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.
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$\begingroup$ 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? $\endgroup$– Glen_bCommented Nov 11, 2015 at 4:17
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$\begingroup$ 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. $\endgroup$– JustinLanCommented Nov 12, 2015 at 4:48
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4$\begingroup$ 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? $\endgroup$– Glen_bCommented Nov 12, 2015 at 6:32
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1$\begingroup$ See stats.stackexchange.com/questions/152850/… $\endgroup$– kjetil b halvorsen ♦Commented May 29, 2017 at 6:44
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$\begingroup$ Also see (maybe a duplicate): stats.stackexchange.com/questions/178081/… $\endgroup$– kjetil b halvorsen ♦Commented Oct 4, 2017 at 18:03
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