Type: | Package |
Title: | Discrete Laplace Exponential Family |
Version: | 1.5.1 |
Author: | Mikkel Meyer Andersen and Poul Svante Eriksen |
Maintainer: | Mikkel Meyer Andersen <mikl@math.aau.dk> |
Description: | The discrete Laplace exponential family for use in fitting generalized linear models. |
License: | GPL-2 |
LazyLoad: | yes |
NeedsCompilation: | no |
Packaged: | 2022-01-27 11:48:54 UTC; mikl |
Repository: | CRAN |
Date/Publication: | 2022-01-27 12:10:09 UTC |
Discrete Laplace Family
Description
Discrete Laplace Family for models such as a generalized linear model.
Details
DiscreteLaplace() ddisclap(x, p) pdisclap(x, p, lower.tail = TRUE) rdisclap(n, p)
Author(s)
Mikkel Meyer Andersen and Poul Svante Eriksen
Maintainer: Mikkel Meyer Andersen <mikl@math.aau.dk>
See Also
DiscreteLaplace
ddisclap
pdisclap
rdisclap
Probability mass function, distribution function, and random generation for the discrete Laplace distribution with parameter 0 <= p < 1
.
Description
Calculates the mass of observations from the discrete Laplace distribution.
Usage
ddisclap(x, p)
pdisclap(x, p, lower.tail = TRUE)
rdisclap(n, p)
Arguments
x |
vector of observations |
p |
the parameter with 0 <= p < 1 |
lower.tail |
logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]. |
n |
number of observations to generate |
Details
The probability mass function for the discrete Laplace distribution with parameter 0 < p < 1
is given by P(X = x) = \frac{1-p}{1+p} p^x
for x \in \mathbf{Z}
.
If x
is a vector, then p
must have either length 1 or the same length as x
. If p
has length 1, then the value will be reused for all values in x
.
Value
'ddisclap' gives the probability mass, 'pdisclap' gives the distribution function, and 'rdisclap' generates random deviates.
Author(s)
Mikkel Meyer Andersen <mikl@math.aau.dk> and Poul Svante Eriksen
See Also
Examples
p <- 0.3
xs <- (-4):4
probd <- ddisclap(xs, p)
data.frame(xs, probd)
plot(xs, probd, type = "l", xlab = "x", ylab = "P(X = x; p)")
Discrete Laplace exponential family
Description
Discrete Laplace exponential family for models such as a generalized linear model.
Usage
DiscreteLaplace()
Details
This family can be used in for example fitting a generalized linear model using the glm
or glm.fit
function.
Value
Author(s)
Mikkel Meyer Andersen <mikl@math.aau.dk> and Poul Svante Eriksen
See Also
glm
glm.fit
ddisclap
binomial
poisson
Examples
xs <- abs(rdisclap(100, 0.1))
fit <- glm(xs ~ 1, family = DiscreteLaplace())
summary(fit)
theta <- as.numeric(coef(fit)[1])
mu <- DiscreteLaplace()$linkinv(theta)
p <- (sqrt(1 + mu^2) - 1) / mu
p