Ratio Distribution: Probability Distribution, Ratio, Random Variable, Cauchy Student's T F Normal Chi Square Distribution

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A ratio distribution (or quotient distribution) is a probability distribution constructed as the distribution of the ratio of random variables having two other known distributions. The Cauchy distribution is an example of a ratio distribution. The random variable associated with this distribution comes about as the ratio of two Gaussian (normal) distributed variables with zero mean. Thus the Cauchy distribution is also called the normal ratio distribution. A number of researchers have considered more general ratio distributions. Two distribution often used in test-statistics, the t-distribution and the F-distribution, are also ratio distributions: The t-distributed random variable is the ratio of a Gaussian random variable divided by an independent chi-distributed random variable (i.e., the square root of a chi-square distribution), while the F-distributed random variable is the ratio of two independent chi-square distributed random variables. Often the ratio distributions are heavy-tailed, and it may be difficult to work with such distributions and develop an associated statistical test. A method based on the median has been suggested as a "work-around".