Description Usage Arguments Details Value Author(s) References See Also Examples
The function provides the maximum likelihood estimates for the parameters of the DSL and the estimate of the inverse of the Fisher information matrix. The method of moments estimates of p and q coincide with the maximum likelihood estimates.
1 | estdlaplace(x)
|
x |
a vector of observations from the DSL |
See the reference. If \bar{x}^{+}=\frac{1}{n}∑_{i=1}^n x_i^{+}, \bar{x}^{-}=\frac{1}{n}∑_{i=1}^n x_i^{-} where x^{+} and x^{-} are the positive and the negative parts of x, respectively: x^{+}=x if x≥q 0 and zero otherwise, x^{-}=(-x)^{+}, then
\hat{q}=\frac{2\bar{x}^{-}(1+\bar{x})}{1+2\bar{x}^{-}\bar{x}+√{1+4\bar{x}^{-}\bar{x}^{+}}}, \hat{p}=\frac{\hat{q}+\bar{x}(1-\hat{q})}{1+\bar{x}(1-\hat{q})}
when \bar{x}≥q 0 and
\hat{p}=\frac{2\bar{x}^{+}(1-\bar{x})}{1-2\bar{x}^{+}\bar{x}+√{1+4\bar{x}^{-}\bar{x}^{+}}}, \hat{q}=\frac{\hat{p}-\bar{x}(1-\hat{p})}{1-\bar{x}(1-\hat{p})}
when \bar{x}≤q 0.
A list comprising
hatp |
estimate of p |
hatq |
estimate of q |
hatSigma |
estimate of the inverse of the Fisher information matrix |
Alessandro Barbiero, Riccardo Inchingolo
T. J. Kozubowski, S. Inusah (2006) A skew Laplace distribution on integers, Annals of the Institute of Statistical Mathematics, 58: 555-571
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | p<-0.6
q<-0.3
n<-20
x<-rdlaplace(n, p, q)
est<-estdlaplace(x)
est[1]
est[2]
est[3]
# increase n
n<-100
x<-rdlaplace(n, p, q)
est<-estdlaplace(x)
est[1]
est[2]
est[3]
# swap the parameters
x<-rdlaplace(n, q, p)
est<-estdlaplace(x)
est[1]
est[2]
est[3]
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