scholarly journals On double stage minimax-shrinkage estimator for generalized Rayleigh model

2016 ◽  
Vol 5 (1) ◽  
pp. 39 ◽  
Author(s):  
Abbas Najim Salman ◽  
Maymona Ameen
Keyword(s):  
Sample Size ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Rayleigh Distribution ◽  
Shrinkage Estimator ◽  
Squared Error ◽  
Expected Sample Size ◽  
Generalized Rayleigh Distribution ◽  
The Mean

<p>This paper is concerned with minimax shrinkage estimator using double stage shrinkage technique for lowering the mean squared error, intended for estimate the shape parameter (a) of Generalized Rayleigh distribution in a region (R) around available prior knowledge (a<sub>0</sub>) about the actual value (a) as initial estimate in case when the scale parameter (l) is known .</p><p>In situation where the experimentations are time consuming or very costly, a double stage procedure can be used to reduce the expected sample size needed to obtain the estimator.</p><p>The proposed estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor y(<strong>×</strong>) and suitable region R.</p><p>Expressions for Bias, Mean squared error (MSE), Expected sample size [E (n/a, R)], Expected sample size proportion [E(n/a,R)/n], probability for avoiding the second sample and percentage of overall sample saved  for the proposed estimator are derived.</p><p>Numerical results and conclusions for the expressions mentioned above were displayed when the consider estimator are testimator of level of significanceD.</p><p>Comparisons with the minimax estimator and with the most recent studies were made to shown the effectiveness of the proposed estimator.</p>

scholarly journals Empirical Application of Generalized Rayleigh Distribution for Mineral Resource Estimation of Seabed Polymetallic Nodules

2021 ◽  
Author(s):  
Gordon Yu ◽  
John Michael Parianos
Keyword(s):  
Mineral Resource ◽  
Reasonable Agreement ◽  
Field Measurements ◽  
Rayleigh Distribution ◽  
Core Sample ◽  
Resource Estimation ◽  
Mining Equipment ◽  
Polymetallic Nodules ◽  
Generalized Rayleigh Distribution ◽  
Offshore Mining

An effective empirical statistical method is developed to improve the process of mineral resource estimation of seabed polymetallic nodules and is applied to analyse the abundance of seabed polymetallic nodules in the Clarion Clipperton Zone (CCZ). The newly proposed method is based on three hypotheses as the foundation for a model of &ldquo;Idealized Nodules&rdquo;, which was validated by analysing nodule samples collected from the seabed within the Tonga Offshore Mining Limited (TOML) exploration contract. Once validated, the &ldquo;Idealized Nodule&rdquo; model was used to deduce a set of empirical formulae for predicting the nodule resources, in terms of Percentage Coverage and Abundance. The formulae were then applied to analysing a total of 188 sets of nodule samples collected across the TOML areas, comprising box-core samples and towed camera images collected by one of the authors and detailed in [4]. The analysis also relies upon detailed box-core sample measurements from other areas reported by [7]. Numerical results for resource prediction were compared with field measurements, and reasonable agreement has been achieved. The new method has the potential to achieve more accurate mineral resource estimation with reduced sample numbers and sizes. They may also have application in improving the efficiency of design and configuration of mining equipment.

scholarly journals Survival estimation for singly type one censored sample based on generalized Rayleigh distribution

2014 ◽  
Vol 11 (2) ◽  
pp. 193-201
Author(s):  
Baghdad Science Journal
Keyword(s):  
Current Model ◽  
Survival Function ◽  
Information Matrix ◽  
Interval Estimation ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Point Estimation ◽  
Distribution Model ◽  
Unknown Parameters ◽  
Generalized Rayleigh Distribution

This paper interest to estimation the unknown parameters for generalized Rayleigh distribution model based on censored samples of singly type one . In this paper the probability density function for generalized Rayleigh is defined with its properties . The maximum likelihood estimator method is used to derive the point estimation for all unknown parameters based on iterative method , as Newton – Raphson method , then derive confidence interval estimation which based on Fisher information matrix . Finally , testing whether the current model ( GRD ) fits to a set of real data , then compute the survival function and hazard function for this real data.

A new lifetime model: the Kumaraswamy generalized Rayleigh distribution

2012 ◽  
Vol 84 (2) ◽  
pp. 290-309 ◽  
Author(s):  
Antonio E. Gomes ◽  
Cibele Q. da-Silva ◽  
Gauss M. Cordeiro ◽  
Edwin M.M. Ortega
Keyword(s):  
Rayleigh Distribution ◽  
Generalized Rayleigh Distribution ◽  
Lifetime Model
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