skellam.mle {skellam} | R Documentation |
Maximum Likelihood Estimation for the Skellam Distribution
Description
Estimates the parameters of a Skellam distribution using maximum likelihood.
Usage
skellam.mle(x)
Arguments
x |
A vector of integers (positive or negative). |
Details
Instead of having to maximize the log-likelihood with respect to both parameters
(\lambda_1
and \lambda_2
), the function maximizes with respect to
\lambda_2
while setting \lambda_1 = \lambda_2 + \bar{x}
. This
approach improves computational efficiency. The optimization is performed using
nlm
as it proved faster than optimise
.
Value
A list with components:
- iters
Number of iterations required by
nlm
.- loglik
Maximized log-likelihood value.
- param
Estimated parameters (
\hat{\lambda}_1
,\hat{\lambda}_2
).
Author(s)
Michail Tsagris
References
Butler, R. (2007) Saddlepoint Approximations with Applications, Cambridge University Press.
Johnson, N. L. (1959) On an extension of the connection between Poisson and
\chi^2
distributions. Biometrika 46, 352-362.Johnson, N. L.; Kotz, S.; Kemp, A. W. (1993) Univariate Discrete Distributions, 2nd ed., John Wiley and Sons.
Skellam, J. G. (1946) The frequency distribution of the difference between two Poisson variates belonging to different populations. Journal of the Royal Statistical Society, Series A 109(3), 296.
Strackee, J.; van der Gon, J. J. D. (1962) The frequency distribution of the difference between two Poisson variates. Statistica Neerlandica 16(1), 17-23.
Abdulhamid, A. A.; Maha, A. O. (2010) On The Poisson Difference Distribution Inference and Applications. Bulletin of the Malaysian Mathematical Sciences Society 33(1), 17-45.
Wikipedia: Skellam distribution https://en.wikipedia.org/wiki/Skellam_distribution
Examples
# Basic example
x1 <- rpois(1000, 10)
x2 <- rpois(1000, 6)
x <- x1 - x2
skellam.mle(x)
# Larger sample size
x1 <- rpois(10000, 10)
x2 <- rpois(10000, 6)
x <- x1 - x2
skellam.mle(x)