scholarly journals Maximum likelihood estimators uniformly minimize distribution variance among distribution unbiased estimators in exponential families

Bernoulli ◽  
2015 ◽  
Vol 21 (4) ◽  
pp. 2120-2138
Author(s):  
Paul Vos ◽  
Qiang Wu
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Exponential Families ◽  
Unbiased Estimators

On Existence of Maximum Likelihood Estimators in Exponential Families

Statistics ◽  
2000 ◽  
Vol 34 (2) ◽  
pp. 137-149 ◽  
Author(s):  
Krzysztof Bogdan ◽  
Małgorzata Bogdan
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Exponential Families

scholarly journals Estimating the Reliability Function for a Family of Exponentiated Distributions

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ajit Chaturvedi ◽  
Anupam Pathak
Keyword(s):  
Maximum Likelihood ◽  
Comparative Study ◽  
Simulation Study ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Minimum Variance ◽  
Unbiased Estimators

A family of exponentiated distributions is proposed. The problems of estimating the reliability function are considered. Uniformly minimum variance unbiased estimators and maximum likelihood estimators are derived. A comparative study of the two methods of estimation is done. Simulation study is preformed.

Using Approximation Non-Bayesian Computation with Fuzzy Data to Estimation Inverse Weibull Parameters and Reliability Function

2018 ◽  
pp. 397
Author(s):  
Nadia Hashim Al-Noor ◽  
Shurooq A.K. Al-Sultany
Keyword(s):  
Maximum Likelihood ◽  
Expectation Maximization ◽  
Mean Squared Error ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Fuzzy Data ◽  
Monte Carlo Simulation Study ◽  
Weibull Parameters ◽  
Squared Error ◽  
Newton Raphson

        In real situations all observations and measurements are not exact numbers but more or less non-exact, also called fuzzy. So, in this paper, we use approximate non-Bayesian computational methods to estimate inverse Weibull parameters and reliability function with fuzzy data. The maximum likelihood and moment estimations are obtained as non-Bayesian estimation. The maximum likelihood estimators have been derived numerically based on two iterative techniques namely “Newton-Raphson” and the “Expectation-Maximization” techniques. In addition, we provide compared numerically through Monte-Carlo simulation study to obtained estimates of the parameters and reliability function in terms of their mean squared error values and integrated mean squared error values respectively.

Inference on P(Y

2020 ◽  
Vol 72 (2) ◽  
pp. 89-110
Author(s):  
Manoj Chacko ◽  
Shiny Mathew
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Maximum Likelihood Estimators ◽  
Record Values ◽  
Asymptotic Distributions ◽  
Bayes Estimators ◽  
Generalized Pareto ◽  
Pareto Distributions ◽  
Generalized Pareto Distributions

In this article, the estimation of [Formula: see text] is considered when [Formula: see text] and [Formula: see text] are two independent generalized Pareto distributions. The maximum likelihood estimators and Bayes estimators of [Formula: see text] are obtained based on record values. The Asymptotic distributions are also obtained together with the corresponding confidence interval of [Formula: see text]. AMS 2000 subject classification: 90B25

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