Maximum likelihood estimation based on ranked set sampling designs for two extensions of the Lindley distribution with uncensored and right-censored data

2020 ◽  
Vol 35 (4) ◽  
pp. 1827-1851
Author(s):  
Cesar Augusto Taconeli ◽  
Suely Ruiz Giolo
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Censored Data ◽  
Likelihood Estimation ◽  
Ranked Set Sampling ◽  
Right Censored Data ◽  
Lindley Distribution

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 New class of Lindley distributions: properties and applications

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Data Sets ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
New Class

AbstractA new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

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