[R] How to solve this complex equation

[Chel Hee Lee]

A~ha~!!  Thank you, Prof. Peter Dalgaard, so much for your wonderful 
lesson!!!  Learning new things everyday from this R-help mailing list!

Chel Hee Lee

On 2/11/2015 10:37 AM, peter dalgaard wrote:
>
> On 11 Feb 2015, at 17:11 , Chel Hee Lee <chl948 at mail.usask.ca> wrote:
>
>> The functional form given in the post written by Ssuhanchen captures my eyes.   It is the cumulative distribution function of Poisson when the number of counts is less than or equal to 2 with unknown parameter mu=x/2.   Since it is a nonlinear function, there may be multiple solutions but the solution should be greater than 0 (if I am in the right track).   I am assuming this functional form is originated from the Poisson.  Under this assumption, one solution is found as below:
>>
>>> rt <- uniroot(function(x) ppois(2, lambda=x)-0.05, interval=c(0.5,1), extendInt="yes")
>> Warning messages:
>> 1: In ppois(2, lambda = x) : NaNs produced
>> 2: In ppois(2, lambda = x) : NaNs produced
>> 3: In ppois(2, lambda = x) : NaNs produced
>>> ppois(2, lambda=rt$root)
>> [1] 0.0500001
>>> rt$root
>> [1] 6.295791
>>
>> Thus, the solution x would be rt$root*2 (Note that I did not try to find other solutions).  I hope this helps.
>>
>
> Given the Poisson connection, I would pretty strongly expect the solution to be unique.
>
> Notice also that your rt$root comes out as the upper end of the confidence interval in
>
>> poisson.test(2, alt="l")
>
> 	Exact Poisson test
>
> data:  2 time base: 1
> number of events = 2, time base = 1, p-value = 0.9197
> alternative hypothesis: true event rate is less than 1
> 95 percent confidence interval:
>   0.000000 6.295794
> sample estimates:
> event rate
>           2
>
>
>
>
>
>> Chel Hee Lee
>>
>> On 2/10/2015 2:29 AM, Rolf Turner wrote:
>>> On 10/02/15 14:04, Ssuhanchen wrote:
>>>> Hi!
>>>>
>>>> I want to use R to calculate the variable x which is in a complex equation
>>>> in below:
>>>>
>>>>   2
>>>>   Σ[exp(-x/2)*(x^k)/(2^k*k!)]=0.05
>>>> k=0
>>>>
>>>> how to solve this equation to get the exact x in R?
>>>
>>> Is this homework?  Sure looks like it.  Talk to your prof.  Or do a bit of work on learning how to use R --- which is presumably the point of the exercise.
>>>
>>> cheers,
>>>
>>> Rolf Turner
>>>
>>
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>