مطالعه و مدل بندي داده هاي شمارشي دوگانه آماسيده

چكيده انگليسي :

Study and Modeling of dual inflation count Data Maryam Loghmanian m loghmanin@math iut ac ir July 2 2019 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Zahra Saberi z saberi@cc iut ac ir2000 MSC 62F10 62J12 60E99 Keywords Zero inflated poisson distribution overdispersion Gibbs sampling Abstract This M S c thesis is based on the following papers Wagh Y S and Kamalja K K Zero Inflated models and estimation in Zero Inflated Poisson distribution Communications in Statistics Simulation and Computation 2017 Lin T H and Tsai M H Modeling data with a truncated and inflated Poisson distribution Statistical Method ology Vol 41 No 3 pp 253 272 2017 The modeling of count data is of a primary interest in many fields such as insurance public health epidemiology psy chology and many other research areas The Poisson model is most commonly used for modeling such a count data Itassumes that the mean and variance are equal However this restriction is violated in many applications because data isoften overdispersed In this case Poisson distribution P D underestimates the dispersion of the observed counts One cause of overdispersion is excess zeroes in the data and detected when the frequency of zero is significantly higherthan the one predicted by the Poisson model Sine the presence of excess zeros and the problem of over dispersion oftenoccur with count data few methods have been developed to deal with extra zeros that occur in response count variables Such methods include zero inflated distribution as zero inflated poisson ZIP In this thesis we propose a zero inflated poisson distribution Estimation of the model parameter using the method ofmaximum likelihood M LE and method of moments estimator M M E is provided Also we propose a new esti mator referred to as probability estimator P E of inflation parameter of ZIP distribution based on moment estimator M M E of the mean parameter which performs as well as M LE We compare the performance of P E M M Eand M LE through simulation study We then proceed to show how datasets from some recent natural disasters can bemodeled by the ZIP distribution The ZIP model is shown to be a member of the two parameter exponential family and hence the asymptotic normalityof the M M E is established Further details of computing the Fisher information matrix corresponding to this modelare shown According to simulation studies the P E distribution is close to the normal distribution The M M E and theM LE and the P E are asymptotically compared we discuss how the Bayesian approach may be applied to a ZIP regression model taking account of the uncertainty inthe parameters We start with an unconditional ZIP model without covariates followed by the ZIP regression modelincluding covariates It is shown that due to the complexity of the ZIP distribution there is no closed form for postirordistribution so full conditional distributions calculated and Gibbs sampling method was used for sampling the posteriordistribution We are interested in focusing light on the performance of M LE of mean and zero inflation parameters of count datawhen different possible count data models are fitted to the data so we briefly overview different zero inflated distribu tions which are most popular for modeling zero inflated count data We present the results of simulation studies whichfits Poisson generalized poisson GP ZIP zero inflated generalized poisson ZIGP and zero inflated negativebinomial ZIN B models to the sample data from ZIP distribution We compare the mean square error M SE biasand standard error SE of the mean parameter for these fits

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مطالعه و مدل بندي داده هاي شمارشي دوگانه آماسيده

توزيع پواسون صفر آماسيده , بيش پراكندگي , نمونه گيري گيبز