A characterization of the exponential distribution

1972 ◽  
Vol 9 (2) ◽  
pp. 457-461 ◽  
Author(s):  
M. Ahsanullah ◽  
M. Rahman
Keyword(s):  
Probability Distribution ◽  
Order Statistics ◽  
Lebesgue Measure ◽  
Random Variable ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Positive Random Variable ◽  
Absolutely Continuous ◽  
Necessary And Sufficient

A necessary and sufficient condition based on order statistics that a positive random variable having an absolutely continuous probability distribution (with respect to Lebesgue measure) will be exponential is given.

A characterization of the exponential distribution

1972 ◽  
Vol 9 (02) ◽  
pp. 457-461 ◽  
Author(s):  
M. Ahsanullah ◽  
M. Rahman
Keyword(s):  
Probability Distribution ◽  
Order Statistics ◽  
Lebesgue Measure ◽  
Random Variable ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Positive Random Variable ◽  
Absolutely Continuous ◽  
Necessary And Sufficient

A necessary and sufficient condition based on order statistics that a positive random variable having an absolutely continuous probability distribution (with respect to Lebesgue measure) will be exponential is given.

A note on stochastic ordering of order statistics

1997 ◽  
Vol 34 (03) ◽  
pp. 785-789 ◽  
Author(s):  
Chunsheng Ma
Keyword(s):  
Order Statistics ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Stochastic Comparisons ◽  
Homogeneous Population ◽  
Independent Components ◽  
Binomial Random Variable ◽  
Necessary And Sufficient

A necessary and sufficient condition is obtained for a Poisson binomial random variable to be stochastically larger (or smaller) than a binomial random variable. It is then used to deal with the stochastic comparisons of order statistics from heterogeneous populations with those from a homogeneous population. The result has obvious applications in the stochastic comparisons of lifetimes of k-out-of-n systems having independent components.

A note on stochastic ordering of order statistics

1997 ◽  
Vol 34 (3) ◽  
pp. 785-789 ◽  
Author(s):  
Chunsheng Ma
Keyword(s):  
Order Statistics ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Stochastic Comparisons ◽  
Homogeneous Population ◽  
Independent Components ◽  
Binomial Random Variable ◽  
Necessary And Sufficient

A necessary and sufficient condition is obtained for a Poisson binomial random variable to be stochastically larger (or smaller) than a binomial random variable. It is then used to deal with the stochastic comparisons of order statistics from heterogeneous populations with those from a homogeneous population. The result has obvious applications in the stochastic comparisons of lifetimes of k-out-of-n systems having independent components.

Binomial subsampling

2006 ◽  
Vol 462 (2068) ◽  
pp. 1181-1195 ◽  
Author(s):  
Carsten Wiuf ◽  
Michael P.H Stumpf
Keyword(s):  
Mathematical Biology ◽  
Power Series ◽  
Generating Functions ◽  
Binomial Distribution ◽  
Random Variable ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
The Family ◽  
Necessary And Sufficient ◽  
Finite Moments

In this paper, we discuss statistical families with the property that if the distribution of a random variable X is in , then so is the distribution of Z ∼Bi( X ,  p ) for 0≤ p ≤1. (Here we take Z ∼Bi( X ,  p ) to mean that given X = x ,  Z is a draw from the binomial distribution Bi( x ,  p ).) It is said that the family is closed under binomial subsampling. We characterize such families in terms of probability generating functions and for families with finite moments of all orders we give a necessary and sufficient condition for the family to be closed under binomial subsampling. The results are illustrated with power series and other examples, and related to examples from mathematical biology. Finally, some issues concerning inference are discussed.

On representation of Poisson mixtures as Poisson sums and a characterization of the gamma distribution

1977 ◽  
Vol 82 (2) ◽  
pp. 297-300 ◽  
Author(s):  
A. V. Godambe
Keyword(s):  
Gamma Distribution ◽  
Exponential Type ◽  
Similar Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Poisson Mixture ◽  
Mixing Distribution ◽  
Poisson Mixtures ◽  
Necessary And Sufficient

AbstractA necessary and sufficient condition for a Poisson mixture with an exponential type mixing distribution to be equivalently represented as a Poisson sum is obtained. The problem of deriving a similar condition under any mixing distribution on (0, ∞) is discussed. Finally, a characterization of the gamma distribution is obtained.

A characterization of the Poisson process

1974 ◽  
Vol 11 (1) ◽  
pp. 72-85 ◽  
Author(s):  
S. M. Samuels
Keyword(s):  
Poisson Process ◽  
Renewal Process ◽  
Poisson Processes ◽  
Renewal Processes ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Complete Proof ◽  
Necessary And Sufficient

Theorem: A necessary and sufficient condition for the superposition of two ordinary renewal processes to again be a renewal process is that they be Poisson processes.A complete proof of this theorem is given; also it is shown how the theorem follows from the corresponding one for the superposition of two stationary renewal processes.

scholarly journals Isometric Signal Processing under Information Geometric Framework

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 332 ◽  
Author(s):  
Hao Wu ◽  
Yongqiang Cheng ◽  
Hongqiang Wang
Keyword(s):  
Signal Processing ◽  
Probability Distribution ◽  
Geometric Structure ◽  
Information Geometry ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Statistical Manifold ◽  
Intrinsic Parameter ◽  
Geometric Framework ◽  
Necessary And Sufficient

Information geometry is the study of the intrinsic geometric properties of manifolds consisting of a probability distribution and provides a deeper understanding of statistical inference. Based on this discipline, this letter reports on the influence of the signal processing on the geometric structure of the statistical manifold in terms of estimation issues. This letter defines the intrinsic parameter submanifold, which reflects the essential geometric characteristics of the estimation issues. Moreover, the intrinsic parameter submanifold is proven to be a tighter one after signal processing. In addition, the necessary and sufficient condition of invariant signal processing of the geometric structure, i.e., isometric signal processing, is given. Specifically, considering the processing with the linear form, the construction method of linear isometric signal processing is proposed, and its properties are presented in this letter.

On weak convergence within the hnbue family of life distributions

1984 ◽  
Vol 21 (03) ◽  
pp. 654-660 ◽  
Author(s):  
Sujit K. Basu ◽  
Manish C. Bhattacharjee
Keyword(s):  
Weak Convergence ◽  
Exponential Distribution ◽  
Limiting Distribution ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Moment Sequence ◽  
Positive Order ◽  
Life Distributions ◽  
Necessary And Sufficient

We show that the HNBUE family of life distributions is closed under weak convergence and that weak convergence within this family is equivalent to convergence of each moment sequence of positive order to the corresponding moment of the limiting distribution. A necessary and sufficient condition for weak convergence to the exponential distribution is given, based on a new characterization of exponentials within the HNBUE family of life distributions.

A dynamical characterization of diagonal-preserving -isomorphisms of graph -algebras

2017 ◽  
Vol 38 (7) ◽  
pp. 2401-2421 ◽  
Author(s):  
SARA E. ARKLINT ◽  
SØREN EILERS ◽  
EFREN RUIZ
Keyword(s):  
Directed Graphs ◽  
Sufficient Condition ◽  
Orbit Equivalence ◽  
Necessary And Sufficient Condition ◽  
Graph Algebras ◽  
Boundary Path ◽  
Necessary And Sufficient

We characterize when there exists a diagonal-preserving $\ast$-isomorphism between two graph $C^{\ast }$-algebras in terms of the dynamics of the boundary path spaces. In particular, we refine the notion of ‘orbit equivalence’ between the boundary path spaces of the directed graphs $E$ and $F$ and show that this is a necessary and sufficient condition for the existence of a diagonal-preserving $\ast$-isomorphism between the graph $C^{\ast }$-algebras $C^{\ast }(E)$ and $C^{\ast }(F)$.

scholarly journals QKSpaces on the Unit Circle

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Jizhen Zhou
Keyword(s):  
Sobolev Space ◽  
Unit Circle ◽  
Measurable Function ◽  
Weight Functions ◽  
Sufficient Condition ◽  
General Criterion ◽  
Necessary And Sufficient Condition ◽  
New Space ◽  
Necessary And Sufficient

We introduce a new spaceQK(∂D)of Lebesgue measurable functions on the unit circle connecting closely with the Sobolev space. We obtain a necessary and sufficient condition onKsuch thatQK(∂D)=BMO(∂D), as well as a general criterion on weight functionsK1andK2,K1≤K2, such thatQK1(∂D)QK2(∂D). We also prove that a measurable function belongs toQK(∂D)if and only if it is Möbius bounded in the Sobolev spaceLK2(∂D). Finally, we obtain a dyadic characterization of functions inQK(∂D)spaces in terms of dyadic arcs on the unit circle.

Sign in / Sign up

Export Citation Format

Share Document