling","authors":"M. Ibrahim, E. Ea, H. Yousof","doi":"10.19139/soic-2310-5070-678","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-678","url":null,"abstract":"In this paper and after introducing a new model along with its properties, we estimate the unknown parameter of the new model using the maximum likelihood method, Cramér-Von-Mises method, bootstrapping method, least square method and weighted least square method. We assess the performance of all estimation method employing simulations. All methods perform well but bootstrapping method is the best in modeling relief times whereas the maximum likelihood method is the best in modeling survival times. Censored data modeling with covariates is addressed along with the index plot of the modified deviance residuals and its Q-Q plot.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"610-630"},"PeriodicalIF":0.0,"publicationDate":"2020-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48725986","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 : 2020-05-28DOI: 10.19139/soic-2310-5070-802
M. Hashempour, M. Doostparast, Zohreh Pakdaman
This paper deals with systems consisting of independent and heterogeneous exponential components. Since failures of components may change lifetimes of surviving components because of load sharing, a linear trend for conditionally proportional hazard rates is considered. Estimates of parameters, both point and interval estimates, are derived on the basis of observed component failures for s(≥ 2) systems. Fisher information matrix of the available data is also obtained which can be used for studying asymptotic behaviour of estimates. The generalized likelihood ratio test is implemented for testing homogeneity of s systems. Illustrative examples are also given.
{"title":"Statistical Inference on the Basis of Sequential Order Statistics under a Linear Trend for Conditional Proportional Hazard Rates","authors":"M. Hashempour, M. Doostparast, Zohreh Pakdaman","doi":"10.19139/soic-2310-5070-802","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-802","url":null,"abstract":"This paper deals with systems consisting of independent and heterogeneous exponential components. Since failures of components may change lifetimes of surviving components because of load sharing, a linear trend for conditionally proportional hazard rates is considered. Estimates of parameters, both point and interval estimates, are derived on the basis of observed component failures for s(≥ 2) systems. Fisher information matrix of the available data is also obtained which can be used for studying asymptotic behaviour of estimates. The generalized likelihood ratio test is implemented for testing homogeneity of s systems. Illustrative examples are also given.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"462-470"},"PeriodicalIF":0.0,"publicationDate":"2020-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45751076","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 : 2020-05-28DOI: 10.19139/soic-2310-5070-751
Narinder Pushkarna, J. Saran, Kanika Verma
In this paper some recurrence relations satisfied by single and product moments of progressively Type-II right censored order statistics from Hjorth distribution have been obtained. Then we use these results to compute the moments for all sample sizes and all censoring schemes (R1, R2, ..., Rm),m ≤ n, which allow us to obtain BLUEs of location and scale parameters based on progressively Type-II right censored samples. The best linear unbiased predictors of censored failure times are then discussed briefly. Finally, a numerical example with real data is presented to illustrate the inferential method developed here.
{"title":"Progressively Type-II Right Censored Order Statistics from Hjorth Distribution and Related Inference","authors":"Narinder Pushkarna, J. Saran, Kanika Verma","doi":"10.19139/soic-2310-5070-751","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-751","url":null,"abstract":"In this paper some recurrence relations satisfied by single and product moments of progressively Type-II right censored order statistics from Hjorth distribution have been obtained. Then we use these results to compute the moments for all sample sizes and all censoring schemes (R1, R2, ..., Rm),m ≤ n, which allow us to obtain BLUEs of location and scale parameters based on progressively Type-II right censored samples. The best linear unbiased predictors of censored failure times are then discussed briefly. Finally, a numerical example with real data is presented to illustrate the inferential method developed here.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"481-498"},"PeriodicalIF":0.0,"publicationDate":"2020-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48966773","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 : 2020-05-28DOI: 10.19139/soic-2310-5070-638
G. Askari, M. Gordji
In this paper, we provide an interpretation of the rationality in game theory in which player consider the profit or loss of the opponent in addition to personal profit at the game. The goal of a game analysis with two hyper-rationality players is to provide insight into real-world situations that are often more complex than a game with two rational players where the choices of strategy are only based on individual preferences. The hyper-rationality does not mean perfect rationality but an insight toward how human decision-makers behave in interactive decisions. The findings of this research can help to enlarge our understanding of the psychological aspects of strategy choices in games and also provide an analysis of the decision-making process with cognitive economics approach at the same time.
{"title":"Decision Making: Rational Choice or Hyper-Rational Choice","authors":"G. Askari, M. Gordji","doi":"10.19139/soic-2310-5070-638","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-638","url":null,"abstract":"In this paper, we provide an interpretation of the rationality in game theory in which player consider the profit or loss of the opponent in addition to personal profit at the game. The goal of a game analysis with two hyper-rationality players is to provide insight into real-world situations that are often more complex than a game with two rational players where the choices of strategy are only based on individual preferences. The hyper-rationality does not mean perfect rationality but an insight toward how human decision-makers behave in interactive decisions. The findings of this research can help to enlarge our understanding of the psychological aspects of strategy choices in games and also provide an analysis of the decision-making process with cognitive economics approach at the same time.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"583-589"},"PeriodicalIF":0.0,"publicationDate":"2020-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46911344","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 : 2020-05-28DOI: 10.19139/soic-2310-5070-869
Rafid S. A. Alshkaki
In this paper, a generalized modification of the Kumaraswamy distribution is proposed, and its distributional and characterizing properties are studied. This distribution is closed under scaling and exponentiation, and has some well-known distributions as special cases, such as the generalized uniform, triangular, beta, power function, Minimax, and some other Kumaraswamy related distributions. Moment generating function, Lorenz and Bonferroni curves, with its moments consisting of the mean, variance, moments about the origin, harmonic, incomplete, probability weighted, L, and trimmed L moments, are derived. The maximum likelihood estimation method is used for estimating its parameters and applied to six different simulated data sets of this distribution, in order to check the performance of the estimation method through the estimated parameters mean squares errors computed from the different simulated sample sizes. Finally, four real-life data sets are used to illustrate the usefulness and the flexibility of this distribution in application to real-life data.
{"title":"A Generalized Modification of the Kumaraswamy Distribution for Modeling and Analyzing Real-Life Data","authors":"Rafid S. A. Alshkaki","doi":"10.19139/soic-2310-5070-869","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-869","url":null,"abstract":"In this paper, a generalized modification of the Kumaraswamy distribution is proposed, and its distributional and characterizing properties are studied. This distribution is closed under scaling and exponentiation, and has some well-known distributions as special cases, such as the generalized uniform, triangular, beta, power function, Minimax, and some other Kumaraswamy related distributions. Moment generating function, Lorenz and Bonferroni curves, with its moments consisting of the mean, variance, moments about the origin, harmonic, incomplete, probability weighted, L, and trimmed L moments, are derived. The maximum likelihood estimation method is used for estimating its parameters and applied to six different simulated data sets of this distribution, in order to check the performance of the estimation method through the estimated parameters mean squares errors computed from the different simulated sample sizes. Finally, four real-life data sets are used to illustrate the usefulness and the flexibility of this distribution in application to real-life data.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"521-548"},"PeriodicalIF":0.0,"publicationDate":"2020-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41871209","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 : 2020-05-27DOI: 10.19139/soic-2310-5070-628
B. Sartono, A. Syaiful, Dian Ayuningtyas, F. Afendi, R. Anisa, A. Salim
The sparsity principle suggests that the number of effects that contribute significantly to the response variable of an experiment is small. It means that the researchers need an efficient selection procedure to identify those active effects. Most common procedures can be found in literature work by considering an effect as an individual entity so that selection process works on individual effect. Another principle we should consider in experimental data analysis is the heredity principle. This principle allows an interaction effect is included in the model only if the correspondence main effects are there in. This paper addresses the selection problem that takes into account the heredity principle as Yuan and Lin [23] did using least angle regression (LARS). Instead of selecting the effects individually, the proposed approach perform the selection process in groups. The advantage our proposed approach, using genetic algorithm, is on the opportunity to determine the number of desired effect, which the LARS approach cannot.
{"title":"Active Effects Selection which Considers Heredity Principle in Multi-Factor Experiment Data Analysis","authors":"B. Sartono, A. Syaiful, Dian Ayuningtyas, F. Afendi, R. Anisa, A. Salim","doi":"10.19139/soic-2310-5070-628","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-628","url":null,"abstract":"The sparsity principle suggests that the number of effects that contribute significantly to the response variable of an experiment is small. It means that the researchers need an efficient selection procedure to identify those active effects. Most common procedures can be found in literature work by considering an effect as an individual entity so that selection process works on individual effect. Another principle we should consider in experimental data analysis is the heredity principle. This principle allows an interaction effect is included in the model only if the correspondence main effects are there in. This paper addresses the selection problem that takes into account the heredity principle as Yuan and Lin [23] did using least angle regression (LARS). Instead of selecting the effects individually, the proposed approach perform the selection process in groups. The advantage our proposed approach, using genetic algorithm, is on the opportunity to determine the number of desired effect, which the LARS approach cannot.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"414-424"},"PeriodicalIF":0.0,"publicationDate":"2020-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42423398","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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