The sample mean as an estimator of the location parameter in the case of a Laplacian loss function and a nuisance scale parameter

1978 ◽  
Vol 9 (6) ◽  
pp. 850-862
Author(s):  
A. A. Zinger ◽  
A. M. Kagan
Keyword(s):  
Loss Function ◽  
Scale Parameter ◽  
Location Parameter ◽  
Sample Mean

scholarly journals Quasi-E-Bayesian criteria versus quasi-Bayesian, quasi-hierarchical Bayesian and quasi-empirical Bayesian methods for estimating the scale parameter of the Erlang distribution

2016 ◽  
Vol 4 (1) ◽  
pp. 62 ◽  
Author(s):  
Hesham Reyad ◽  
Adil Younis ◽  
Amal Alkhedir
Keyword(s):  
Loss Function ◽  
Bayesian Method ◽  
Scale Parameter ◽  
Likelihood Function ◽  
Hierarchical Bayes ◽  
Erlang Distribution ◽  
Quadratic Loss ◽  
Hierarchical Bayesian ◽  
Empirical Bayesian ◽  
Symmetric Loss

This paper proposes a new modification for the E-Bayesian method of estimation to introduce a new technique namely Quasi E-Bayesian method (or briefly QE-Bayesian). The suggested criteria built in replacing the likelihood function by the quasi likelihood function in the E-Bayesian technique. This study is devoted to evaluate the performance of the new method versus the quasi-Bayesian, quasi-hierarchical Bayesian and quasi-empirical Bayesian approaches in estimating the scale parameter of the Erlang distribution. All estimators are obtained under symmetric loss function [squared error loss (SELF))] and four different asymmetric loss functions [Precautionary loss function (PLF), entropy loss function (ELF), Degroot loss function (DLF) and quadratic loss function (QLF)]. The properties of the QE-Bayesian estimates are introduced and the relations between the QE-Bayes and quasi-hierarchical Bayes estimates are discussed. Comparisons among all estimators are performed in terms of mean square error (MSE) via Monte Carlo simulation.

scholarly journals Sequential point and interval estimation of scale parameter of exponential distribution

1995 ◽  
Vol 18 (2) ◽  
pp. 383-390
Author(s):  
Z. Govindarajulu
Keyword(s):  
Exponential Distribution ◽  
Scale Parameter ◽  
Stopping Time ◽  
Interval Estimation ◽  
Location Parameter ◽  
Exact Expression ◽  
Point Estimation ◽  
Quadratic Loss ◽  
Negative Exponential Distribution ◽  
Negative Exponential

Sequential fixed-width confidence intervals are obtained for the scale parameterσwhen the location parameterθof the negative exponential distribution is unknown. Exact expressions for the stopping time and the confidence coefficient associated with the sequential fixed-width interval are derived. Also derived is the exact expression for the stopping time of sequential point estimation with quadratic loss and linear cost. These are numerically evaluated for certain nominal confidence coefficients, widths of the interval and cost functions, and are compared with the second order asymptotic expressions.

scholarly journals Modelling non-stationary annual maximum flood heights in the lower Limpopo River basin of Mozambique

2016 ◽  
Vol 8 (1) ◽  
Author(s):  
Daniel Maposa ◽  
James J. Cochran ◽  
Maseka Lesaoana
Keyword(s):  
River Basin ◽  
Scale Parameter ◽  
Linear Trend ◽  
Location Parameter ◽  
Extreme Value ◽  
Time Dependent ◽  
Sufficient Evidence ◽  
Annual Maximum ◽  
Significant Linear Trend ◽  
Gev Distribution

In this article we fit a time-dependent generalised extreme value (GEV) distribution to annual maximum flood heights at three sites: Chokwe, Sicacate and Combomune in the lower Limpopo River basin of Mozambique. A GEV distribution is fitted to six annual maximum time series models at each site, namely: annual daily maximum (AM1), annual 2-day maximum (AM2), annual 5-day maximum (AM5), annual 7-day maximum (AM7), annual 10-day maximum (AM10) and annual 30-day maximum (AM30). Non-stationary time-dependent GEV models with a linear trend in location and scale parameters are considered in this study. The results show lack of sufficient evidence to indicate a linear trend in the location parameter at all three sites. On the other hand, the findings in this study reveal strong evidence of the existence of a linear trend in the scale parameter at Combomune and Sicacate, whilst the scale parameter had no significant linear trend at Chokwe. Further investigation in this study also reveals that the location parameter at Sicacate can be modelled by a nonlinear quadratic trend; however, the complexity of the overall model is not worthwhile in fit over a time-homogeneous model. This study shows the importance of extending the time-homogeneous GEV model to incorporate climate change factors such as trend in the lower Limpopo River basin, particularly in this era of global warming and a changing climate.Keywords: nonstationary extremes; annual maxima; lower Limpopo River; generalised extreme value

Sign in / Sign up

Export Citation Format

Share Document