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)

“We don’t want bores in the theatre. We don’t want standardised acting, standard actors with standard-shaped legs. Acting needs everybody, cripples, dwarfs and people with noses so long. Give us something that is different.”
—Dame Sybil Thorndike (1882–1976)

“Normality highly values its normal man. It educates children to lose themselves and to become absurd, and thus to be normal. Normal men have killed perhaps 100,000,000 of their fellow normal men in the last fifty years.”
—R.D. (Ronald David)

“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)