Description Usage Arguments Details Value Author(s) References See Also Examples
Density, normalizing constant, distribution function, quantile function and random number generation for the Touchard distribution
with Poisson-like parameter equal to lambda
and shape/dispersion parameter equal to delta
.
1 2 3 4 5 | dtouch(x, lambda, delta, N=NULL, eps=sqrt(.Machine$double.eps), log = FALSE)
ptouch(x, lambda, delta, N=NULL, eps=sqrt(.Machine$double.eps))
qtouch(p, lambda, delta, N=NULL, eps=sqrt(.Machine$double.eps))
rtouch(n, lambda, delta, N=NULL, eps=sqrt(.Machine$double.eps))
tau(lambda, delta, N=NULL, eps=sqrt(.Machine$double.eps))
|
x |
vector of quantiles |
p |
vector of probabilities. |
n |
number of observations. |
lambda |
Poisson-like (location) parameter which corresponds to the mean of the distribution when |
delta |
shape/dispersion parameter which produces unequal dispersion (var x mean) when different from zero and mild zero excess compared to the Poisson distribution |
N |
number of terms in the computation (series) of the normalizing constant. If |
eps |
relative error in the computation (series) of the normalizing constant. Only used if |
log |
logical; if TRUE, probability p is given as log(p). |
The Touchard distribution with parameters λ and δ has density
[ lambda^x (x+1)^delta ] / [ x! tau(lambda,delta) ]
for y=0,1,2,..., λ > 0 and δ real.
dtouch
gives the density, ptouch
gives the distribution function, qnorm
gives the quantile function,
and rtouch
generates random deviates.
rtouch
uses the inverse transform method. The length of the result is determined by n
and is the maximum of the lengths of the numerical arguments for the other functions.
The numerical arguments other than n
are recycled to the length of the result.
qtouch
uses an initial approximation based on the Cornish-Fisher expansion followed by
a search in the appropriate direction.
tau
gives the value of the normalizing constant in the Touchard density.
Bernardo Andrade and Sandro Oliveira
Matsushita RY, Pianto D, Andrade BB, Cancado A, Silva S (2018) The Touchard distribution, Communications in Statistics - Theory and Methods, <doi:10.1080/03610926.2018.1444177>
1 2 3 4 5 6 |
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