Simulation-Based Maximum Likelihood Median Pragmatic A-Basis and B-Basis Statistical Tolerance Limits Given Fatigue Datum Values with No Censoring or with Potential or Actual Type I Censoring

2010 ◽  
Vol 38 (4) ◽  
pp. 102648
Author(s):  
M. R. Mitchell ◽  
R. E. Link ◽  
R. E. Little
Keyword(s):  
Maximum Likelihood ◽  
Type I ◽  
Tolerance Limits ◽  
Type I Censoring ◽  
Simulation Based ◽  
Actual Type ◽  
Statistical Tolerance

scholarly journals Optimal Plan and Estimation for Bivariate Step-Stress Accelerated Life Test under Progressive Type-I Censoring

2021 ◽  
pp. 683-694
Author(s):  
Mashroor Ahmad Khan ◽  
Navin Chandra
Keyword(s):  
Maximum Likelihood ◽  
Accelerated Life Test ◽  
Maximum Likelihood Estimates ◽  
Cumulative Exposure ◽  
Type I ◽  
Life Test ◽  
Type I Censoring ◽  
Accelerated Life ◽  
Progressive Type ◽  
Stress Levels

 In this paper, a step-stress accelerated life test with two stress variables for Weibull distribution under progressive type-I censoring is considered. The stress-life relationship as a log-linear function of stress levels, and for each combination of stress levels, a cumulative exposure model is assumed. The maximum likelihood and Bayes estimates of the model parameters are obtained. The optimum test plan is developed using variance-optimality criterion, which consists in finding out the optimal stress change time by minimizing asymptotic variance of the maximum likelihood estimates of the log of the scale parameter at the design stress. The proposed study illustrated by using simulated data.

A statistical method for determining normal ranges from laboratory data including values below the minimum detectable value.

1979 ◽  
Vol 25 (12) ◽  
pp. 2011-2014 ◽  
Author(s):  
J Y Tsay ◽  
I W Chen ◽  
H R Maxon ◽  
L Heminger
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Statistical Method ◽  
Laboratory Data ◽  
Likelihood Estimation ◽  
Type I ◽  
Tolerance Limits ◽  
Normal Range ◽  
Normal Ranges

Abstract Determination of normal ranges from laboratory data containing undectable values is a frequently encountered problem in the radioimmunoassay of peptide hormones. In the past, such determinations usually have been based on the mid-point method or the one-end Winsorized method. A graphic method involving the use of probability paper has also been reported. We propose that the maximum-likelihood estimation is a more appropriate statistical method for the determination of normal range from this type of data (Type I censored data). With this method, the mean and standard deviation, and hence the tolerance limits, can be estimated. We used the maximum-likelihood estimation method to determine the normal range of serum thyrotropin values obtained from 93 healthy subjects, based on a log normal distribution. Although the serum thyrotropin content was undetectable in 14% of the subjects, a normal range could be calculated. Using tolerance limits for 95% coverage of the population with 90% confidence, we calculated the normal range of thyrotropin to be 0.51-5.75 milliunits/L, with a mean value of 1.71 milliunits/L, and predicted that 91.4% of undetectable serum thyrotropin values will fall within the normal range.

scholarly journals Estimation of the Parameters of Type-II Discrete Weibull Distribution Under Type-I Censoring

2021 ◽  
Vol 10 (5) ◽  
pp. 1
Author(s):  
Mohamed S. A. Muiftah ◽  
Samir K. Ashour
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Simulation Study ◽  
Maximum Likelihood Estimates ◽  
Type I ◽  
Type Ii ◽  
Comparison Study ◽  
Numerical Examples ◽  
Mean Squared Errors ◽  
Type I Censoring

Maximum likelihood and proportion estimators of the parameters of the discrete Weibull type II distribution with type I censored data are discussed. A simulation study is performed to generate data from this distribution for suggested values of its parameters and to get the Maximum likelihood estimates of the parameters numerically. The method of proportions suggested by Khan et al. (1989) is also used to estimate the model's parameters. Numerical examples are used to perform a comparison study between the two method results according the values of the estimates and their corresponding mean squared errors.

A Note on Tolerance Limits with Type I Censoring

Technometrics ◽  
1968 ◽  
Vol 10 (2) ◽  
pp. 392-392
Author(s):  
Robert Bohrer
Keyword(s):  
Type I ◽  
Tolerance Limits ◽  
Type I Censoring

scholarly journals Measurement of entropy and quantum coherence properties of two type-I entangled photonic qubits

2021 ◽  
Vol 53 (7) ◽  
Author(s):  
Ali Motazedifard ◽  
Seyed Ahmad Madani ◽  
N. S. Vayaghan
Keyword(s):  
Maximum Likelihood ◽  
Quantum Coherence ◽  
Single Photon ◽  
Bell Inequality ◽  
Bell State ◽  
Von Neumann Entropy ◽  
Entangled State ◽  
Type I ◽  
Variable Theory ◽  
High Brightness

AbstractUsing the type-I SPDC process in BBO nonlinear crystal, we generate a polarization-entangled state near to the maximally-entangled Bell-state with high-visibility (high-brightness) 98.50 ± 1.33% (87.71 ± 4.45%) for HV (DA) basis. We calculate the CHSH version of the Bell inequality, as a nonlocal realism test, and find a strong violation from the classical physics or any hidden variable theory, S = 2.71 ± 0.10. Via measuring the coincidence count rate in the SPDC process, we obtain the quantum efficiency of single-photon detectors around (25.5 ± 3.4)%, which is in good agreement to their manufacturer company. As expected, we verify the linear dependency of the CC rate vs. pump power of input CW-laser, which may yield to find the effective second-order susceptibility crystal. Using the theory of the measurement of qubits, includes a tomographic reconstruction of quantum states due to the linear set of 16 polarization-measurement, together with a maximum-likelihood-technique, which is based on the numerical optimization, we calculate the physical non-negative definite density matrices, which implies on the non-separability and entanglement of prepared state. By having the maximum likelihood density operator, we calculate precisely the entanglement measures such as Concurrence, entanglement of formation, tangle, logarithmic negativity, and different entanglement entropies such as linear entropy, Von-Neumann entropy, and Renyi 2-entropy. Finally, this high-brightness and low-rate entangled photons source can be used for short-range quantum measurements in the Lab.

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