Ratio Distribution - Ratio of Standard Normal To Standard Uniform

Ratio of Standard Normal To Standard Uniform

If X has a standard normal distribution and Y has a standard uniform distribution, then Z = X / Y has a distribution known as the slash distribution, with probability density function

p_Z(z) = \begin{cases}
\left / z^2 \quad & z \ne 0 \\
\phi(0) / 2 \quad & z = 0, \\
\end{cases}

where φ(z) is the probability density function of the standard normal distribution.

Read more about this topic:  Ratio Distribution

Famous quotes containing the words ratio of, ratio, standard, normal and/or uniform:

    Personal rights, universally the same, demand a government framed on the ratio of the census: property demands a government framed on the ratio of owners and of owning.
    Ralph Waldo Emerson (1803–1882)

    Official dignity tends to increase in inverse ratio to the importance of the country in which the office is held.
    Aldous Huxley (1894–1963)

    I don’t have any problem with a reporter or a news person who says the President is uninformed on this issue or that issue. I don’t think any of us would challenge that. I do have a problem with the singular focus on this, as if that’s the only standard by which we ought to judge a president. What we learned in the last administration was how little having an encyclopedic grasp of all the facts has to do with governing.
    David R. Gergen (b. 1942)

    Philosophically, incest asks a fundamental question of our shifting mores: not simply what is normal and what is deviant, but whether such a thing as deviance exists at all in human relationships if they seem satisfactory to those who share them.
    Elizabeth Janeway (b. 1913)

    He may be a very nice man. But I haven’t got the time to figure that out. All I know is, he’s got a uniform and a gun and I have to relate to him that way. That’s the only way to relate to him because one of us may have to die.
    James Baldwin (1924–1987)