International Journal of Statistics and Probability, 2013
ABSTRACT The binomial outcome data are widely encountered in many real world applications. The Bi... more ABSTRACT The binomial outcome data are widely encountered in many real world applications. The Binomial distribution often fails to model the binomial outcomes since the variance of the observed binomial outcome data exceeds the nominal Binomial distribution variance, a phenomenon known as overdispersion. One way of handling overdispersion is modeling the success probability of the Binomial distribution using a continuous distribution defined on the standard unit interval. The resultant general class of univariate discrete distributions is known as the class of Binomial mixture distributions. The Beta-Binomial (BB) distribution is a prominent member of this class of distributions. The Kumaraswamy-Binomial (KB) distribution is another recent member of this class. In this paper we focus the emphasis on the McDonald's Generalized Beta distribution of the first kind as the mixing distribution and introduce a new Binomial mixture distribution called the McDonald Generalized Beta-Binomial distribution(McGBB). Some theoretical properties of McGBB are discussed. The parameters of the McGBB distribution are estimated via maximum likelihood estimation technique. A real world dataset is modeled by using the new McGBB mixture distribution, and it is shown that this model gives better fit than its nested models. Finally, an extended simulation study is presented to compare the McGBB distribution with its nested distributions in handling overdispersed binomial outcome data.
ABSTRACT Proceedings of the Peradeniya University Research Sessions, Sri Lanka, Vol. 16, 24th Nov... more ABSTRACT Proceedings of the Peradeniya University Research Sessions, Sri Lanka, Vol. 16, 24th November 2011 - page 163 A Spatial Analysis of the Human-Elephant Conflict in Sri Lanka S. Thiripura3, P. Wijekoon1, C. Santiapillai2 and S. Wijeyamohan3 1Department of Statistics and Computer Science, Faculty of Science, University of Peradeniya 2Department of Zoology, Faculty of Science, University of Peradeniya 3Postgraduate Institute of Science, University of Peradeniya The Human-Elephant Conflict (HEC) is normally viewed from the point of view of the elephants, but this survey was conducted to identify the difficulties farmers face due to elephants in their day-to-day life. With the increase in human population density and changes in land-use patterns, elephant habitat is being continuously reduced and as a result, much of the present day elephant range extends into and overlaps with agricultural lands. The main objectives of the survey were to discover a spatial pattern of the conflict, identify hot spots and formulate a plan to decrease HEC in Sri Lanka based on the identified spatial pattern. An assessment of HEC by the Ringling Center for Elephant Conservation (CEC) was carried out from January to March, 2009, within 186 villages in seven provinces (Central, Northern, Uva, Eastern, North Central, North Western and Southern). The sample was selected using judgmental sampling within the elephant range and was collected by stopping every 10 km. Ordinary statistics and geospatial statistics were used to analyse in this survey. All variables were examined separately in order to identify its behaviour and plots were drawn based on preliminary analysis. A spatial analysis was performed to identify the high conflict areas. The tabular and graphical forms of the severity points were included and a spatial model found. R, Minitab and SPSS statistical software and ArcGIS spatial software were used in this analysis. According to the spatial analysis, a Gaussian model could be identified as the spatial model for severity of the conflict. The minimum minimised square was obtained using weighted least square methods (WLS). Therefore, the model obtained for WLS was used as the best-estimated variogram. Due to small sample size, a provincial level krigging could not be done. Based on the plots and model obtained, it was noted that Puttalam and Kuchavelli are the areas with the highest level of conflict. Correlations among parameters affect the spatial distribution of the conflict level. Therefore, krigging and co-krigging methods could be used to identify highly correlated variables in further studies.
International Journal of Statistics and Probability, 2013
ABSTRACT The binomial outcome data are widely encountered in many real world applications. The Bi... more ABSTRACT The binomial outcome data are widely encountered in many real world applications. The Binomial distribution often fails to model the binomial outcomes since the variance of the observed binomial outcome data exceeds the nominal Binomial distribution variance, a phenomenon known as overdispersion. One way of handling overdispersion is modeling the success probability of the Binomial distribution using a continuous distribution defined on the standard unit interval. The resultant general class of univariate discrete distributions is known as the class of Binomial mixture distributions. The Beta-Binomial (BB) distribution is a prominent member of this class of distributions. The Kumaraswamy-Binomial (KB) distribution is another recent member of this class. In this paper we focus the emphasis on the McDonald's Generalized Beta distribution of the first kind as the mixing distribution and introduce a new Binomial mixture distribution called the McDonald Generalized Beta-Binomial distribution(McGBB). Some theoretical properties of McGBB are discussed. The parameters of the McGBB distribution are estimated via maximum likelihood estimation technique. A real world dataset is modeled by using the new McGBB mixture distribution, and it is shown that this model gives better fit than its nested models. Finally, an extended simulation study is presented to compare the McGBB distribution with its nested distributions in handling overdispersed binomial outcome data.
ABSTRACT Proceedings of the Peradeniya University Research Sessions, Sri Lanka, Vol. 16, 24th Nov... more ABSTRACT Proceedings of the Peradeniya University Research Sessions, Sri Lanka, Vol. 16, 24th November 2011 - page 163 A Spatial Analysis of the Human-Elephant Conflict in Sri Lanka S. Thiripura3, P. Wijekoon1, C. Santiapillai2 and S. Wijeyamohan3 1Department of Statistics and Computer Science, Faculty of Science, University of Peradeniya 2Department of Zoology, Faculty of Science, University of Peradeniya 3Postgraduate Institute of Science, University of Peradeniya The Human-Elephant Conflict (HEC) is normally viewed from the point of view of the elephants, but this survey was conducted to identify the difficulties farmers face due to elephants in their day-to-day life. With the increase in human population density and changes in land-use patterns, elephant habitat is being continuously reduced and as a result, much of the present day elephant range extends into and overlaps with agricultural lands. The main objectives of the survey were to discover a spatial pattern of the conflict, identify hot spots and formulate a plan to decrease HEC in Sri Lanka based on the identified spatial pattern. An assessment of HEC by the Ringling Center for Elephant Conservation (CEC) was carried out from January to March, 2009, within 186 villages in seven provinces (Central, Northern, Uva, Eastern, North Central, North Western and Southern). The sample was selected using judgmental sampling within the elephant range and was collected by stopping every 10 km. Ordinary statistics and geospatial statistics were used to analyse in this survey. All variables were examined separately in order to identify its behaviour and plots were drawn based on preliminary analysis. A spatial analysis was performed to identify the high conflict areas. The tabular and graphical forms of the severity points were included and a spatial model found. R, Minitab and SPSS statistical software and ArcGIS spatial software were used in this analysis. According to the spatial analysis, a Gaussian model could be identified as the spatial model for severity of the conflict. The minimum minimised square was obtained using weighted least square methods (WLS). Therefore, the model obtained for WLS was used as the best-estimated variogram. Due to small sample size, a provincial level krigging could not be done. Based on the plots and model obtained, it was noted that Puttalam and Kuchavelli are the areas with the highest level of conflict. Correlations among parameters affect the spatial distribution of the conflict level. Therefore, krigging and co-krigging methods could be used to identify highly correlated variables in further studies.
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