cbp {cpd} | R Documentation |
The Complex Biparametric Pearson (CBP) Distribution
Description
Probability mass function, distribution function, quantile function and random generation for the Complex Biparametric Pearson (CBP) distribution with parameters and
.
Usage
dcbp(x, b, gamma)
pcbp(q, b, gamma, lower.tail = TRUE)
qcbp(p, b, gamma, lower.tail = TRUE)
rcbp(n, b, gamma)
Arguments
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 |
Details
The CBP distribution with parameters and
has pmf
where is the imaginary unit,
the gamma function and
the normalizing constant.
The CBP is a particular case of the CTP when .
The mean and the variance of the CBP distribution are
and
so
.
It is always overdispersed.
Value
dcbp
gives the pmf, pcbp
gives the distribution function, qcbp
gives the quantile function and rcbp
generates random values.
References
Jose Rodriguez-Avi J, Conde-Sanchez A, Saez-Castillo AJ (2003). “A new class of discrete distributions with complex parameters.” Stat. Pap., 44, 67–88. doi:10.1007/s00362-002-0134-7.
See Also
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
# 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)