cbp | R Documentation |
Probability mass function, distribution function, quantile function and random generation for the Complex Biparametric Pearson (CBP) distribution with parameters b
and \gamma
.
dcbp(x, b, gamma)
pcbp(q, b, gamma, lower.tail = TRUE)
qcbp(p, b, gamma, lower.tail = TRUE)
rcbp(n, b, gamma)
x |
vector of (non-negative integer) quantiles. |
b |
parameter b (real) |
gamma |
parameter gamma (positive) |
q |
vector of quantiles. |
lower.tail |
if TRUE (default), probabilities are |
p |
vector of probabilities. |
n |
number of observations. If |
The CBP distribution with parameters b
and \gamma
has pmf
f(x|b,\gamma) = C \Gamma(ib+x) \Gamma(-ib+x) / (\Gamma(\gamma+x) x!), x=0,1,2,...
where i
is the imaginary unit, \Gamma(ยท)
the gamma function and
C = \Gamma(\gamma-ib) \Gamma(\gamma+ib) / (\Gamma(\gamma) \Gamma(ib) \Gamma(-ib))
the normalizing constant.
The CBP is a particular case of the CTP when a=0
.
The mean and the variance of the CBP distribution are
E(X)=\mu=b^2/(\gamma-1)
and Var(X)=\mu(\mu+\gamma-1)/(\gamma-2)
so \gamma > 2
.
It is always overdispersed.
dcbp
gives the pmf, pcbp
gives the distribution function, qcbp
gives the quantile function and rcbp
generates random values.
RCS2003cpd
Probability mass function, distribution function, quantile function and random generation for the CTP distribution: dctp
, pctp
, qctp
and rctp
.
Functions for maximum-likelihood fitting of the CBP distribution: fitcbp
.
# Examples for the function dcbp
dcbp(3,2,5)
dcbp(c(3,4),2,5)
# Examples for the function pcbp
pcbp(3,2,3)
pcbp(c(3,4),2,3)
# Examples for the function qcbp
qcbp(0.5,2,3)
qcbp(c(.8,.9),2,3)
# Examples for the function rcbp
rcbp(10,1,3)
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