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# Sometimes_ count data explicitly omit Teto counte Examples include the numbers of days patients spend hospital (only patients who actually stay overnight in hospita...

## Question

###### Sometimes_ count data explicitly omit Teto counte Examples include the numbers of days patients spend hospital (only patients who actually stay overnight in hospital are considered and the smallest possible count is one); the number of people per using rural road (the driver at least must be in the car); and suVer of the number of people living in each household (to respond the households must have at least one person) _ Using Poisson distribution is inadequate, the zero counts will be modeled t

Sometimes_ count data explicitly omit Teto counte Examples include the numbers of days patients spend hospital (only patients who actually stay overnight in hospital are considered and the smallest possible count is one); the number of people per using rural road (the driver at least must be in the car); and suVer of the number of people living in each household (to respond the households must have at least one person) _ Using Poisson distribution is inadequate, the zero counts will be modeled true zero counts In these situations, the zero-truncated Poisson distribution may be suitable, with probability function exp( AJAU f(y; A) {1 _ exp(_ A)}yl where 1,2,- and [3 marks] Show that the zero-truncated Poisson distribution is member of the exponential family by identifying p, a(0), 6(0) ; and cly; 0). b) [2 marks] Show that E[Y] = M/{1 exp(-A)} [3 marks] Find expression for the Deviance statistic for sample of independent zero-truncated Poisson observations with rates At What is distribution of the Deviance statistic? [2 marks_ Plot the zero-truncated Poisson distribution and the Poisson distribution for A = 2, and compare

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