A characterization of probability distributions by moments of sums of independent random variables

1994 ◽  
Vol 7 (1) ◽  
pp. 187-198 ◽  
Author(s):  
Michael Braverman
Keyword(s):  
Probability Distributions ◽  
Random Variables ◽  
Independent Random Variables ◽  
Characterization Of Probability Distributions

A characterization of the negative exponential distribution with application to reliability theory

1981 ◽  
Vol 18 (3) ◽  
pp. 652-659 ◽  
Author(s):  
M. J. Phillips
Keyword(s):  
Exponential Distribution ◽  
Random Variables ◽  
Reliability Theory ◽  
The Other ◽  
Independent Random Variables ◽  
System Availability ◽  
Failure Times ◽  
Negative Exponential Distribution ◽  
Negative Exponential

The negative exponential distribution is characterized in terms of two independent random variables. Only one of the random variables has a negative exponential distribution whilst the other can belong to a wide class of distributions. This result is then applied to two models for the reliability of a system of two modules subject to revealed and unrevealed faults to show when the models are equivalent. It is also shown, under certain conditions, that the system availability is only independent of the distribution of revealed failure times in one module when unrevealed failure times in the other module have a negative exponential distribution.

Some new approaches to probability distributions

1980 ◽  
Vol 12 (04) ◽  
pp. 903-921 ◽  
Author(s):  
S. Kotz ◽  
D. N. Shanbhag
Keyword(s):  
Probability Distributions ◽  
Random Variables ◽  
Representation Theorems ◽  
Practical Applications ◽  
New Approaches ◽  
Characterization Of Distributions ◽  
Stability Theorems ◽  
Conditional Expectations

We develop some approaches to the characterization of distributions of real-valued random variables, useful in practical applications, in terms of conditional expectations and hazard measures. We prove several representation theorems generalizing earlier results, and establish stability theorems for two general characteristics introduced in this paper.

A joint characterization of the multinomial distribution and the Poisson process

1983 ◽  
Vol 20 (01) ◽  
pp. 202-208 ◽  
Author(s):  
George Kimeldorf ◽  
Peter F. Thall
Keyword(s):  
Poisson Process ◽  
Present Article ◽  
Point Process ◽  
Random Variables ◽  
Multinomial Distribution ◽  
Process Theory ◽  
Independent Random Variables ◽  
Mutually Independent

It has been recently proved that if N, X 1, X 2, … are non-constant mutually independent random variables with X 1,X 2, … identically distributed and N non-negative and integer-valued, then the independence of and implies that X 1 is Bernoulli and N is Poisson. A well-known theorem in point process theory due to Fichtner characterizes a Poisson process in terms of a sum of independent thinnings. In the present article, simultaneous generalizations of both of these results are provided, including a joint characterization of the multinomial distribution and the Poisson process.

A characterization of the negative exponential distribution with application to reliability theory

1981 ◽  
Vol 18 (03) ◽  
pp. 652-659 ◽  
Author(s):  
M. J. Phillips
Keyword(s):  
Exponential Distribution ◽  
Random Variables ◽  
Reliability Theory ◽  
The Other ◽  
Independent Random Variables ◽  
System Availability ◽  
Failure Times ◽  
Negative Exponential Distribution ◽  
Negative Exponential

The negative exponential distribution is characterized in terms of two independent random variables. Only one of the random variables has a negative exponential distribution whilst the other can belong to a wide class of distributions. This result is then applied to two models for the reliability of a system of two modules subject to revealed and unrevealed faults to show when the models are equivalent. It is also shown, under certain conditions, that the system availability is only independent of the distribution of revealed failure times in one module when unrevealed failure times in the other module have a negative exponential distribution.

On read-once transformations of random variables over finite fields

2015 ◽  
Vol 25 (5) ◽  
Author(s):  
Aleksey D. Yashunsky
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Probability Distributions ◽  
Random Variables ◽  
Independent Random Variables ◽  
Independent Identically Distributed ◽  
Family Of Distributions

AbstractTransformations of independent random variables over a finite field by read-once formulas are considered. Subsets of probability distributions that are preserved by read-once transformations are constructed. Also we construct a family of distributions that may be arbitrarily closely approximated by a read-once combination of independent identically distributed random variables, whose distributions have no zero components.

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