Distribution of A=1/B, where B is normally distributed.

Asked Mar 12 '17 at 12:56

Active Mar 12 '17 at 12:56

Viewed 24 times

Take a variable, B, which has standard normal distribution.

Let A = 1/B. What is the distribution of A?

One way to go about this problem would be to take the CDF of the standard normal curve, and to use this to compute points on the new distribution. For instance, the probability that B>1 is approximately 0.16. Therefore, the probability that 01) = 0.34. In the same way, P(A>0.5) = 0.48. This method can yield the CDF of A to an arbitrary degree of precision. However, I would like to know the exact function of A's distribution.

asked Mar 12 '17 at 12:56

Thomas Delaney

1,683

According to wikipedia, https://en.wikipedia.org/wiki/Inverse_distribution#Reciprocal_normal_distribution there does not seem to exist a closed form. – Maximilian Matthé Mar 12 '17 at 13:08
3

No closed form? What the... The most usual change of variable theorem yields readily $$f_{1/X}(y)=\frac1{y^2}f_X\left(\frac1y\right)$$ – Did Mar 12 '17 at 13:20
Today $3$ goals by Thomas Delaney!! – Dietrich Burde Apr 01 '17 at 18:09

Distribution of A=1/B, where B is normally distributed.

0 Answers0