On the distribution of quotient of random variables conditioned to the positive quadrant

Yuancheng Si, Saralees Nadarajah and Xiaodong Song

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 10, 2514-2528

Abstract: Motivated by Caginalp and Caginalp [Physica A—Statistical Mechanics and Its Applications, 499, 2018, 457–471], we derive the exact distribution of X/Y conditioned on X > 0, Y > 0 for more than ten classes of distributions, including the bivariate t, bivariate Cauchy, bivariate Lomax, Arnold and Strauss’ bivariate exponential, Balakrishna and Shiji’s bivariate exponential, Mohsin et al.’s bivariate exponential, Morgenstern type bivariate exponential, bivariate gamma exponential and bivariate alpha skew normal distributions. The results can be useful in finance and other areas.

Date: 2020
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DOI: 10.1080/03610926.2019.1576893

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