ON MAXIMUM LIKELIHOOD ESTIMATORS OF SHAPE AND SCALE PARAMETERS AND THEIR APPLICATION IN CONSTRUCTING CONFIDENCE CONTOURS

1970 ◽  
Author(s):  
Sam C. Saunders
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Scale Parameters

scholarly journals Maximum likelihood estimation in location-scale families using varied L ranked set sampling

2020 ◽  
Author(s):  
Amer Al-Omari
Keyword(s):  
Maximum Likelihood ◽  
Random Sampling ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Sampling Schemes ◽  
Scale Parameters ◽  
Insight Into ◽  
Family Of Distributions

Recently, a generalized ranked set sampling (RSS) scheme has been introduced which encompasses several existing RSS schemes, namely varied L RSS (VLRSS), and it provides more precise estimators of the population mean than the estimators with the traditional simple random sampling (SRS) and RSS schemes. In this paper, we extend the work and consider the maximum likelihood estimators (MLEs) of the location and scale parameters when sampling from a location-scale family of distributions. In order to give more insight into the performance of VLRSS with respect to SRS and RSS schemes, the asymptotic relative precisions of the MLEs using VLRSS relative to that using SRS and RSS are compared for some usual location-scale distributions. It turns out that the MLEs with VLRSS are more precise than those with the existing sampling schemes.

A Property of Maximum Likelihood Estimators of Location and Scale Parameters

SIAM Review ◽  
1969 ◽  
Vol 11 (2) ◽  
pp. 251-253 ◽  
Author(s):  
Charles E. Antle ◽  
Lee J. Bain
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Scale Parameters

scholarly journals An Asymmetric Bimodal Double Regression Model

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2279
Author(s):  
Yolanda M. Gómez ◽  
Diego I. Gallardo ◽  
Osvaldo Venegas ◽  
Tiago M. Magalhães
Keyword(s):  
Maximum Likelihood ◽  
Regression Model ◽  
Simulation Study ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Cauchy Distribution ◽  
Scale Parameters ◽  
Finite Samples ◽  
Data Application ◽  
Different Shapes

In this paper, we introduce an extension of the sinh Cauchy distribution including a double regression model for both the quantile and scale parameters. This model can assume different shapes: unimodal or bimodal, symmetric or asymmetric. We discuss some properties of the model and perform a simulation study in order to assess the performance of the maximum likelihood estimators in finite samples. A real data application is also presented.

scholarly journals Estimating the Reliability Function of some Stress- Strength Models for the Generalized Inverted Kumaraswamy Distribution

2021 ◽  
pp. 240-251
Author(s):  
Hakeem Hussain Hamad ◽  
Nada Sabah Karam
Keyword(s):  
Maximum Likelihood ◽  
Shape Parameter ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Least Square ◽  
Mean Square ◽  
Kumaraswamy Distribution ◽  
Scale Parameters ◽  
Strength Models ◽  
Best Estimator

This paper discusses reliability of the stress-strength model. The reliability functions 𝑅1 and 𝑅2 were obtained for a component which has an independent strength and is exposed to two and three stresses, respectively. We used the generalized inverted Kumaraswamy distribution GIKD with unknown shape parameter as well as known shape and scale parameters. The parameters were estimated from the stress- strength models, while the reliabilities 𝑅1, 𝑅2 were estimated by three methods, namely the Maximum Likelihood,  Least Square, and Regression.  A numerical simulation study a comparison between the three estimators by mean square error is performed. It is found that best estimator between the three estimators is Maximum likelihood estimators.  

A Property of Maximum Likelihood Estimators for Invariant Statistical Models

1975 ◽  
Vol 18 (3) ◽  
pp. 405-409 ◽  
Author(s):  
Peter Tan ◽  
Constantin Drossos
Keyword(s):  
Maximum Likelihood ◽  
Statistical Models ◽  
Structural Model ◽  
Likelihood Function ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimator ◽  
Scale Parameters ◽  
Transformation Variable ◽  
Correct Definition ◽  
Definition Of

AbstractThis paper generalizes some results on pivotal functions of maximum likelihood estimators of location and scale parameters and the related ancillary statistics obtained by Antle and Bain, and Fisher. It shows that the maximum likelihood estimator of the parameter in an invariant statistical model is an essentially equivariant estimator or a transformation variable in a structural model. In the latter case, ancillary statistics in the sense of Fisher used in conjunction with the maximum likelihood estimators can be easily recognized. It is also remarked that the values of maximum likelihood estimators from samples having the same “complexion” are simply related to those of other, perhaps simpler, transformation variables. In the development it also points out the importance of using the correct definition of the likelihood function originally proposed by Fisher.

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