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.

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.

Investigating the Effect of Prior Distributions on Posterior Estimates of Common Cause Failure Parameters Using Bayesian Method

2020 ◽  
Vol 6 (3) ◽  
Author(s):  
Edward Shitsi ◽  
Emmanuel K. Boafo ◽  
Felix Ameyaw ◽  
H. C. Odoi
Keyword(s):  
Bayesian Analysis ◽  
Confidence Level ◽  
Bayesian Method ◽  
Jeffreys Prior ◽  
Uncertainty Interval ◽  
Prior Distributions ◽  
Common Cause ◽  
Common Cause Failure ◽  
Dirichlet Prior ◽  
The Mean

Abstract Quantification of common cause failure (CCF) parameters and their application in multi-unit PSA are important to the safety and operation of nuclear power plants (NPPs) on the same site. CCF quantification mainly involves the estimation of potential failure of redundant components of systems in a NPP. The components considered in quantification of CCF parameters include motor operated valves, pumps, safety relief valves, air-operated valves, solenoid-operated valves, check valves, diesel generators, batteries, inverters, battery chargers, and circuit breakers. This work presents the results of the CCF parameter quantification using check valves and pumps. The systems considered as case studies for the demonstration of the proposed methodology are auxiliary feedwater system (AFWS) and high-pressure safety injection (HPSI) systems of a pressurized water reactor (PWR). The posterior estimates of alpha factors assuming two different prior distributions (Uniform Dirichlet prior and Jeffreys prior) using the Bayesian method were investigated. This analysis is important due to the fact that prior distributions assumed for alpha factors may affect the shape of posterior distribution and the uncertainty of the mean posterior estimates. For the two different priors investigated in this study, the shape of the posterior distribution is not influenced by the type of prior selected for the analysis. The mean of the posterior distributions was also analyzed at 90% confidence level. These results show that the type of prior selected for Bayesian analysis could have effects on the uncertainty interval (or the confidence interval) of the mean of the posterior estimates. The longer the confidence interval, the better the type of prior selected at a particular confidence level for Bayesian analysis. These results also show that Jeffreys prior is preferred over Uniform Dirichlet prior for Bayesian analysis because it yields longer confidence intervals (or shorter uncertainty interval) at 90% confidence level discussed in this work.

scholarly journals On the Convolution of Heterogeneous Bernoulli Random Variables

2011 ◽  
Vol 48 (3) ◽  
pp. 877-884 ◽  
Author(s):  
Maochao Xu ◽  
N. Balakrishnan
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Random Variables ◽  
Likelihood Ratio Order ◽  
Hazard Rate Order ◽  
Reversed Hazard Rate ◽  
Bernoulli Random Variables

In this paper, some ordering properties of convolutions of heterogeneous Bernoulli random variables are discussed. It is shown that, under some suitable conditions, the likelihood ratio order and the reversed hazard rate order hold between convolutions of two heterogeneous Bernoulli sequences. The results established here extend and strengthen the previous results of Pledger and Proschan (1971) and Boland, Singh and Cukic (2002).

Likelihood ratio order of the second spacing in multiple-outlier exponential models

Statistics ◽  
2015 ◽  
Vol 50 (1) ◽  
pp. 206-218
Author(s):  
Peng Zhao ◽  
Jianfei Qiao ◽  
N. Balakrishnan
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Order ◽  
Exponential Models

APPLICATIONS OF LIKELIHOOD RATIO ORDER IN BAYESIAN INFERENCES

2018 ◽  
Vol 34 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Kai Huang ◽  
Jie Mi
Keyword(s):  
Likelihood Ratio ◽  
Bayes Factor ◽  
Loss Functions ◽  
Posterior Distributions ◽  
Likelihood Ratio Order ◽  
Predictive Distributions ◽  
Sufficient Statistic ◽  
Bayesian Inferences ◽  
Bayesian Estimators ◽  
General Error

The present paper studies the likelihood ratio order of posterior distributions of parameter when the same order exists between the corresponding prior of the parameter, or when the observed values of the sufficient statistic for the parameter differ. The established likelihood order allows one to compare the Bayesian estimators associated with many common and general error loss functions analytically. It can also enable one to compare the Bayes factor in hypothesis testing without using numerical computation. Moreover, using the likelihood ratio (LR) order of the posterior distributions can yield the LR order between marginal predictive distributions, and posterior predictive distributions.

STOCHASTIC MONOTONICITY OF CONDITIONAL ORDER STATISTICS IN MULTIPLE-OUTLIER SCALE POPULATION

2016 ◽  
Vol 31 (3) ◽  
pp. 366-380
Author(s):  
Ebrahim Amini-Seresht ◽  
Yiying Zhang
Keyword(s):  
Distribution Function ◽  
Order Statistics ◽  
Likelihood Ratio ◽  
Monotonicity Property ◽  
Independent Random Variables ◽  
Likelihood Ratio Order ◽  
Stochastic Monotonicity ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Parametric Families

This paper discusses the stochastic monotonicity property of the conditional order statistics from independent multiple-outlier scale variables in terms of the likelihood ratio order. Let X1, …, Xn be a set of non-negative independent random variables with Xi, i=1, …, p, having common distribution function F(λ1x), and Xj, j=p+1, …, n, having common distribution function F(λ2x), where F(·) denotes the baseline distribution. Let Xi:n(p, q) be the ith smallest order statistics from this sample. Denote by $X_{i,n}^{s}(p,q)\doteq [X_{i:n}(p,q)|X_{i-1:n}(p,q)=s]$. Under the assumptions that xf′(x)/f(x) is decreasing in x∈ℛ+, λ1≤λ2 and s1≤s2, it is shown that $X_{i:n}^{s_{1}}(p+k,q-k)$ is larger than $X_{i:n}^{s_{2}}(p,q)$ according to the likelihood ratio order for any 2≤i≤n and k=1, 2, …, q. Some parametric families of distributions are also provided to illustrate the theoretical results.

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