scholarly journals On the ratio of Pearson type VII and Bessel random variables

2005 ◽  
Vol 2005 (4) ◽  
pp. 191-199 ◽  
Author(s):  
Saralees Nadarajah ◽  
Samuel Kotz
Keyword(s):  
Bessel Function ◽  
Random Variables ◽  
Exact Distribution ◽  
Correction Factors ◽  
Pearson Type

The exact distribution of the ratio |X/Y| is derived when X and Y are, respectively, Pearson type VII and Bessel function random variables distributed independently of each other. The work is motivated by previously published approximate relationships between these two distributions. An application of the result is provided by computing “correction factors” for some of these approximations.

scholarly journals Exact Distributions of the Product and Ratio of Absolute Values of Pearson Type VII and Bessel Function Random Variables

2006 ◽  
Vol 13 (2) ◽  
pp. 333-341
Author(s):  
Saralees Nadarajah ◽  
Samuel Kotz
Keyword(s):  
Bessel Function ◽  
Random Variables ◽  
Pearson Type ◽  
Exact Distributions

Abstract Exact distributions of |𝑋𝑌| and |𝑋/𝑌| are derived when 𝑋 and 𝑌 are Pearson type VII and Bessel function random variables distributed independently of each other.

Sample Size Calculation for Poisson Endpoint Using the Exact Distribution of Difference Between Two Poisson Random Variables

2011 ◽  
Vol 3 (3) ◽  
pp. 497-504 ◽  
Author(s):  
Sandeep Menon ◽  
Joseph Massaro ◽  
Jerry Lewis ◽  
Michael Pencina ◽  
Yong-Cheng Wang ◽  
...  
Keyword(s):  
Sample Size ◽  
Sample Size Calculation ◽  
Random Variables ◽  
Exact Distribution

The log-normal approximation in financial and other computations

2004 ◽  
Vol 36 (03) ◽  
pp. 747-773 ◽  
Author(s):  
Daniel Dufresne
Keyword(s):  
Brownian Motion ◽  
Explicit Formula ◽  
Normal Approximation ◽  
Random Variables ◽  
Exact Distribution ◽  
Financial Mathematics ◽  
Asian Options ◽  
Basket Options ◽  
Asymptotic Formulae ◽  
Log Normal

Sums of log-normals frequently appear in a variety of situations, including engineering and financial mathematics. In particular, the pricing of Asian or basket options is directly related to finding the distributions of such sums. There is no general explicit formula for the distribution of sums of log-normal random variables. This paper looks at the limit distributions of sums of log-normal variables when the second parameter of the log-normals tends to zero or to infinity; in financial terms, this is equivalent to letting the volatility, or maturity, tend either to zero or to infinity. The limits obtained are either normal or log-normal, depending on the normalization chosen; the same applies to the reciprocal of the sums of log-normals. This justifies the log-normal approximation, much used in practice, and also gives an asymptotically exact distribution for averages of log-normals with a relatively small volatility; it has been noted that all the analytical pricing formulae for Asian options perform poorly for small volatilities. Asymptotic formulae are also found for the moments of the sums of log-normals. Results are given for both discrete and continuous averages. More explicit results are obtained in the case of the integral of geometric Brownian motion.

Exact Distribution for the Product of Two Correlated Gaussian Random Variables

2016 ◽  
Vol 23 (11) ◽  
pp. 1662-1666 ◽  
Author(s):  
Guolong Cui ◽  
Xianxiang Yu ◽  
Salvatore Iommelli ◽  
Lingjiang Kong
Keyword(s):  
Random Variables ◽  
Exact Distribution ◽  
Gaussian Random Variables
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