Parameter estimation truncated Laplace distribution

Question

Hello to the community,

I have a problem with the parameter estimation from a model.

Let's guess we have a sample $X = (X_1,...,X_n)$, $\forall i=1,...,n$ $X_i$ follows a truncated Laplace distribution with parameters $\mu, \sigma$.

Thus, if $a \leq X_i \leq b$, $g(x_i) = \dfrac{f_{Y}(x_i, \mu, \sigma)}{F_{Y}(b)-F_{Y}(a)}$, Y follows the Laplace distribution of parameters $\mu, \sigma$.

Is there a way to estimate theses parameters ? It seems to be a difficult task if we choose MLE method.

Thanks to the community.

Answer 1

1) there is an error (I suppose it is only a typo) in your $g(x)$ denominator... it's $F(b)-F(a)$

2) calculate the usual MLE estimators and choose them if they are in $[a;b]$. Otherwise choose $a$ or $b$