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I am working on the problem relating to the difference of log-normal distribution. I have found several papers about this topic, however, none of them gives me the answer I want. More specifically, the variable I look at is the ratio of two difference of log-normal variables, i.e., $$\frac{e^{x_1}-e^{y_1}}{e^{x_2}-e^{y_2}}$$ where $x_1, x_2, y_1, y_2$ are normal distributed; $x_1, x_2$ are correlated, and $y_1, y_2$ are correlated.

kjetil b halvorsen
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JustinLan
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  • I expect there's a very good reason why you're having trouble finding that exact case. Is there any reason you really need that in closed form? – Glen_b Nov 11 '15 at 04:17
  • yes, I need the exact form of the distribution or an approximation. I want to examine the properties of this ratio, which is an important estimator in my current project. I have worked out the estimator with normal distribution which is relatively easy. – JustinLan Nov 12 '15 at 04:48
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    It's not clear why you need an algebraic formula to "examine properties"; what can you find out that you couldn't find out from simulation? – Glen_b Nov 12 '15 at 06:32
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    See https://stats.stackexchange.com/questions/152850/difference-of-two-i-i-d-lognormal-random-variables/176374#176374 – kjetil b halvorsen May 29 '17 at 06:44
  • Also see (maybe a duplicate): https://stats.stackexchange.com/questions/178081/distribution-of-ratio-of-2-points-drawn-from-normal-distribution/306073#306073 – kjetil b halvorsen Oct 04 '17 at 18:03

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