Maximum likelihood estimation of un1modal and decreasing densities based on arbitrarily right-censored data

1982 ◽  
Vol 11 (20) ◽  
pp. 2259-2270 ◽  
Author(s):  
D.T. McNichols ◽  
W.J. Padgett
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Censored Data ◽  
Likelihood Estimation ◽  
Right Censored Data

scholarly journals Simulation of generalized Gamma distribution with maximum likelihood estimation and expectation-maximization algorithm on right censored data type 1

2021 ◽  
Vol 10 (3) ◽  
pp. 415-424
Author(s):  
Dian Kurniasari ◽  
Warsono Warsono ◽  
Nourma Indryani ◽  
Mustofa Usman ◽  
Sutopo Hadi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Censored Data ◽  
Gamma Distribution ◽  
Expectation Maximization ◽  
Likelihood Estimation ◽  
Right Censored Data ◽  
Generalized Gamma Distribution ◽  
Generalized Gamma

The Generalized Gamma distribution is very suitable for modeling data with various forms of hazard (risk) functions, which makes the Generalized Gamma distribution useful in survival analysis. Survival analysis aims are to predict chances of survival, disease recurrence, death, and other events over a period of time. One characteristic of survival data is the possibility of sensors. Let X be the life span of the person being studied and the right censorship time of Cr, X is assumed to be independent with the probability density function f(x), the survival function S(x), and the hazard function h(x). A person's X life span will be known if X is less than or equal to Cr. If X is greater than Cr, the individual X survives or is censored right now. Statistical inference, especially parameter estimation is needed in analyzing empirical data. Obviously the estimation results obtained are expected to be a good estimator, namely to meet the nature of unbiased and minimum variance. This paper will discuss the results of the estimation of Generalized Gamma distribution parameters with type 1 right censored data through simulations using the Expectation Maximization method and the Maximum Likelihood Estimation method. The simulation is conducted by generating data with the sample size: 25, 50, 100, 200, 500, 1000, 1500 and 2000 as well as determining censored data of 10%, 20% and 30% by first setting the parameters used which are obtained from the data of patients with gastric cancer namely α = 1.0649, β = 1,072, θ = 59.766. Based on the results obtained from the simulations on the two estimation methods that the parameter estimation using the Maximum Likelihood Estimation method is better than the Expectation Maximization method because it provides a smaller bias and MSE value where the larger the sample size used, the estimated parameter value will get closer to the parameter in fact. In addition, the Expectation Maximization method can also be used as an alternative estimation of generalized gamma distribution parameters with type 1 right censored data because it has a bias value and MSE approaching the MLE method.

scholarly journals Maximum Likelihood Estimation for the Generalized Pareto Distribution and Goodness-of-Fit Test with Censored Data

2019 ◽  
Vol 17 (2) ◽  
Author(s):  
Minh H. Pham ◽  
Chris Tsokos ◽  
Bong-Jin Choi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Censored Data ◽  
Goodness Of Fit ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Likelihood Estimation ◽  
R Package ◽  
Goodness Of Fit Test ◽  
Generalized Pareto

The generalized Pareto distribution (GPD) is a flexible parametric model commonly used in financial modeling. Maximum likelihood estimation (MLE) of the GPD was proposed by Grimshaw (1993). Maximum likelihood estimation of the GPD for censored data is developed, and a goodness-of-fit test is constructed to verify an MLE algorithm in R and to support the model-validation step. The algorithms were composed in R. Grimshaw’s algorithm outperforms functions available in the R package ‘gPdtest’. A simulation study showed the MLE method for censored data and the goodness-of-fit test are both reliable.

scholarly journals Microbial-Maximum Likelihood Estimation Tool for Microbial Quantification in Food From Left-Censored Data Using Maximum Likelihood Estimation for Microbial Risk Assessment

2021 ◽  
Vol 12 ◽  
Author(s):  
Gyung Jin Bahk ◽  
Hyo Jung Lee
Keyword(s):  
Risk Assessment ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Censored Data ◽  
Limit Of Detection ◽  
Likelihood Estimation ◽  
Food Microbiology ◽  
Quantitative Microbial Risk Assessment ◽  
Microbial Risk Assessment ◽  
Microbial Risk

In food microbial measurements, when most or very often bacterial counts are below to the limit of quantification (LOQ) or the limit of detection (LOD) in collected food samples, they are either ignored or a specified value is substituted. The consequence of this approach is that it may lead to the over or underestimation of quantitative results. A maximum likelihood estimation (MLE) or Bayesian models can be applied to deal with this kind of censored data. Recently, in food microbiology, an MLE that deals with censored results by fitting a parametric distribution has been introduced. However, the MLE approach has limited practical application in food microbiology as practical tools for implementing MLE statistical methods are limited. We therefore developed a user-friendly MLE tool (called “Microbial-MLE Tool”), which can be easily used without requiring complex mathematical knowledge of MLE but the tool is designated to adjust log-normal distributions to observed counts, and illustrated how this method may be implemented for food microbial censored data using an Excel spreadsheet. In addition, we used two case studies based on food microbial laboratory measurements to illustrate the use of the tool. We believe that the Microbial-MLE tool provides an accessible and comprehensible means for performing MLE in food microbiology and it will also be of help to improve the outcome of quantitative microbial risk assessment (MRA).

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