如何在 R 中定义概率质量 function

Question

I want to define (implement) the probability mass function into the R environment when dealing with another calculation. Since not having much R experience, I do not know how to translate the equation with these parameters into code (already tried to search everywhere). Thanks for help. [![probability mass function given by this equation][1]][1]

Answer 1

This could be expressed via Beta distribution

Your expression = BetaPDF(r, x) t (1-t) / x

P <- function(x, theta) {
    shape1 <- 2
    shape2 <- x
    dbeta(theta, shape1, shape2)*theta*(1.0-theta)/x
}

Please check the math, see also here .

UPDATE

Or express it as Beta PDF of higher powers

Your expression = BetaPDF(r+1, x+1) r /((r+x+1)*(r+x))

Answer 2

It's already a built in pmf in R - its there when you install R. If you have r and theta already defined, just call dnbinom

dnbinom(x, size=r, prob=theta)

See the help ?dnbinom

Don't waste your time debugging your own code when there's code that's already debugged and which is tested daily by large numbers of highly knowledgeable users (many research statisticians use it for example) - who should certainly have spotted anything but very rare problems by now. It will also likely be considerably more numerically stable and more efficiently implemented than you will write.