Computing the exact distribution of a linear combination of generalized logistic random variables and its applications

2021 ◽  
pp. 1-19
Author(s):  
Božidar V. Popović ◽  
Andjela Mijanović ◽  
Viktor Witkovský
Keyword(s):  
Linear Combination ◽  
Random Variables ◽  
Exact Distribution

scholarly journals Exact Distributions of the Linear Combination of Gamma and Rayleigh Random Variables

2016 ◽  
Vol 38 (1) ◽  
Author(s):  
Mohammad Shakil ◽  
B.M. Golam Kibria
Keyword(s):  
Linear Combination ◽  
Random Variables ◽  
Exact Distribution ◽  
Statistical Application ◽  
Exact Distributions

The distribution of a linear combination of random variables arise in many applied problems, and have been extensively studied by different researchers. This article derived the exact distribution of the linear combination aX + bY , where a > 0 and b are real constants, and X and Y denote gamma and Rayleigh random variables respectively and are distributed independently of each other. The associated cdfs and pdfs have been derived. The plots for the cdf and pdf, percentile points for selected coefficients and parameters, and the statistical application of the results have been provided. We hope thefindings of the paper will be useful for practitioners in various fields.

Estimating the cumulative distribution function for the linear combination of gamma random variables

2017 ◽  
Vol 20 (5) ◽  
pp. 939-951
Author(s):  
Amal Almarwani ◽  
Bashair Aljohani ◽  
Rasha Almutairi ◽  
Nada Albalawi ◽  
Alya O. Al Mutairi
Keyword(s):  
Distribution Function ◽  
Linear Combination ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Cumulative Distribution

Continuity for multi-type branching processes with varying environments

1999 ◽  
Vol 36 (01) ◽  
pp. 139-145 ◽  
Author(s):  
Owen Dafydd Jones
Keyword(s):  
Linear Combination ◽  
Branching Process ◽  
Branching Processes ◽  
Random Variables ◽  
Main Tool ◽  
Concentration Function ◽  
Independent Random Variables ◽  
Varying Environments

Conditions are derived for the components of the normed limit of a multi-type branching process with varying environments, to be continuous on (0, ∞). The main tool is an inequality for the concentration function of sums of independent random variables, due originally to Petrov. Using this, we show that if there is a discontinuity present, then a particular linear combination of the population types must converge to a non-random constant (Equation (1)). Ensuring this can not happen provides the desired continuity conditions.

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
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