Existence of maximum likelihood estimation for three-parameter log-normal distribution

2009 ◽  
Author(s):  
Yincai Tang ◽  
Xiaoling Wei
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Normal Distribution ◽  
Likelihood Estimation ◽  
Log Normal ◽  
Log Normal Distribution

scholarly journals PENDUGAAN PARAMETER MIU DARI DISTRIBUSI LOG-NORMAL DENGAN MENGGUNAKAN METODE MAXIMUM LIKELIHOOD ESTIMATION (MLE) DAN METODE BAYES

2020 ◽  
Vol 9 (2) ◽  
pp. 84
Author(s):  
INDAH PRATIWI ◽  
FERRA YANUAR ◽  
HAZMIRA YOZZA
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Log Normal

Penelitian ini membahas tentang pendugaan parameter µ dari distribusi LogNormal dengan σ 2 diketahui. Penelitian ini menggunakan metode Maximum Likelihood Estimation (MLE) dan metode Bayes dengan prior konjugat. Penduga parameter µ dengan metode MLE dinyatakan sebagai µbMLE = Σn i=1ln(Xi) n dan penduga parameter µ dengan metode Bayes dinyatakan sebagai µbB = mσ2 + nx ∗p σ2 + np . Pada penelitian ini kriteria evaluasi penduga yang digunakan adalah MSE dan sifat tak bias. Berdasarkan studi analitik dan studi kasus diperoleh bahwa pendugaan µ dari distribusi Log-Normal dengan metode Bayes lebih baik di bandingkan metode Maximum Likelihood Estimation (MLE). Kata Kunci: Metode Bayes, Metode Maximum Likelihood Estimation Distribusi LogNormal, Prior Konjugat

The Odd Log-Logistic Log-Normal Distribution with Theory and Applications

2018 ◽  
Vol 10 (04) ◽  
pp. 1850009 ◽  
Author(s):  
Gamze Ozel ◽  
Emrah Altun ◽  
Morad Alizadeh ◽  
Mahdieh Mozafari
Keyword(s):  
Normal Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Procedure ◽  
Quantile Function ◽  
Logistic Distribution ◽  
Unknown Parameters ◽  
Heavy Tailed ◽  
Log Normal ◽  
Log Normal Distribution

In this paper, a new heavy-tailed distribution is used to model data with a strong right tail, as often occuring in practical situations. The proposed distribution is derived from the log-normal distribution, by using odd log-logistic distribution. Statistical properties of this distribution, including hazard function, moments, quantile function, and asymptotics, are derived. The unknown parameters are estimated by the maximum likelihood estimation procedure. For different parameter settings and sample sizes, a simulation study is performed and the performance of the new distribution is compared to beta log-normal. The new lifetime model can be very useful and its superiority is illustrated by means of two real data sets.

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