Processing math: 100%

Laplace (Double Exponential, Bilateral Exponential) Distribution

f(x)=12e|x|F(x)={12exx0112exx>0G(q)={log(2q)q12log(22q)q>12
md=mn=μ=0μ2=2γ1=0γ2=3

The ML estimator of the location parameter is

ˆL=median(Xi)

where Xi is a sequence of N mutually independent Laplace RV’s and the median is some number between the 12Nth and the (N/2+1)th order statistic ( e.g. take the average of these two) when N is even. Also,

ˆS=1NNj=1|XjˆL|.

Replace ˆL with L if it is known. If L is known then this estimator is distributed as (2N)1Sχ22N .

h[X]=log(2e)1.6931471805599453094.

Implementation: scipy.stats.laplace