scholarly journals Pretest shrinkage estimators for the shape parameter of a Pareto model using prior point knowledge and record observations

2017 ◽  
Vol 14 (1) ◽  
Author(s):  
Leila Barmoodeh ◽  
Mehran Naghizadeh Qomi
Keyword(s):  
Unbiased Estimator ◽  
Shape Parameter ◽  
Shrinkage Estimators ◽  
Numerical Example ◽  
Scale Parameters ◽  
Error Loss ◽  
Pareto Model

Considering a Pareto model with unknown shape and scale parameters \(\alpha\) and \(\beta\), respectively, we are interested in Thompson shrinkage test estimation for the shape parameter \(\alpha\) under the Squared Log Error Loss (SLEL) function. We find a risk-unbiased estimator for \(\alpha\) and compute its risk under the SLEL. According to Thompson (1986), we construct the pretest shrinkage (PTS) estimators for \(\alpha\) with the help of a point guess value \(\alpha_0\) and record observations. We investigate the risk-bias of these estimators and compute their risks numerically. A comparison is performed between the PTS estimators and a risk-unbiased estimator. A numerical example is presented for illustrative and comparative purposes. We end the paper by discussion and concluding remarks.

scholarly journals Estimation of the Shape Parameter of a Wear-Out Failure Period for a Three-Parameter Weibull Distribution in a Small Sample

2020 ◽  
Vol 9 (6) ◽  
pp. 39
Author(s):  
Toru Ogura ◽  
Takatoshi Sugiyama ◽  
Nariaki Sugiura
Keyword(s):  
Monte Carlo ◽  
Weibull Distribution ◽  
Sample Size ◽  
Unbiased Estimator ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Minimum Variance ◽  
Small Sample ◽  
Scale Parameters ◽  
Squared Error

We propose a method to estimate a shape parameter for a three-parameter Weibull distribution. The proposed method first derives an unbiased estimator for the shape parameter independent of the location and scale parameters and then estimates the shape parameter using a minimum-variance linear unbiased estimator. Since the proposed method is expressed using a hyperparameter, its optimal hyperparameter is searched using Monte Carlo simulations. The recommended hyperparameter used for estimating the shape parameter depends on the sample size, and this causes no problems since the sample size is known when data is obtained. The proposed method is evaluated using a bias and a root mean squared error, and the results are very promising when the population shape parameter is 2 or more in the Weibull distribution representing the wear-out failure period. A numerical dataset is analyzed to demonstrate the practical use of the proposed method.

scholarly journals Non-stationary analysis of water level extremes in Latvian waters, Baltic Sea, during 1961–2018

2020 ◽  
Author(s):  
Nadezhda Kudryavtseva ◽  
Tarmo Soomere ◽  
Rain Männikus
Keyword(s):  
Time Series ◽  
Baltic Sea ◽  
Water Level ◽  
Shape Parameter ◽  
Extreme Value Distribution ◽  
Scale Parameters ◽  
Stationary Analysis ◽  
Gulf Of Riga ◽  
Baltic Proper ◽  
The Baltic

Abstract. Analysis and prediction of water level extremes in the eastern Baltic Sea is a difficult task because of the contribution of various drivers to the water level, the presence of outliers in time series and possibly non-stationarity of the extremes owing to the changes in the atmospheric forcing. Non-stationary modelling of extremes was performed to the block maxima of water level derived from the time series at six locations in the Gulf of Riga and one location in the Baltic proper, Baltic Sea, during 1961–2018. Several parameters of the Generalised Extreme Value distribution of the measured water maxima both in the Baltic proper and in the interior of the Gulf of Riga exhibit statistically significant changes over these years. The most considerable changes occur to the shape parameter ξ. All stations in the interior of the Gulf of Riga experienced a regime shift: a drastic abrupt drop of the shape parameter from ξ ≈ 0.03 ± 0.02 to ξ ≈ −0.36 ± 0.04 around 1986 followed by an increase of a similar magnitude around 1990. This means a sudden switch from a Fréchet distribution to a three-parameter Weibull distribution and back. The water level extremes at Liepaja in the Baltic proper and Kolka at the entrance to the Gulf of Riga reveal significant linear trends in the location and scale parameters. This pattern indicates a different course of the water level extremes in the Baltic proper and the interior of the Gulf of Riga. The described changes may lead to greatly different projections for long-term behaviour of water level extremes and their return periods based on data from different intervals.

scholarly journals Bayesian Estimation for the Parameters and Reliability Function of Basic Gompertz Distribution under Squared Log Error Loss Function

2020 ◽  
pp. 1433-1439
Author(s):  
Manahel Kh. Awad ◽  
Huda A. Rasheed
Keyword(s):  
Monte Carlo Simulation ◽  
Loss Function ◽  
Shape Parameter ◽  
Reliability Function ◽  
Shape Parameters ◽  
Likelihood Estimator ◽  
Gompertz Distribution ◽  
Mean Squared Errors ◽  
Error Loss ◽  
Bayesian Estimators

In this paper, some estimators for the unknown shape parameters and reliability function of Basic Gompertz distribution were obtained, such as Maximum likelihood estimator and some Bayesian estimators under Squared log error loss function by using Gamma and Jefferys priors. Monte-Carlo simulation was conducted to compare the performance of all estimates of the shape parameter and Reliability function, based on mean squared errors (MSE) and integrated mean squared errors (IMSE's), respectively. Finally, the discussion is provided to illustrate the results that are summarized in tables.

scholarly journals The Efficiency of Some Shrinkage Estimators for Shape Parameter of the Pareto-Rayleigh Distribution

2022 ◽  
Vol 15 (2) ◽  
pp. 407-426
Author(s):  
Mehdi Balui ◽  
Einolah Deiri ◽  
Farshin Hormozinejad ◽  
Ezzatallah Baloui Jamkhaneh ◽  
◽  
...  
Keyword(s):  
Shape Parameter ◽  
Rayleigh Distribution ◽  
Shrinkage Estimators
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