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Poisson regression
In case of Poisson regression we use ηi = g(µi) = log(µi) and a variance V ar(Yi) = φµi. The case φ = 1 corresponds to standard Poisson model. Poisson regression is used when the response to model is counts which typically follow a Poisson distribution. Examples include colony counts for bacteria or viruses, accidents, equipment failures, insurance claims, incidence of disease. Interest often lies in estimating a rate of incidence and determining its relationship to a set of explanatory variables. Again, an IRLS procedure is used to ?nd the MLE estimators of the β coeffcients. When we can not assume φ = 1, (this is the case of over- or under- dispersion discussed in McCullagh and Nelder (1989)), the iterative procedure is changed to so called "quasi-likelihood estimation". Finally in this section, we shall also mention shortly the extension of GLM to GAM.
Technically the multivariate analogue of the quasi-likelihood with the same feature that it leads to consistent inferences about the mean responses without needing specific supposi
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Length-biased data is a data which arise when the probability that an item is sampled is proportional to its own length. A main example of this situation occurs in the renewal the
The number of employees absent from work at a large electronics manufacturing plant over aperiod of 106 days is given in the table below. 146 141 139 140 145 141 142 131 142 140
1) Question on the first day questionnaire asked students to rate their response to the question Are you deeply moved by the arts or music? Assume the population that is sampled
Cauchy distribution : The probability distribution, f (x), can be given as follows where α is the position of the parameter (median) and the beta β a scale parameter. Moments
Non parametric maximum likelihood (NPML) is a likelihood approach which does not need the specification of the full parametric family for the data. Usually, the non parametric max
Time series : The values of a variable recorded, generally at a regular interval, over the long period of time. The observed movement and fluctuations of several such series are
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Randomized response technique : The procedure for collecting the information on sensitive issues by means of the survey, in which an element of chance is introduced as to what quer
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