scholarly journals Minimax Estimation of the Mean of a Normal Distribution when the Parameter Space is Restricted

1981 ◽  
Vol 9 (6) ◽  
pp. 1301-1309 ◽  
Author(s):  
P. J. Bickel
Keyword(s):  
Normal Distribution ◽  
Parameter Space ◽  
Minimax Estimation ◽  
The Mean

Limit tolerances for sums of measurement errors

2018 ◽  
Vol 934 (4) ◽  
pp. 59-62
Author(s):  
V.I. Salnikov
Keyword(s):  
Normal Distribution ◽  
Mean Square Error ◽  
Gaussian Distribution ◽  
Measurement Errors ◽  
Theory And Practice ◽  
Mean Square ◽  
The Mean ◽  
Limiting Values ◽  
Limiting Value

The question of calculating the limiting values of residuals in geodesic constructions is considered in the case when the limiting value for measurement errors is assumed equal to 3m, ie ∆рred = 3m, where m is the mean square error of the measurement. Larger errors are rejected. At present, the limiting value for the residual is calculated by the formula 3m√n, where n is the number of measurements. The article draws attention to two contradictions between theory and practice arising from the use of this formula. First, the formula is derived from the classical law of the normal Gaussian distribution, and it is applied to the truncated law of the normal distribution. And, secondly, as shown in [1], when ∆рred = 2m, the sums of errors naturally take the value equal to ?pred, after which the number of errors in the sum starts anew. This article establishes its validity for ∆рred = 3m. A table of comparative values of the tolerances valid and recommended for more stringent ones is given. The article gives a graph of applied and recommended tolerances for ∆рred = 3m.

The Mean of the Inverse of a Punctured Normal Distribution and Its Application

2004 ◽  
Vol 46 (4) ◽  
pp. 420-429 ◽  
Author(s):  
C. D. Lai ◽  
G. R. Wood ◽  
C. G. Qiao
Keyword(s):  
Normal Distribution ◽  
The Mean
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