Bayesian estimation for the symmetric double Pareto distribution with multi-parameter Jeffreys prior information

2013 ◽  
Vol 5 (3) ◽  
pp. 36-45
Author(s):  
Faris M. Al-Athari ◽  
Khaled K. Jaber
Keyword(s):  
Bayesian Estimation ◽  
Prior Information ◽  
Pareto Distribution ◽  
Jeffreys Prior

scholarly journals Bayesian Estimation of Two-Parameter Weibull Distribution Using Extension of Jeffreys' Prior Information with Three Loss Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Chris Bambey Guure ◽  
Noor Akma Ibrahim ◽  
Al Omari Mohammed Ahmed
Keyword(s):  
Weibull Distribution ◽  
Bayesian Estimation ◽  
Mean Square Error ◽  
Loss Function ◽  
Prior Information ◽  
Loss Functions ◽  
Bayesian Estimator ◽  
Mean Square ◽  
Jeffreys Prior ◽  
Two Parameter

The Weibull distribution has been observed as one of the most useful distribution, for modelling and analysing lifetime data in engineering, biology, and others. Studies have been done vigorously in the literature to determine the best method in estimating its parameters. Recently, much attention has been given to the Bayesian estimation approach for parameters estimation which is in contention with other estimation methods. In this paper, we examine the performance of maximum likelihood estimator and Bayesian estimator using extension of Jeffreys prior information with three loss functions, namely, the linear exponential loss, general entropy loss, and the square error loss function for estimating the two-parameter Weibull failure time distribution. These methods are compared using mean square error through simulation study with varying sample sizes. The results show that Bayesian estimator using extension of Jeffreys' prior under linear exponential loss function in most cases gives the smallest mean square error and absolute bias for both the scale parameterαand the shape parameterβfor the given values of extension of Jeffreys' prior.

scholarly journals A Bayesian model for binary Markov chains

2004 ◽  
Vol 2004 (8) ◽  
pp. 421-429 ◽  
Author(s):  
Souad Assoudou ◽  
Belkheir Essebbar
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chains ◽  
Bayesian Estimation ◽  
Bayesian Model ◽  
Transition Probabilities ◽  
Simulated Data ◽  
Bayesian Estimator ◽  
Jeffreys Prior ◽  
Data Set

This note is concerned with Bayesian estimation of the transition probabilities of a binary Markov chain observed from heterogeneous individuals. The model is founded on the Jeffreys' prior which allows for transition probabilities to be correlated. The Bayesian estimator is approximated by means of Monte Carlo Markov chain (MCMC) techniques. The performance of the Bayesian estimates is illustrated by analyzing a small simulated data set.

Bayesian Estimation of Transmuted Pareto Distribution for Complete and Censored Data

2020 ◽  
Vol 7 (4) ◽  
pp. 663-695
Author(s):  
Muhammad Aslam ◽  
Rahila Yousaf ◽  
Sajid Ali
Keyword(s):  
Bayesian Estimation ◽  
Censored Data ◽  
Pareto Distribution

scholarly journals Bayesian estimation of a bivariate copula using the Jeffreys prior

Bernoulli ◽  
2012 ◽  
Vol 18 (2) ◽  
pp. 496-519 ◽  
Author(s):  
Simon Guillotte ◽  
François Perron
Keyword(s):  
Bayesian Estimation ◽  
Jeffreys Prior ◽  
Bivariate Copula

A Bayesian estimation of the lactation curve of a dairy cow

1985 ◽  
Vol 40 (2) ◽  
pp. 189-193 ◽  
Author(s):  
E. A. Goodall ◽  
D. Sprevak
Keyword(s):  
Kalman Filter ◽  
Bayesian Estimation ◽  
Milk Yield ◽  
Dairy Cow ◽  
Prior Information ◽  
Recursive Procedure ◽  
Early Stages ◽  
Lactation Curve ◽  
Total Milk

ABSTRACTA recursive procedure for the estimation of the lactation curve of a dairy cow, which allows the inclusion of prior information on the curve and which takes account of the correlation between successive observations, is described. The method is based on the Kalman filter. It was found to give accurate estimates of the total milk yield at early stages of lactation.

scholarly journals Bayesian Estimation of Inequality and Poverty Indices in Case of Pareto Distribution Using Different Priors under LINEX Loss Function

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Kamaljit Kaur ◽  
Sangeeta Arora ◽  
Kalpana K. Mahajan
Keyword(s):  
Loss Function ◽  
Pareto Distribution ◽  
Loss Functions ◽  
Conjugate Prior ◽  
Jeffreys Prior ◽  
Linex Loss Function ◽  
Poverty Measure ◽  
Noninformative Priors ◽  
Simulation Techniques ◽  
Linex Loss

Bayesian estimators of Gini index and a Poverty measure are obtained in case of Pareto distribution under censored and complete setup. The said estimators are obtained using two noninformative priors, namely, uniform prior and Jeffreys’ prior, and one conjugate prior under the assumption of Linear Exponential (LINEX) loss function. Using simulation techniques, the relative efficiency of proposed estimators using different priors and loss functions is obtained. The performances of the proposed estimators have been compared on the basis of their simulated risks obtained under LINEX loss function.

IMAGE DENOISING BASED ON GAUSSIAN AND NON-GAUSSIAN ASSUMPTION

2012 ◽  
Vol 10 (02) ◽  
pp. 1250014 ◽  
Author(s):  
PING ZHAO ◽  
ZHAOWEI SHANG ◽  
CHUN ZHAO
Keyword(s):  
Wavelet Transformation ◽  
Prior Information ◽  
Noise Removal ◽  
Bivariate Distribution ◽  
Smoothing Algorithm ◽  
Wavelet Coefficients ◽  
Jeffreys Prior ◽  
Orthogonal Wavelet ◽  
Adaptive Noise ◽  
Non Gaussian

In this paper, we first present an adaptive intra-scale noise removal scheme, and estimate clean wavelet coefficients using new prior information with Bayesian estimation techniques. A new model using the non-informative improper Jeffreys' prior is given under the supposed Gaussian distribution for orthogonal wavelet transformation. Then, we propose a computationally feasible adaptive noise smoothing algorithm that considers the dependency characteristics of images. The wavelet coefficients are assumed to be non-Gaussian random variables for non-orthogonal redundancy transformation. The variances of the wavelet coefficients are estimated locally by a centered square-shaped window for every pixel within each subband. The experimental results show that the orthogonal wavelet transformation provides better results at the Gaussian assumption, while the non-orthogonal redundancy wavelet transformation performance tends to increase when the non-Gaussian bivariate distribution is used.

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