In loss models, we focus on studying the properties of continuous distributions that are defined only for positive real numbers. Models built under this assumption are widely used in actuarial practice to model insurance claim severities. However, in reality, the dataset in hand may not be so clean, and sometimes there may be negative values observed. In this case, existing claims models may suffer, and we must use alternative models. The asymmetric Laplace distribution (ALD) provides one such alternative, where the response variable is allowed to be negative. We present a modified version of the ALD, and explain the motivation behind it. A shrinkage estimation approach is used to estimate the regression coefficients for the model with induced sparsity. We present an algorithm for estimating the parameters quickly using the majorization minimization approach, and the algorithm is implemented in a low level programming language (C++) for fast estimation. The resulting model out-performs the model without shrinkage estimation in a case study using crop insurance indemnities as the response variable.
Gee Y. Lee (Wed,) studied this question.