Description Usage Arguments Details Value Author(s) References Examples
MLE of the Skellam distribution.
1 | skellam.mle(x)
|
x |
A vector of integers, positive or negative. |
Instead of having to maximise the log-likelihood with respect to the two parameters, λ_1 and λ_2, we maximise with respect to λ_2 and then λ_1 = λ_2 + \bar{x}. This makes it faster. The command "nlm" is used to optimise the log-likelihood as it proved to be faster than the "optimise".
A list including:
iters |
The number of iterations required by "nlm". |
loglik |
The maximised log-likelihood value. |
param |
The estimated parameters, \hat{λ}_1 and \hat{λ}_2. |
Michail Tsagris
Butler, R. (2007) Saddlepoint Approximations with Applications, Cambridge University Press, Cambridge & New York, p.17.
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, New York, pp.190-192.
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, 26.
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 http://en.wikipedia.org/wiki/Skellam_distribution
1 2 3 4 5 6 7 8 9 10 11 | require('skellam')
x1 <- rpois(1000, 10)
x2 <- rpois(1000, 6)
x <- x1 - x2
skellam.mle(x)
x1 <- rpois(10000, 10)
x2 <- rpois(10000, 6)
x <- x1 - x2
skellam.mle(x)
|
$iters
[1] 2
$loglik
[1] -2804.175
$param
mu 1 mu 2
10.116531 5.887531
$iters
[1] 1
$loglik
[1] -28089.81
$param
mu 1 mu 2
10.08463 6.05933
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