scholarly journals Convex transform order of Beta distributions with some consequences

2021 ◽  
Author(s):  
Idir Arab ◽  
Paulo Eduardo Oliveira ◽  
Tilo Wiklund
Keyword(s):  
Beta Distributions ◽  
Convex Transform Order

Optimal bounds on expectations of order statistics and spacings from nonparametric families of distributions generated by convex transform order

Metrika ◽  
2014 ◽  
Vol 78 (2) ◽  
pp. 175-204 ◽  
Author(s):  
Agnieszka Goroncy ◽  
Tomasz Rychlik
Keyword(s):  
Order Statistics ◽  
Convex Transform Order ◽  
Optimal Bounds

On stochastic comparisons of k-out-of-n systems with Weibull components

2018 ◽  
Vol 55 (1) ◽  
pp. 216-232 ◽  
Author(s):  
Narayanaswamy Balakrishnan ◽  
Ghobad Barmalzan ◽  
Abedin Haidari
Keyword(s):  
Weibull Model ◽  
Exponential Model ◽  
Parallel System ◽  
Stochastic Orders ◽  
Open Problems ◽  
Increasing Convex Order ◽  
Scale Parameters ◽  
Convex Transform Order ◽  
Right Spread Order ◽  
The Right

Abstract In this paper we prove that a parallel system consisting of Weibull components with different scale parameters ages faster than a parallel system comprising Weibull components with equal scale parameters in the convex transform order when the lifetimes of components of both systems have different shape parameters satisfying some restriction. Moreover, while comparing these two systems, we show that the dispersive and the usual stochastic orders, and the right-spread order and the increasing convex order are equivalent. Further, some of the known results in the literature concerning comparisons of k-out-of-n systems in the exponential model are extended to the Weibull model. We also provide solutions to two open problems mentioned by Balakrishnan and Zhao (2013) and Zhao et al. (2016).

The Non-Central Chi-Squared and Beta Distributions

Biometrika ◽  
1963 ◽  
Vol 50 (3/4) ◽  
pp. 542 ◽  
Author(s):  
G. A. F. Seber
Keyword(s):  
Beta Distributions ◽  
Chi Squared

scholarly journals Dot Detection of Braille Images Using A Mixture of Beta Distributions

2011 ◽  
Vol 7 (11) ◽  
pp. 1749-1759 ◽  
Author(s):  
Al-Saleh
Keyword(s):  
Beta Distributions

scholarly journals Dual Lukacs regressions of negative orders for noncommutative variables

2014 ◽  
Vol 17 (03) ◽  
pp. 1450021 ◽  
Author(s):  
Kamil Szpojankowski
Keyword(s):  
Free Probability ◽  
Random Variable ◽  
Probability Measures ◽  
Classical Probability ◽  
Binomial Distributions ◽  
Beta Distributions

In the paper we study characterizations of probability measures in free probability. By constancy of regressions for random variable 𝕍1/2(𝕀 - 𝕌)𝕍1/2 given by 𝕍1/2𝕌𝕍1/2, where 𝕌 and 𝕍 are free, we characterize free Poisson and free binomial distributions. Our paper is a free probability analogue of results known in classical probability,3 where gamma and beta distributions are characterized by constancy of 𝔼((V(1 - U))i|UV), for i ∈ {-2, -1, 1, 2}. This paper together with previous results18 exhaust all cases of characterizations from Ref. 3.

scholarly journals Comparisons of Parallel Systems According to the Convex Transform Order

2009 ◽  
Vol 46 (2) ◽  
pp. 342-352 ◽  
Author(s):  
Subhash Kochar ◽  
Maochao Xu
Keyword(s):  
Hazard Rate ◽  
Parallel Systems ◽  
Sufficient Condition ◽  
Proportional Hazard ◽  
Rate Model ◽  
Hazard Rate Model ◽  
Convex Transform Order ◽  
Right Spread Order ◽  
The Right ◽  
Equivalent Conditions

A parallel system with heterogeneous exponential component lifetimes is shown to be more skewed (according to the convex transform order) than the system with independent and identically distributed exponential components. As a consequence, equivalent conditions for comparing the variabilities of the largest order statistics from heterogeneous and homogeneous exponential samples in the sense of the dispersive order and the right-spread order are established. A sufficient condition is also given for the proportional hazard rate model.

Some Bimatrix Beta Distributions

2012 ◽  
Vol 41 (5) ◽  
pp. 869-879 ◽  
Author(s):  
Arjun K. Gupta ◽  
Daya K. Nagar
Keyword(s):  
Beta Distributions

scholarly journals The Hurwicz Decision Rule’s Relationship to Decision Making with the Triangle and Beta Distributions and Exponential Utility

2018 ◽  
Vol 15 (3) ◽  
pp. 139-153 ◽  
Author(s):  
Sarat Sivaprasad ◽  
Cameron A. MacKenzie
Keyword(s):  
Decision Making ◽  
Exponential Utility ◽  
Beta Distributions

scholarly journals Beta Distributions and Sonine Integrals for Bessel Functions on Symmetric Cones

2018 ◽  
Vol 141 (4) ◽  
pp. 474-500 ◽  
Author(s):  
Margit Rösler ◽  
Michael Voit
Keyword(s):  
Bessel Functions ◽  
Symmetric Cones ◽  
Beta Distributions
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