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$root*2 (Note that I did not try to find other solutions). I hope this helps. Chel Hee Lee On 2/10/2015 2:29 AM, Rolf Turner wrote:> On 10/02/15 14:04, Ssuhanchen wrote: >> Hi! >> >> I want to use R to calculate the variable x which is in a complex >> equation >> in below: >> >> 2 >> ?[exp(-x/2)*(x^k)/(2^k*k!)]=0.05 >> k=0 >> >> how to solve this equation to get the exact x in R? > > Is this homework? Sure looks like it. Talk to your prof. Or do a > bit of work on learning how to use R --- which is presumably the point > of the exercise. > > cheers, > > Rolf Turner >
On 11 Feb 2015, at 17:11 , Chel Hee Lee <chl948 at mail.usask.ca> wrote:> The functional form given in the post written by Ssuhanchen captures my eyes. It is the cumulative distribution function of Poisson when the number of counts is less than or equal to 2 with unknown parameter mu=x/2. Since it is a nonlinear function, there may be multiple solutions but the solution should be greater than 0 (if I am in the right track). I am assuming this functional form is originated from the Poisson. Under this assumption, one solution is found as below: > > > rt <- uniroot(function(x) ppois(2, lambda=x)-0.05, interval=c(0.5,1), extendInt="yes") > Warning messages: > 1: In ppois(2, lambda = x) : NaNs produced > 2: In ppois(2, lambda = x) : NaNs produced > 3: In ppois(2, lambda = x) : NaNs produced > > ppois(2, lambda=rt$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 >>> ?[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 >> > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code.-- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com
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 >>>> ?[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 >>> >> >> ______________________________________________ >> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. >