# fitODBOD v1.4.1-1

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## Modeling Over Dispersed Binomial Outcome Data Using BMD and ABD

Contains Probability Mass Functions, Cumulative Mass Functions, Negative Log Likelihood value, parameter estimation and modeling data using Binomial Mixture Distributions (BMD) (Manoj et al (2013) <doi:10.5539/ijsp.v2n2p24>) and Alternate Binomial Distributions (ABD) (Paul (1985) <doi:10.1080/03610928508828990>), also Journal article to use the package(<doi:10.21105/joss.01505>).

## Functions in fitODBOD

 Name Description EstMLEMcGBB Estimating the shape parameters a,b and c for McDonald Generalized Beta Binomial distribution EstMLETriBin Estimating the mode value for Triangular Binomial Distribution Exam_data Exam Data EstMLEGammaBin Estimating the shape parameters c and l for Gamma Binomial distribution EstMLEGrassiaIIBin Estimating the shape parameters a and b for Grassia II Binomial distribution NegLLGrassiaIIBin Negative Log Likelihood value of Grassia II Binomial Distribution EstMLEMultiBin Estimating the probability of success and theta for Multiplicative Binomial Distribution NegLLKumBin Negative Log Likelihood value of Kumaraswamy Binomial Distribution EstMLECorrBin Estimating the probability of success and correlation for Correlated Binomial Distribution EstMLEGHGBB Estimating the shape parameters a,b and c for Gaussian Hypergeometric Generalized Beta Binomial Distribution Course_data Course Data NegLLGHGBB Negative Log Likelihood value of Gaussian Hypergeometric Generalized Beta Binomial Distribution EstMLELMBin Estimating the probability of success and theta for Lovinson Multiplicative Binomial Distribution EstMLEKumBin Estimating the shape parameters a and b and iterations for Kumaraswamy Binomial Distribution NegLLBetaBin Negative Log Likelihood value of Beta-Binomial Distribution NegLLGammaBin Negative Log Likelihood value of Gamma Binomial Distribution Overdispersion Overdispersion dAddBin Additive Binomial Distribution NegLLMcGBB Negative Log Likelihood value of McDonald Generalized Beta Binomial Distribution dKUM Kumaraswamy Distribution NegLLLMBin Negative Log Likelihood value of Lovinson Multiplicative Binomial distribution dGHGBB Gaussian Hypergeometric Generalized Beta Binomial Distribution dGHGBeta Gaussian Hypergeometric Generalized Beta Distribution NegLLBetaCorrBin Negative Log Likelihood value of Beta-Correlated Binomial distribution dBETA Beta Distribution dKumBin Kumaraswamy Binomial Distribution fitLMBin Fitting the Lovinson Multiplicative Binomial Distribution when binomial random variable, frequency, probability of success and theta parameter are given fitKumBin Fitting the Kumaraswamy Binomial Distribution when binomial random variable, frequency and shape parameters a and b, iterations parameter it are given dCorrBin Correlated Binomial Distribution fitAddBin Fitting the Additive Binomial Distribution when binomial random variable, frequency, probability of success and alpha are given Plant_DiseaseData Plant Disease Incidence data dUniBin Uniform Binomial Distribution dCOMPBin COM Poisson Binomial Distribution fitBin Fitting the Binomial Distribution when binomial random variable, frequency and probability value are given Male_Children Male children data fitCOMPBin Fitting the COM Poisson Binomial Distribution when binomial random variable, frequency, probability of success and v parameter are given dBetaCorrBin Beta-Correlated Binomial Distribution NegLLCorrBin Negative Log Likelihood value of Correlated Binomial distribution NegLLTriBin Negative Log Likelihood value of Triangular Binomial Distribution dUNI Uniform Distribution Bounded Between [0,1] NegLLCOMPBin Negative Log Likelihood value of COM Poisson Binomial distribution NegLLMultiBin Negative Log Likelihood value of Multiplicative Binomial distribution dTriBin Triangular Binomial Distribution dBetaBin Beta-Binomial Distribution NegLLAddBin Negative Log Likelihood value of Additive Binomial distribution dGammaBin Gamma Binomial Distribution Terror_data_ARG Terror Data ARG mazBETA Beta Distribution fitTriBin Fitting the Triangular Binomial Distribution when binomial random variable, frequency and mode value are given dMcGBB McDonald Generalized Beta Binomial Distribution fitGrassiaIIBin Fitting the Grassia II Binomial distribution when binomial random variable, frequency and shape parameters are given dGrassiaIIBin Grassia-II-Binomial Distribution mazGHGBeta Gaussian Hypergeometric Generalized Beta Distribution fitGammaBin Fitting the Gamma Binomial distribution when binomial random variable, frequency and shape parameters are given dLMBin Lovinson Multiplicative Binomial Distribution Terror_data_USA Terror Data USA mazKUM Kumaraswamy Distribution pGHGBB Gaussian Hypergeometric Generalized Beta Binomial Distribution mazTRI Triangular Distribution Bounded Between [0,1] pBetaBin Beta-Binomial Distribution pKumBin Kumaraswamy Binomial Distribution pAddBin Additive Binomial Distribution pKUM Kumaraswamy Distribution mazGAMMA Gamma Distribution mazUNI Uniform Distribution Bounded Between [0,1] fitBetaBin Fitting the Beta-Binomial Distribution when binomial random variable, frequency and shape parameters a and b are given dGAMMA Gamma Distribution fitBetaCorrBin Fitting the Beta-Correlated Binomial Distribution when binomial random variable, frequency, covariance, alpha and beta parameters are given pBETA Beta Distribution dGBeta1 Generalized Beta Type-1 Distribution mazGBeta1 Generalized Beta Type-1 Distribution pLMBin Lovinson Multiplicative Binomial Distribution pBetaCorrBin Beta-Correlated Binomial Distribution pMcGBB McDonald Generalized Beta Binomial Distribution pGammaBin Gamma Binomial Distribution pUniBin Uniform Binomial Distribution pGrassiaIIBin Grassia-II-Binomial Distribution pGHGBeta Gaussian Hypergeometric Generalized Beta Distribution pGBeta1 Generalized Beta Type-1 Distribution pMultiBin Multiplicative Binomial Distribution pGAMMA Gamma Distribution dMultiBin Multiplicative Binomial Distribution dTRI Triangular Distribution Bounded Between [0,1] fitCorrBin Fitting the Correlated Binomial Distribution when binomial random variable, frequency, probability of success and covariance are given fitGHGBB Fitting the Gaussian Hypergeometric Generalized Beta Binomial Distribution when binomial random variable, frequency and shape parameters a,b and c are given pCOMPBin COM Poisson Binomial Distribution fitMultiBin Fitting the Multiplicative Binomial Distribution when binomial random variable, frequency, probability of success and theta parameter are given fitMcGBB Fitting the McDonald Generalized Beta Binomial distribution when binomial random variable, frequency and shape parameters are given pTRI Triangular Distribution Bounded Between [0,1] pTriBin Triangular Binomial Distribution pUNI Uniform Distribution Bounded Between [0,1] pCorrBin Correlated Binomial Distribution Alcohol_data Alcohol data EstMLEBetaBin Estimating the shape parameters a and b for Beta-Binomial Distribution EstMLEAddBin Estimating the probability of success and alpha for Additive Binomial Distribution EstMLECOMPBin Estimating the probability of success and v parameter for COM Poisson Binomial Distribution EstMLEBetaCorrBin Estimating the covariance, alpha and beta parameter values for Beta-Correlated Binomial Distribution Epidemic_Cold Family Epidemics BODextract Binomial Data Extraction from Raw data Chromosome_data Chromosome Data EstMGFBetaBin Estimating the shape parameters a and b for Beta-Binomial Distribution No Results!