Design problems for the pure birth process

1983 ◽  
Vol 15 (02) ◽  
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.

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.

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 Estimation of Reliability for a Two Component Survival Stress-Strength Model

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
S. B. Munoli ◽  
Rohit R. Mutkekar
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Strength Model ◽  
Life Testing ◽  
Likelihood Estimator ◽  
Two Component ◽  
Testing Experiment

The reliability function for a parallel system of two identical components is derived from a stress-strength model, where failure of one component increases the stress on the surviving component of the system. The Maximum Likelihood Estimators of parameters and their asymptotic distribution are obtained. Further the Maximum Likelihood Estimator and Bayes Estimator of reliability function are obtained using the data from a life-testing experiment. Computation of estimators is illustrated through simulation study.

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 Parametric Bootstrapping Predictive Estimator for Logistic Regression

2019 ◽  
pp. 1-15
Author(s):  
Kunio Takezawa
Keyword(s):  
Logistic Regression ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Cross Validation ◽  
Bootstrap Method ◽  
Maximum Likelihood Estimators ◽  
Parametric Bootstrap ◽  
Likelihood Estimator ◽  
Parametric Bootstrapping

This paper proposes a method for constructing a predictive estimator for logistic regression. We make a provisional assumption that the predictive estimator is given by multiplying the maximum likelihood estimators by constants, which are estimated using a parametric bootstrap method. The relative merits of the maximum likelihood estimator and the predictive estimator produced by this method are determined by cross-validation. The results show that the predictiveestimators derived by this method lead to a smaller deviance than that obtained by the maximum likelihood estimator in many instances.

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.

The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

2018 ◽  
pp. 439
Author(s):  
Hazim Mansour Gorgees ◽  
Bushra Abdualrasool Ali ◽  
Raghad Ibrahim Kathum
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Reliability Function ◽  
Bayes Estimator ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Technique ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Better Than

     In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

scholarly journals Transforming variables to central normality

2021 ◽  
Author(s):  
Jakob Raymaekers ◽  
Peter J. Rousseeuw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Real Data ◽  
Data Sets ◽  
Transformation Parameter ◽  
Likelihood Estimator ◽  
Extensive Simulation ◽  
Highly Sensitive

AbstractMany real data sets contain numerical features (variables) whose distribution is far from normal (Gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box–Cox and Yeo–Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose a modification of these transformations as well as an estimator of the transformation parameter that is robust to outliers, so the transformed data can be approximately normal in the center and a few outliers may deviate from it. It compares favorably to existing techniques in an extensive simulation study and on real data.

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