### Section 5.4: Other Discrete Probability Distributions

?dhyper #hypergeometric?dmultinom #multinomial

?dnbinom #negative binomial

#There are also options in various packages later for regression to use different distributions,

#although of these I've only ever used negative binomial.

#The logarithmic distribution requires an extra package.

#https://cran.r-project.org/web/views/Distributions.html

#extraDistr, VGAM, or gamlss.dst

#I installed extraDistr to test it out.

library(extraDistr)

?LogSeries

#and

?dlgser #The distributions in this package follow the same us of d, p, and q prefixes.

### Exercises 5

#I'm doing the exercises that require new coding beyond what we have done already.#Exercise 5.5

#The organism is present or absent in any given slide, assuming the person is diseased

#(if the person has the disease, their samples contain the organism but it's not very common).

#We want a false negative <1% of the time. The organism is visible in 20% of the slides.

#At first I thought this was a Bayesian problem but I don't see how to do it that way.

#p=0.2 (organism visible), thus q=0.8 (organism present but not visible).

#We need to find the power of q=0.8 that equals 0.01 or smaller

#(1% false negative, which would be present but not visible).

#So, I made a while loop that cycled through to see how many times we need to raise 0.8

#to get to 0.01. This explanation helped me figure out how to do this type of loop.

n<-0

i<-1

print(n)

while (i > 0.01) {

print(i)

print(n)

i<-0.8^n

n=n+1

}

#the last number printed is the number of slides needed.

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