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On a discrete version of Laplace distribution and its application in financial modeling. (English) Zbl 1358.62021
Summary: We consider the symmetric discrete Laplace distribution as the distribution of the difference of two identically and independently distributed (i.i.d.) geometric random variables. This distribution is same as the discrete Laplace distribution of S. Inusah and T. J. Kozubowski [J. Stat. Plann. Inference 136, No. 3, 1090–1102 (2006; Zbl 1081.60011)] and its properties are reviewed. Integer valued autoregressive (INAR) processes with this marginal distribution are developed. In this paper, we consider the application of discrete Laplace distribution in financial modeling. We use this distribution to model a financial data on exchange rate of US Dollar to Indian Rupee and establish that the discrete Laplace distribution is a good fit.
MSC:
62E15 Exact distribution theory in statistics
60E05 Probability distributions: general theory
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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