scholarly journals Bounds for the Maximum Likelihood Estimates in Two-Parameter Gamma Distribution

2000 ◽  
Vol 245 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Hai Dang ◽  
Govinda Weerakkody
Keyword(s):  
Maximum Likelihood ◽  
Gamma Distribution ◽  
Maximum Likelihood Estimates ◽  
Two Parameter

scholarly journals Classical and Bayesian Estimation of Two-Parameter Power Function Distribution

2021 ◽  
Author(s):  
Xuechen Liu ◽  
Muhammad Arslan ◽  
Majid Khan ◽  
Syed Masroor Anwar ◽  
Zahid Rasheed
Keyword(s):  
Maximum Likelihood ◽  
Power Function ◽  
Real Life ◽  
Maximum Likelihood Estimates ◽  
Time Model ◽  
Data Set ◽  
Bayes Estimates ◽  
Function Distribution ◽  
Power Function Distribution ◽  
Two Parameter

The power function distribution is a flexible waiting time model that may provide better fit for some failure data. This paper presents the comparison of the maximum likelihood estimates and the Bayes estimates of two-parameter power function distribution. The Bayes estimates are obtained, using conjugate priors, under five loss functions consist of square error, precautionary, weighted, LINEX and DeGroot loss function. The Gibbs sampling algorithm is proposed to generate samples from posterior distributions and in result the Bayes estimates are computed. The comparison of the maximum likelihood estimates and the Bayes estimates are done through the root mean squared errors. One real-life data set is analyzed to illustrate the evaluation of proposed methods of estimation. Finally, results from the simulation are discussed to assess the performance behavior of the maximum likelihood estimates and the Bayes estimates.

Estimation of Two-Parameter Logistic Item Response Curves

1984 ◽  
Vol 9 (4) ◽  
pp. 263-276 ◽  
Author(s):  
Robert K. Tsutakawa
Keyword(s):  
Maximum Likelihood ◽  
Item Response ◽  
Information Matrix ◽  
Simulated Data ◽  
Maximum Likelihood Estimates ◽  
Response Curves ◽  
Numerical Work ◽  
Item Parameters ◽  
The Em Algorithm ◽  
Two Parameter

Under the assumption that ability parameters are sampled from a normal distribution, the EM algorithm is used to derive maximum likelihood estimates for item parameters of the two-parameter logistic item response curves. The observed information matrix is then used to approximate the covariance matrix of these estimates. Responses to a questionnaire on general arthritis knowledge are used to illustrate the procedure and simulated data are used to compare the estimated and actual item parameters. The resulting estimates are found to be very close to those obtained from LOGIST. A computational note is included to facilitate the extensive numerical work required to implement the procedure.

Estimation for a family of life distributions with applications to fatigue

1969 ◽  
Vol 6 (2) ◽  
pp. 328-347 ◽  
Author(s):  
Z.W. Birnbaum ◽  
S.C. Saunders
Keyword(s):  
Fatigue Crack ◽  
Maximum Likelihood ◽  
Fatigue Crack Growth ◽  
Maximum Likelihood Estimate ◽  
Maximum Likelihood Estimates ◽  
Practical Significance ◽  
Simple Estimate ◽  
Fatigue Data ◽  
Life Distributions ◽  
Two Parameter

SummaryThe estimation problem is studied for a new two-parameter family of life length distributions which has been previously derived from a model of fatigue crack growth. Maximum likelihood estimates of both parameters are obtained and iterative computing procedures are given and examined. A simple estimate of the median life is exhibited, shown to be consistent and then compared, favorably, with the maximum likelihood estimate. More important, the asymptotic distribution of this estimate is shown to be within the same class of distributions as the observations themselves. This model, and these estimation procedures, are tried by fitting this distribution to several extensive sets of fatigue data and then some comparisons of practical significance are made.

scholarly journals Consistency and Asymptotic Normality of the Maximum Likelihood Estimator in GaGLM

2021 ◽  
Author(s):  
Benchao Wang ◽  
Hong Gu ◽  
Pan Qin
Keyword(s):  
Maximum Likelihood ◽  
Gamma Distribution ◽  
Theoretical Foundation ◽  
Asymptotic Properties ◽  
Information Matrix ◽  
Maximum Likelihood Estimates ◽  
Theoretical Research ◽  
Order Moment ◽  
Interval Estimates ◽  
Application Condition

This paper theoretically investigates the asymptotic properties of maximum likelihood estimates of GaGLM, and discusses some properties about Gamma distribution. It can provide theoretical foundation for expanding the application scope of gamma distribution based regression model, and benefit the further interval estimates, hypothesis tests and stochastic control design.The existence of the Gamma function in Gamma distribution makes correlation analysis certain specificity, and few researchers do relevant theoretical research. To complement this part, we established the asymptotic properties and the application condition of maximum likelihood estimates of GaGLM. In addition to this, we also discussed the propertis of the Fisher information matrix ,and n-order moment of Z and log(Z).

Estimation for a family of life distributions with applications to fatigue

1969 ◽  
Vol 6 (02) ◽  
pp. 328-347 ◽  
Author(s):  
Z.W. Birnbaum ◽  
S.C. Saunders
Keyword(s):  
Fatigue Crack ◽  
Maximum Likelihood ◽  
Fatigue Crack Growth ◽  
Maximum Likelihood Estimate ◽  
Maximum Likelihood Estimates ◽  
Practical Significance ◽  
Simple Estimate ◽  
Fatigue Data ◽  
Life Distributions ◽  
Two Parameter

Summary The estimation problem is studied for a new two-parameter family of life length distributions which has been previously derived from a model of fatigue crack growth. Maximum likelihood estimates of both parameters are obtained and iterative computing procedures are given and examined. A simple estimate of the median life is exhibited, shown to be consistent and then compared, favorably, with the maximum likelihood estimate. More important, the asymptotic distribution of this estimate is shown to be within the same class of distributions as the observations themselves. This model, and these estimation procedures, are tried by fitting this distribution to several extensive sets of fatigue data and then some comparisons of practical significance are made.

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