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.

scholarly journals On the product and ratio of Bessel random variables

2005 ◽  
Vol 2005 (18) ◽  
pp. 2977-2989 ◽  
Author(s):  
Saralees Nadarajah ◽  
Arjun K. Gupta
Keyword(s):  
Bessel Function ◽  
Random Variables ◽  
Percentage Points ◽  
Ratios Of Random Variables ◽  
Exact Distributions

The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product|XY|and the ratio|X/Y|are derived whenXandYare independent Bessel function random variables. An application of the results is provided by tabulating the associated percentage points.

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 On the product and ratio of Laplace and Bessel random variables

2005 ◽  
Vol 2005 (4) ◽  
pp. 393-402 ◽  
Author(s):  
Saralees Nadarajah
Keyword(s):  
Bessel Function ◽  
Random Variables ◽  
Ratios Of Random Variables ◽  
Exact Distributions

The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product|XY|and the ratio|X/Y|are derived whenXandYare Laplace and Bessel function random variables distributed independently of each other.

scholarly journals Exact distributions of order statistics of dependent random variables from ln,p-symmetric sample distributions, n ∈ {3,4}

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
K. Müller ◽  
W.-D. Richter
Keyword(s):  
Computer Program ◽  
Order Statistics ◽  
Stock Exchange ◽  
Random Variables ◽  
Integral Representations ◽  
Symmetric Distribution ◽  
Random Vectors ◽  
Dependent Random Variables ◽  
Exact Distributions

AbstractIntegral representations of the exact distributions of order statistics are derived in a geometric way when three or four random variables depend on each other as the components of continuous ln,psymmetrically distributed random vectors do, n ∈ {3,4}, p > 0. Once the representations are implemented in a computer program, it is easy to change the density generator of the ln,p-symmetric distribution with another one for newly evaluating the distribution of interest. For two groups of stock exchange index residuals, maximum distributions are compared under dependence and independence modeling.

Some exact distributions of a last one-sided exit time in the simple random walk

1986 ◽  
Vol 23 (02) ◽  
pp. 332-340
Author(s):  
Chern-Ching Chao ◽  
John Slivka
Keyword(s):  
Random Walk ◽  
Positive Integer ◽  
Exit Time ◽  
Random Variables ◽  
Random Variable ◽  
Simple Random Walk ◽  
Exact Distribution ◽  
Partial Sum ◽  
Exact Distributions ◽  
Special Case

For each positive integer n, let Sn be the nth partial sum of a sequence of i.i.d. random variables which assume the values +1 and −1 with respective probabilities p and 1 – p, having mean μ= 2p − 1. The exact distribution of the random variable , where sup Ø= 0, is given for the case that λ > 0 and μ+ λ= k/(k + 2) for any non-negative integer k. Tables to the 99.99 percentile of some of these distributions, as well as a limiting distribution, are given for the special case of a symmetric simple random walk (p = 1/2).

scholarly journals On the Product and Ratio of Pearson Type VII and Laplace Random Variables

2016 ◽  
Vol 34 (1) ◽  
Author(s):  
Saralees Nadarajah ◽  
Samuel Kotz
Keyword(s):  
Random Variables ◽  
Percentage Points ◽  
Pearson Type

The distributions of the product |XY|  and the ratio |X/Y| are derived when X and Y are Pearson type VII and Laplace random variables distributed independently of each other. Extensive tabulations of the associated percentage points are also given.

Saddle point approximation for the distribution of the sum of independent random variables

1980 ◽  
Vol 12 (2) ◽  
pp. 475-490 ◽  
Author(s):  
Robert Lugannani ◽  
Stephen Rice
Keyword(s):  
Probability Distribution ◽  
Saddle Point ◽  
Probability Density ◽  
Excellent Agreement ◽  
Good Accuracy ◽  
Asymptotic Series ◽  
Random Variables ◽  
Independent Random Variables ◽  
Saddle Point Approximation ◽  
Exact Distributions

In the present paper a uniform asymptotic series is derived for the probability distribution of the sum of a large number of independent random variables. In contrast to the usual Edgeworth-type series, the uniform series gives good accuracy throughout its entire domain. Our derivation uses the fact that the major components of the distribution are determined by a saddle point and a singularity at the origin. The analogous series for the probability density, due to Daniels, depends only on the saddle point. Two illustrative examples are presented that show excellent agreement with the exact distributions.

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