[R] Is there dpois equivalent for zero-inflated Poisson?

[Matti Viljamaa]

And why is the first term of ifelse(x == 0, zero, 0) + dpois(x, lambda) / (1 - zero)

ifelse(x == 0, zero, 0)

rather than something corresponding to

zero+(1-zero)e^{-lambda}

https://en.wikipedia.org/wiki/Zero-inflated_model#Zero-inflated_Poisson

> On 22 Mar 2016, at 14:25, Matti Viljamaa <mviljamaa at kapsi.fi> wrote:
> 
> Could you clarify what are the parameters and why it’s formulated that way?
> 
> -Matti
> 
>> On 22 Mar 2016, at 14:17, Thierry Onkelinx <thierry.onkelinx at inbo.be <mailto:thierry.onkelinx at inbo.be>> wrote:
>> 
>> Dear Matti,
>> 
>> What about this?
>> 
>> dzeroinflpois <- function(x, lambda, zero){
>>   ifelse(x == 0, zero, 0) + dpois(x, lambda) / (1 - zero)
>> }
>> plot(x, dzeroinflpois(x, lambda = 10, zero = 0.2), type = "l")
>> 
>> 
>> 
>> ir. Thierry Onkelinx
>> Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest 
>> team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance 
>> Kliniekstraat 25
>> 1070 Anderlecht
>> Belgium
>> 
>> To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of. ~ Sir Ronald Aylmer Fisher
>> The plural of anecdote is not data. ~ Roger Brinner 
>> The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data. ~ John Tukey
>> 
>> 2016-03-22 13:04 GMT+01:00 Matti Viljamaa <mviljamaa at kapsi.fi <mailto:mviljamaa at kapsi.fi>>:
>> I’m doing some optimisation that I first did with normal Poisson (only parameter theta was estimated), but now I’m doing the same with a zero-inflated Poisson model which
>> gives me two estimated parameters theta and p (p is also pi in some notation).
>> 
>> My question is, is there something equivalent to dpois that would use both of the parameters (or is the p parameter possibly unnecessary)?
>> 
>> I’m calculating the “fit” of the Poisson model
>> 
>> i.e. like
>> 
>> x = c(0,1,2,3,4,5,6)
>> y = c(3062,587,284,103,33,4,2)
>> fit1 <- sum(y)*dpois(x, est_theta)
>> 
>> and then comparing fit1 to the real observations.
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>> 
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> 

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