scholarly journals Geometric infinite divisibility, stability, and self-similarity: an overview

2010 ◽  
Author(s):  
Tomasz J. Kozubowski
Keyword(s):  
Infinite Divisibility ◽  
Self Similarity ◽  
Geometric Infinite Divisibility

scholarly journals Distributions with complete monotone derivative and geometric infinite divisibility

1990 ◽  
Vol 22 (3) ◽  
pp. 751-754 ◽  
Author(s):  
R. N. Pillai ◽  
E. Sandhya
Keyword(s):  
Infinite Divisibility ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible ◽  
Proper Subclass ◽  
Geometric Infinite Divisibility

It is shown that a distribution with complete monotone derivative is geometrically infinitely divisible and that the class of distributions with complete monotone derivative is a proper subclass of the class of geometrically infinitely divisible distributions.

scholarly journals Distributions with complete monotone derivative and geometric infinite divisibility

1990 ◽  
Vol 22 (03) ◽  
pp. 751-754
Author(s):  
R. N. Pillai ◽  
E. Sandhya
Keyword(s):  
Infinite Divisibility ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible ◽  
Proper Subclass ◽  
Geometric Infinite Divisibility

It is shown that a distribution with complete monotone derivative is geometrically infinitely divisible and that the class of distributions with complete monotone derivative is a proper subclass of the class of geometrically infinitely divisible distributions.

Geometric Infinite Divisibility and the Waiting Time Paradox

2005 ◽  
Vol 57 (1-2) ◽  
pp. 129-136
Author(s):  
R.N. Pillai ◽  
Saji Kumar V. R.
Keyword(s):  
Waiting Time ◽  
Renewal Process ◽  
Random Variable ◽  
Infinite Divisibility ◽  
Infinitely Divisible ◽  
Geometric Infinite Divisibility

It is shown that the waiting time W in a stationary renewal process generated by X has the form W = X+ Y, with Y non­negative independent of X if and only if X is a geometrically infinitely divisible random variable. This is an improvement over Van Harn and Steutel (1995) where the converse is left unproved .

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