Abstract
The three-parameter asymmetric Laplace distribution is modified by using the discretization method of Roy based on the survival function. The new modified distribution is called the discrete asymmetric Laplace distribution. It is the distribution over integers. We show some of its mathematical properties: the probability mass function, moment, the probability generating function, the characteristic function, the reliability measure, and the quantile function. Moreover, the estimation of parameters for this distribution based on maximum likelihood method is discussed. An application to the change of the stock price data is presented by comparing the proposed distribution with the discrete normal distribution.
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