Abstract
Given the distribution function of x and y, what can be said of the distribution of the product xy? The author has had two inquiries during the last two years, one from an investigator in business statistics and the other from a psychologist, concerning the probable error of the product of two quantities, each of known probable error. There seems to be very little in the literature of mathematical statistics on this question. If x and y are independent and are each distributed according to the same normal frequency law, it is well known that the distribution function of
Keywords
MathematicsQ-functionDistribution (mathematics)Function (biology)Distribution functionStatisticsProduct (mathematics)Normal distributionCalculus (dental)Applied mathematicsMathematical analysisProbability density functionCumulative distribution functionPhysics
Related Publications
On the Exact Variance of Products
Abstract A simple exact formula for the variance of the product of two random variables, say, x and y, is given as a function of the means and central product-moments of x and y...
The Probability Function of the Product of Two Normally Distributed Variables
Let $x$ and $y$ follow a normal bivariate probability function with means $\\bar X, \\bar Y$, standard deviations $\\sigma_1, \\sigma_2$, respectively, $r$ the coefficient of co...
On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other
Let $x$ and $y$ be two random variables with continuous cumulative distribution functions $f$ and $g$. A statistic $U$ depending on the relative ranks of the $x$'s and $y$'s is ...
Mathematical forms of the distribution of the product of two normal variables
This paper finds the mathematical forms of the distribution of the product where x and x follow a bivariate normal distribution In this paper the distribution when PT0 is expres...
A stochastic‐conceptual analysis of one‐dimensional groundwater flow in nonuniform homogeneous media
The most realistic representation of a naturally occurring porous medium is a stochastic set of macroscopic elements in which the values of the three basic hydrogeologic paramet...
Publication Info
- Year
- 1936
- Type
- article
- Volume
- 7
- Issue
- 1
- Pages
- 1-15
- Citations
- 331
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
331
OpenAlex
Cite This
C. C. Craig
(1936).
On the Frequency Function of $xy$.
The Annals of Mathematical Statistics
, 7
(1)
, 1-15.
https://doi.org/10.1214/aoms/1177732541
Identifiers
- DOI
- 10.1214/aoms/1177732541