New Stochastic Orders Based on Double Truncation

1997 ◽  
Vol 11 (3) ◽  
pp. 395-402 ◽  
Author(s):  
Jorge Navarro ◽  
Felix Belzunce ◽  
Jose M. Ruiz
Keyword(s):  
Likelihood Ratio ◽  
Random Variable ◽  
Stochastic Orders ◽  
Likelihood Ratio Order ◽  
Reliability Measures ◽  
Life Distributions ◽  
The Relationship ◽  
Double Truncation

The purpose of this paper is to study definitions and characterizations of orders based on reliability measures related with the doubly truncated random variable X[x, y] = (X|x ≤ X ≤ y). The relationship between these orderings and various existing orderings of life distributions are discussed. Moreover, we give two new characterizations of the likelihood ratio order based on double truncation. These new orders complete a general diagram between orders defined from truncation.

Glaser’s function and stochastic orders for mixture distributions

2016 ◽  
Vol 33 (8) ◽  
pp. 1230-1238
Author(s):  
Jalil Jarrahiferiz ◽  
G.R. Mohtashami Borzadaran ◽  
A.H. Rezaei Roknabadi
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Exponential Family ◽  
Random Variable ◽  
Moment Generating Function ◽  
Stochastic Orders ◽  
Weight Functions ◽  
Likelihood Ratio Order ◽  
Content Type ◽  
Weighted Distributions

Purpose The purpose of this paper is to study likelihood ratio order for mixture and its components via their Glaser’s functions for weighted distributions. So, some theoretical examples using exponential family and their mixtures are presented. Design/methodology/approach First, Glaser’s functions of mixture and its components for weighted distributions in different scenarios are computed. Then by them the likelihood ratio order is investigated between mixture and its components. Findings The authors find conditions for weight functions under which the mixture random variable is between of its components in likelihood ratio order. Originality/value Results are obtained for weight function in general. It is well known that the some special weights are order statistics, up and down records, hazard rate, reversed hazard rate, moment generating function, etc. So, the results are valid for all of them.

Stochastic Orders Generated by Integrals: a Unified Study

1997 ◽  
Vol 29 (02) ◽  
pp. 414-428 ◽  
Author(s):  
Alfred Müller
Keyword(s):  
Functional Analysis ◽  
Weak Convergence ◽  
Likelihood Ratio ◽  
Stochastic Orders ◽  
Probability Measures ◽  
Likelihood Ratio Order ◽  
Unified Study ◽  
Maximal Cone ◽  
Class Of Functions

We consider stochastic orders of the following type. Let be a class of functions and let P and Q be probability measures. Then define , if ∫ ⨍ d P ≦ ∫ ⨍ d Q for all f in . Marshall (1991) posed the problem of characterizing the maximal cone of functions generating such an ordering. We solve this problem by using methods from functional analysis. Another purpose of this paper is to derive properties of such integral stochastic orders from conditions satisfied by the generating class of functions. The results are illustrated by several examples. Moreover, we show that the likelihood ratio order is closed with respect to weak convergence, though it is not generated by integrals.

Stochastic Orders Generated by Integrals: a Unified Study

1997 ◽  
Vol 29 (2) ◽  
pp. 414-428 ◽  
Author(s):  
Alfred Müller
Keyword(s):  
Functional Analysis ◽  
Weak Convergence ◽  
Likelihood Ratio ◽  
Stochastic Orders ◽  
Probability Measures ◽  
Likelihood Ratio Order ◽  
Unified Study ◽  
Maximal Cone ◽  
Class Of Functions

We consider stochastic orders of the following type. Let be a class of functions and let P and Q be probability measures. Then define , if ∫ ⨍ d P ≦ ∫ ⨍ d Q for all f in . Marshall (1991) posed the problem of characterizing the maximal cone of functions generating such an ordering. We solve this problem by using methods from functional analysis. Another purpose of this paper is to derive properties of such integral stochastic orders from conditions satisfied by the generating class of functions. The results are illustrated by several examples. Moreover, we show that the likelihood ratio order is closed with respect to weak convergence, though it is not generated by integrals.

Weighting, likelihood ratio order and life distributions

2006 ◽  
Vol 33 (3-4) ◽  
pp. 283-291
Author(s):  
Magdalena Skolimowska ◽  
Jarosław Bartoszewicz
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Order ◽  
Life Distributions

Stochastic comparisons of series and parallel systems with independent heterogeneous Gumbel and truncated Gumbel components

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Fatih Kızılaslan
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Design Methodology ◽  
Parallel Systems ◽  
Parallel System ◽  
Series System ◽  
Stochastic Comparisons ◽  
Content Type ◽  
Reversed Hazard Rate ◽  
The Relationship

PurposeThe purpose of this paper is to investigate the stochastic comparisons of the parallel system with independent heterogeneous Gumbel components and series and parallel systems with independent heterogeneous truncated Gumbel components in terms of various stochastic orderings.Design/methodology/approachThe obtained results in this paper are obtained by using the vector majorization methods and results. First, the components of series and parallel systems are heterogeneous and having Gumbel or truncated Gumbel distributions. Second, multiple-outlier truncated Gumbel models are discussed for these systems. Then, the relationship between the systems having Gumbel components and Weibull components are considered. Finally, Monte Carlo simulations are performed to illustrate some obtained results.FindingsThe reversed hazard rate and likelihood ratio orderings are obtained for the parallel system of Gumbel components. Using these results, similar new results are derived for the series system of Weibull components. Stochastic comparisons for the series and parallel systems having truncated Gumbel components are established in terms of hazard rate, likelihood ratio and reversed hazard rate orderings. Some new results are also derived for the series and parallel systems of upper-truncated Weibull components.Originality/valueTo the best of our knowledge thus far, stochastic comparisons of series and parallel systems with Gumbel or truncated Gumble components have not been considered in the literature. Moreover, new results for Weibull and upper-truncated Weibull components are presented based on Gumbel case results.

DERIVING ROBUST BAYESIAN PREMIUMS UNDER BANDS OF PRIOR DISTRIBUTIONS WITH APPLICATIONS

2018 ◽  
Vol 49 (1) ◽  
pp. 147-168 ◽  
Author(s):  
M. Sánchez-Sánchez ◽  
M.A. Sordo ◽  
A. Suárez-Llorens ◽  
E. Gómez-Déniz
Keyword(s):  
Bayesian Analysis ◽  
Likelihood Ratio ◽  
Requirements Elicitation ◽  
Likelihood Ratio Order ◽  
Prior Distributions ◽  
Propagation Of Uncertainty ◽  
Distortion Functions ◽  
Wide Family ◽  
Class Of Priors ◽  
Quantities Of Interest

AbstractWe study the propagation of uncertainty from a class of priors introduced by Arias-Nicolás et al. [(2016) Bayesian Analysis, 11(4), 1107–1136] to the premiums (both the collective and the Bayesian), for a wide family of premium principles (specifically, those that preserve the likelihood ratio order). The class under study reflects the prior uncertainty using distortion functions and fulfills some desirable requirements: elicitation is easy, the prior uncertainty can be measured by different metrics, and the range of quantities of interest is easily obtained from the extremal members of the class. We illustrate the methodology with several examples based on different claim counts models.

A Feature-Segmentation Model of Short-Term Visual Memory

Perception ◽  
10.1068/p3320 ◽  
2002 ◽  
Vol 31 (5) ◽  
pp. 579-589 ◽  
Author(s):  
Koji Sakai ◽  
Toshio Inui
Keyword(s):  
Visual Memory ◽  
Random Variable ◽  
Short Term ◽  
Pattern Complexity ◽  
Convex Part ◽  
Good Account ◽  
Feature Segmentation ◽  
Short Term Visual Memory ◽  
The Relationship ◽  
Response Feature

A feature-segmentation model of short-term visual memory (STVM) for contours is proposed. Memory of the first stimulus is maintained until the second stimulus is observed. Three processes interact to determine the relationship between stimulus and response: feature encoding, memory, and decision. Basic assumptions of the model are twofold: (i) the STVM system divides a contour into convex parts at regions of concavity; and (ii) the value of each convex part represented in STVM is an independent Gaussian random variable. Simulation showed that the five-parameter fits give a good account of the effects of the four experimental variables. The model provides evidence that: (i) contours are successfully encoded within 0.5 s exposure, regardless of pattern complexity; (ii) memory noise increases as a linear function of retention interval; (iii) the capacity of STVM, defined by pattern complexity (the degree that a pattern can be handled for several seconds with little loss), is about 4 convex parts; and (iv) the confusability contributing to the decision process is a primary factor in deteriorating recognition of complex figures. It is concluded that visually presented patterns can be retained in STVM with considerable precision for prolonged periods of time, though some loss of precision is inevitable.

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