Density function for the negative binomial distribution with parameters alpha and prob.
Usage
dnegbinom(x, alpha, prob, log.p = FALSE)
Arguments
x
vector of (non-negative integer) quantiles.
alpha
target for number of successful trials. Must be strictly positive, need not be integer.
prob
probability of success in each trial. 0 < prob <= 1.
log.p
logical; if TRUE, probabilities p are given as log(p).
Details
The negative binomial distribution with parameters alpha = α and prob = p has density
frac{Γ(x + α)}{Γ(α) x!} p^α (1-p)^x
for x = 0,1,…,α > 0 and 0 < p ≤q 1.
This represents the number of failures which occur in a sequence of Bernoulli trials before a target number of successes is reached.
Value
dnegbinom gives the density corresponding to the alpha and prob values provided.
DuMouchel W. (1999), "Bayesian Data Mining in Large Frequency Tables, with an Application to the FDA Spontaneous Reporting System". The American Statistician, 53, 177-190.
Myers, J. A., Venturini, S., Dominici, F. and Morlock, L. (2011), "Random Effects Models for Identifying the Most Harmful Medication Errors in a Large, Voluntary Reporting Database". Technical Report.