A Mixed Bivariate Distribution Connected with Geometric Maxima of Exponential Variables |
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| Authors: | Tomasz J. Kozubowski Anna K. Panorska |
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| Affiliation: | 1. Department of Mathematics and Statistics , University of Nevada , Reno, Nevada, USA tkozubow@unr.edu;3. Department of Mathematics and Statistics , University of Nevada , Reno, Nevada, USA |
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| Abstract: | We study the joint distribution of X and N, where N has a geometric distribution and X is the maximum of N i.i.d. exponential variables, independent of N. We present basic properties of these mixed bivariate distributions and discuss parameter estimation for this model. An example from finance, where N represents the number of consecutive positive daily log-returns of currency exchange rates, illustrates stochastic modeling potential of these laws. |
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| Keywords: | Currency exchange rates Generalized exponential distribution Geometric distribution Half-logistic distribution Maximum likelihood estimation Random maximum |
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