A SIMPLE ESTIMATOR FOR THE WEIBULL SHAPE PARAMETER

2012 ◽  
Vol 12 (02) ◽  
pp. 395-402 ◽  
Author(s):  
MAHDI TEIMOURI ◽  
SARALEES NADARAJAH
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Closed Form ◽  
Maximum Likelihood Estimator ◽  
Shape Parameter ◽  
Scale Parameter ◽  
Maximum Likelihood Estimators ◽  
Simulation Studies ◽  
Likelihood Estimator

The Weibull distribution is the most popular model for lifetimes. However, the maximum likelihood estimators for the Weibull distribution are not available in closed form. In this note, we derive a simple, consistent, closed form estimator for the Weibull shape parameter. This estimator is independent of the Weibull scale parameter. Simulation studies show that this estimator performs as well as the maximum likelihood estimator.

scholarly journals Masses of Negative Multinomial Distributions: Application to Polarimetric Image Processing

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Philippe Bernardoff ◽  
Florent Chatelain ◽  
Jean-Yves Tourneret
Keyword(s):  
Image Processing ◽  
Maximum Likelihood ◽  
Closed Form ◽  
Maximum Likelihood Estimator ◽  
Maximum Likelihood Estimators ◽  
Polarization Degree ◽  
Likelihood Estimator ◽  
Unknown Parameters ◽  
The Masses

This paper derives new closed-form expressions for the masses of negative multinomial distributions. These masses can be maximized to determine the maximum likelihood estimator of its unknown parameters. An application to polarimetric image processing is investigated. We study the maximum likelihood estimators of the polarization degree of polarimetric images using different combinations of images.

scholarly journals Direct fast estimator for recombination frequency in the F2 cross

2021 ◽  
Author(s):  
Mathias Lorieux
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Maximum Likelihood Estimator ◽  
Recombination Frequency ◽  
Short Note ◽  
Simulation Studies ◽  
Likelihood Estimator ◽  
Simple Estimate ◽  
Efficient Simulation

AbstractIn this short note, a new unbiased maximum-likelihood estimator is proposed for the recombination frequency in the F2 cross. The estimator is much faster to calculate than its EM algorithm equivalent, yet as efficient. Simulation studies are carried to illustrate the gain over another simple estimate proposed by Benito & Gallego (2004).

Strong Consistency of Maximum Likelihood Estimators n Exponential Sequential Model

2014 ◽  
Vol 519-520 ◽  
pp. 878-882
Author(s):  
Chang Ming Yin ◽  
Bo Hong Chen ◽  
Shuang Hua Liu
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Strong Consistency ◽  
Maximum Likelihood Estimators ◽  
Regression Parameter ◽  
Parameter Vector ◽  
Likelihood Estimator ◽  
Sequential Model ◽  
Mild Conditions ◽  
Strongly Consistent

For the exponential sequential model, we show that maximum likelihood estimator of regression parameter vector is asymptotically existence and strongly consistent under mild conditions

scholarly journals Classical and Bayesian Approach in Estimation of Scale Parameter of Nakagami Distribution

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Kaisar Ahmad ◽  
S. P. Ahmad ◽  
A. Ahmed
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Bayesian Approach ◽  
Simulation Study ◽  
Bayesian Method ◽  
Scale Parameter ◽  
Loss Functions ◽  
Likelihood Estimator ◽  
R Software ◽  
Nakagami Distribution

Nakagami distribution is considered. The classical maximum likelihood estimator has been obtained. Bayesian method of estimation is employed in order to estimate the scale parameter of Nakagami distribution by using Jeffreys’, Extension of Jeffreys’, and Quasi priors under three different loss functions. Also the simulation study is conducted in R software.

Design problems for the pure birth process

1983 ◽  
Vol 15 (2) ◽  
pp. 255-273 ◽  
Author(s):  
Gerhard Becker ◽  
Götz Kersting
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Maximum Likelihood Estimators ◽  
Optimal Designs ◽  
Likelihood Estimator ◽  
Birth Process ◽  
Design Problems ◽  
Continuous Sampling ◽  
Optimal Procedure

Let Y(t) be a pure birth process. If a maximum likelihood estimator of the birth intensity is desired and the number n of observational points and the last observation T are given in advance, it is shown that equidistant sampling is not an optimal procedure. Properties of ‘optimal' designs and the corresponding maximum likelihood estimators are investigated and compared with equidistant and continuous sampling.

Record-Based Estimators for Weibull Distribution

2014 ◽  
Vol 14 (07) ◽  
pp. 1450026 ◽  
Author(s):  
Mahdi Teimouri ◽  
Saralees Nadarajah
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Likelihood Estimation ◽  
Record Values ◽  
Likelihood Estimator ◽  
Squared Error ◽  
Upper Record Values ◽  
Upper Record

Teimouri and Nadarajah [Statist. Methodol.13 (2013) 12–24] considered bias corrected maximum likelihood estimation of the Weibull distribution based on upper record values. Here, we propose an estimator for the Weibull shape parameter based on consecutive upper records. It is shown by simulations that the proposed estimator has less bias and less mean squared error than an estimator due to Soliman et al. [Comput. Statist. Data Anal.51 (2006) 2065–2077] based on all upper records. Also, the proposed estimator can be considered as a good competitor for the maximum likelihood estimator of the shape parameter based on complete data. This is proved by simulations and using a real dataset.

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