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.

Approximations to densities in geometric probability

1980 ◽  
Vol 17 (01) ◽  
pp. 145-153 ◽  
Author(s):  
H. Solomon ◽  
M. A. Stephens
Keyword(s):  
Monte Carlo ◽  
Random Variables ◽  
Monte Carlo Sampling ◽  
Geometric Probability ◽  
Simple Approximation ◽  
Chi Square ◽  
Percentage Points ◽  
Random Polygons

Many random variables arising in problems of geometric probability have intractable densities, and it is very difficult to find probabilities or percentage points based on these densities. A simple approximation, a generalization of the chi-square distribution, is suggested, to approximate such densities; the approximation uses the first three moments. These may be theoretically derived, or may be obtained from Monte Carlo sampling. The approximation is illustrated on random variables (the area, the perimeter, and the number of sides) associated with random polygons arising from two processes in the plane. Where it can be checked theoretically, the approximation gives good results. It is compared also with Pearson curve fits to the densities.

ON THE LINEAR COMBINATION OF LAPLACE RANDOM VARIABLES

2005 ◽  
Vol 19 (4) ◽  
pp. 463-470 ◽  
Author(s):  
Saralees Nadarajah ◽  
Samuel Kotz
Keyword(s):  
Fuzzy Sets ◽  
Linear Combination ◽  
Random Variables ◽  
Percentage Points ◽  
Automation Control

The distribution of the linear combination αX + βY is derived when X and Y are independent Laplace random variables. Extensive tabulations of the associated percentage points are also given. The work is motivated by examples in automation, control, fuzzy sets, neurocomputing, and other areas of informational sciences.

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.

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