The Folded Normal Distribution: Accuracy of Estimation By Maximum Likelihood

Technometrics ◽  
1962 ◽  
Vol 4 (2) ◽  
pp. 249-256 ◽  
Author(s):  
N. L. Johnson
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Folded Normal Distribution

Inadmissibility of the Maximum Likelihood Estimator in the Presence of Prior Information

1970 ◽  
Vol 13 (3) ◽  
pp. 391-393 ◽  
Author(s):  
B. K. Kale
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Maximum Likelihood Estimator ◽  
Loss Function ◽  
Prior Information ◽  
Mean Squared Error ◽  
Closed Interval ◽  
Likelihood Estimator ◽  
Usual Estimator ◽  
Squared Error

Lehmann [1] in his lecture notes on estimation shows that for estimating the unknown mean of a normal distribution, N(θ, 1), the usual estimator is neither minimax nor admissible if it is known that θ belongs to a finite closed interval [a, b] and the loss function is squared error. It is shown that , the maximum likelihood estimator (MLE) of θ, has uniformly smaller mean squared error (MSE) than that of . It is natural to ask the question whether the MLE of θ in N(θ, 1) is admissible or not if it is known that θ ∊ [a, b]. The answer turns out to be negative and the purpose of this note is to present this result in a slightly generalized form.

Estimators which are Uniformly Better than the James-Stein Estimator

1997 ◽  
Vol 47 (3-4) ◽  
pp. 167-180 ◽  
Author(s):  
Nabendu Pal ◽  
Jyh-Jiuan Lin
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Maximum Likelihood Estimator ◽  
Multivariate Normal Distribution ◽  
Multivariate Normal ◽  
Likelihood Estimator ◽  
Mean Estimation ◽  
Stein Estimator ◽  
Mean Vector ◽  
Better Than

Assume i.i.d. observations are available from a p-dimensional multivariate normal distribution with an unknown mean vector μ and an unknown p .d. diaper- . sion matrix ∑. Here we address the problem of mean estimation in a decision theoretic setup. It is well known that the unbiased as well as the maximum likelihood estimator of μ is inadmissible when p ≤ 3 and is dominated by the famous James-Stein estimator (JSE). There are a few estimators which are better than the JSE reported in the literature, but in this paper we derive wide classes of estimators uniformly better than the JSE. We use some of these estimators for further risk study.

scholarly journals Generalized Truncation Positive Normal Distribution

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1361
Author(s):  
Héctor J. Gómez ◽  
Diego I. Gallardo ◽  
Osvaldo Venegas
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Data Sets ◽  
New Model ◽  
Positive Support

In this article we study the properties, inference, and statistical applications to a parametric generalization of the truncation positive normal distribution, introducing a new parameter so as to increase the flexibility of the new model. For certain combinations of parameters, the model includes both symmetric and asymmetric shapes. We study the model’s basic properties, maximum likelihood estimators and Fisher information matrix. Finally, we apply it to two real data sets to show the model’s good performance compared to other models with positive support: the first, related to the height of the drum of the roller and the second, related to daily cholesterol consumption.

AN ANALYSIS OF ACCELERATED PERFORMANCE DEGRADATION TESTS ASSUMING THE ARRHENIUS STRESS-RELATIONSHIP

2008 ◽  
Vol 25 (06) ◽  
pp. 847-864 ◽  
Author(s):  
TAE HYOUNG KANG ◽  
SANG WOOK CHUNG ◽  
WON YOUNG YUN
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Exposure Time ◽  
Failure Time ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Location Parameter ◽  
Performance Degradation ◽  
Maximum Likelihood Estimates ◽  
Degradation Tests

An analytical model is developed for accelerated performance degradation tests. The performance degradations of products at a specified exposure time are assumed to follow a normal distribution. It is assumed that the relationship between the location parameter of normal distribution and the exposure time is a linear function of the exposure time that the slope coefficient of the linear relationship has an Arrhenius dependence on temperature, and that the scale parameter of the normal distribution is constant and independent of temperature or exposure time. The method of maximum likelihood estimation is used to estimate the parameters involved. The likelihood function for the accelerated performance degradation data is derived. The approximated variance-covariance matrix is also derived for calculating approximated confidence intervals of maximum likelihood estimates. Finally we use two real examples for estimating the failure-time distribution, technically defined as the time when performance degrades below a specified level.

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