Folkes, Michael
2011-Jan-27 01:07 UTC
[R] binomial dist: obtaining probability of success on each trial
I'm trying to fathom how to answer two example problems (3.3.2 & 3.3.3)
in:
Krishnamoorthy. 2006. "handbook of statistical distributions with
applications"
The first requires calculating single trial probability of success for a
binomial distribution when we know:
trial size=20, successes k=4, P(x<=k)=0.7
Appreciably all the binomial functions are requiring "prob", which
I'm trying to estimate.
The second problem is similar:
prob=0.2, successes k=6, P(x<=k)=0.4, need to calc # trials ('size'
in R).
I'm sure it'll be obvious once somebody explains, but google and R-help
archive searches have failed me. :(
thanks in advance!
Michael
_______________________________________________________
Michael Folkes
Salmon Stock Assessment
Canadian Dept. of Fisheries & Oceans
Pacific Biological Station
3190 Hammond Bay Rd.
Nanaimo, B.C., Canada
V9T-6N7
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David Winsemius
2011-Jan-27 02:51 UTC
[R] binomial dist: obtaining probability of success on each trial
On Jan 26, 2011, at 8:07 PM, Folkes, Michael wrote:> I'm trying to fathom how to answer two example problems (3.3.2 & > 3.3.3) in: > Krishnamoorthy. 2006. "handbook of statistical distributions with > applications" > > The first requires calculating single trial probability of success > for a binomial distribution when we know: > trial size=20, successes k=4, P(x<=k)=0.7 > Appreciably all the binomial functions are requiring "prob", which > I'm trying to estimate.Yi might try via successive approximation. Here's a start. > dbinom(0:20, 20, prob=0.7) [1] 3.486784e-11 1.627166e-09 3.606885e-08 5.049639e-07 5.007558e-06 3.738977e-05 2.181070e-04 1.017833e-03 [9] 3.859282e-03 1.200665e-02 3.081708e-02 6.536957e-02 1.143967e-01 1.642620e-01 1.916390e-01 1.788631e-01 [17] 1.304210e-01 7.160367e-02 2.784587e-02 6.839337e-03 7.979227e-04 > sum(dbinom(0:20, 20, prob=0.7)) [1] 1 > sum(dbinom(0:4, 20, prob=0.7)) [1] 5.550253e-06 > sum(dbinom(0:4, 20, prob=0.2)) [1] 0.6296483 > sum(dbinom(0:4, 20, prob=0.2)) [1] 0.6296483 > sum(dbinom(0:4, 20, prob=0.18)) [1] 0.7151181 So you have an interval in which the answer lies and should be able to set up a call to optimize or other solving algorithm. > fnbinom <- function(x) abs( sum(dbinom(0:4, 20, prob=x)) - 0.7) > optimize(fnbinom, interval=c(0.15, 0.2)) $minimum [1] 0.1836066 $objective [1] 6.063185e-05> > The second problem is similar: > prob=0.2, successes k=6, P(x<=k)=0.4, need to calc # trials ('size' > in R).Same sort of approach ought to work.> > I'm sure it'll be obvious once somebody explains, but google and R- > help archive searches have failed me. :( > thanks in advance! > Michael > _______________________________________________________ > Michael Folkes > Salmon Stock Assessment > Canadian Dept. of Fisheries & Oceans > Pacific Biological Station-- David Winsemius, MD West Hartford, CT