Let $X$ be a log-normal distribution, let $k\geq0$ be a real value and let $Y=\frac{1}{X+k}$. What is the name of the $Y$ distribution other than 'reciprocal shifted log-normal'? What is the mean of $Y$ in terms of $X$'s mean and variance?
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If $k=1$ then $Y$ is a logistic normal function. In other cases you may relate it to a more general Johnson's $S_b$-distribution (see this similar question on stats.stackexchange). There is no known analytical expression for the mean of $Y$. – Sextus Empiricus Nov 30 '18 at 14:05
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If $k=1$ then $Y$ is a logistic normal function. In other cases you may relate it to a more general Johnson's $S_b$-distribution (see this similar question on stats.stackexchange). There is no known analytical expression for the mean of $Y$.
Sextus Empiricus
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