Density, distribution function, quantile function and random
generation for the zero-inflated negative binomial distribution with parameters
w
, size
and prob
.
1 2 3 4 5 6 7 |
x |
Vector of (non-negative integer) quantiles. |
w |
Weight of the zero-inflation. |
size |
Target for number of successful trials, or dispersion parameter (the shape parameter of the gamma mixing distribution). Must be strictly positive, need not be integer. |
prob |
Probability of success in each trial. |
mu |
Alternative parametrization via mean: see ‘Details’. |
q |
Vector of quantiles. |
lower.tail |
logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x]. |
p |
Vector of probabilities. |
n |
number of observations. If |
The zero-inflated negative binomial distribution with size
= n and
prob
= p has density
w + (1-w) * Γ(x+n)/(Γ(n) x!) p^n (1-p)^x
for x = 0, n > 0, 0 < p ≤ 1 and 0 ≤ w ≤ 1.
(1-w) * Γ(x+n)/(Γ(n) x!) p^n (1-p)^x
for x = 1, 2, …, n > 0, 0 < p ≤ 1 and 0 ≤ w ≤ 1.
dzinbinom gives the density, pzinbinom gives the distribution function, qzinbinom gives the quantile function, and rzinbinom generates random deviates.
dzinbinom
: gives the density
pzinbinom
: gives the cumulative distribution function
qzinbinom
: gives the quantile function
rzinbinom
: random number generation
Matthias Heinig, Aaron Taudt
Distributions for standard distributions, including
dbinom
for the binomial, dnbinom
for the negative binomial, dpois
for the
Poisson and dgeom
for the geometric distribution, which
is a special case of the negative binomial.
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