Reciprocal Shifted Log-Normal Distribution
Let $X$ be a log-normal distribution, let $kgeq0$ 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?
Thanks!
probability-distributions
asked Jul 16 '13 at 10:32
questiondude
1113
add a comment |
Let $X$ be a log-normal distribution, let $kgeq0$ 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?
Thanks!
probability-distributions
asked Jul 16 '13 at 10:32
questiondude
1113
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 $Y$.
– Martijn Weterings
Nov 30 at 14:05
add a comment |
Let $X$ be a log-normal distribution, let $kgeq0$ 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?
Thanks!
probability-distributions
asked Jul 16 '13 at 10:32
questiondude
1113
Let $X$ be a log-normal distribution, let $kgeq0$ 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?
Thanks!
probability-distributions
probability-distributions
asked Jul 16 '13 at 10:32
questiondude
1113
asked Jul 16 '13 at 10:32
questiondude
1113
asked Jul 16 '13 at 10:32
questiondude
1113
asked Jul 16 '13 at 10:32
questiondude
1113
asked Jul 16 '13 at 10:32
questiondude
1113
1113
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 $Y$.
– Martijn Weterings
Nov 30 at 14:05
add a comment |
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 $Y$.
– Martijn Weterings
Nov 30 at 14:05
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 $Y$.
– Martijn Weterings
Nov 30 at 14:05
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 $Y$.
– Martijn Weterings
Nov 30 at 14:05
add a comment |
1 Answer
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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 $Y$.
answered Nov 30 at 14:06
Martijn Weterings
14010
add a comment |
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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 $Y$.
answered Nov 30 at 14:06
Martijn Weterings
14010
add a comment |
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 $Y$.
answered Nov 30 at 14:06
Martijn Weterings
14010
add a comment |
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 $Y$.
answered Nov 30 at 14:06
Martijn Weterings
14010
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 $Y$.
answered Nov 30 at 14:06
Martijn Weterings
14010
answered Nov 30 at 14:06
Martijn Weterings
14010
answered Nov 30 at 14:06
Martijn Weterings
14010
answered Nov 30 at 14:06
Martijn Weterings
14010
14010
add a comment |
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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 $Y$.
– Martijn Weterings
Nov 30 at 14:05