scholarly journals Further Properties and Estimations of Exponentiated Generalized Linear Exponential Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3328
Author(s):  
Chien-Tai Lin ◽  
Yu Liu ◽  
Yun-Wei Li ◽  
Zhi-Wei Chen ◽  
Hassan M. Okasha
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Order Statistics ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Asymptotic Distributions ◽  
Residual Lifetime ◽  
Monte Carlo Simulation Study ◽  
Modified Maximum Likelihood ◽  
Linear Exponential Distribution

The recent exponentiated generalized linear exponential distribution is a generalization of the generalized linear exponential distribution and the exponentiated generalized linear exponential distribution. In this paper, we study some statistical properties of this distribution such as negative moments, moments of order statistics, mean residual lifetime, and their asymptotic distributions for sample extreme order statistics. Different estimation procedures include the maximum likelihood estimation, the corrected maximum likelihood estimation, the modified maximum likelihood estimation, the maximum product of spacing estimation, and the least squares estimation are compared via a Monte Carlo simulation study in terms of their biases, mean squared errors, and their rates of obtaining reliable estimates. Recommendations are made from the simulation results and a numerical example is presented to illustrate its use for modeling a rainfall data from Orlando, Florida.

Topp–Leone Linear Exponential Distribution

2018 ◽  
Vol 33 (1) ◽  
pp. 31-43
Author(s):  
Bol A. M. Atem ◽  
Suleman Nasiru ◽  
Kwara Nantomah
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Simulation Studies ◽  
Finite Sample ◽  
Data Set ◽  
Finite Sample Properties ◽  
Linear Exponential Distribution

Abstract This article studies the properties of the Topp–Leone linear exponential distribution. The parameters of the new model are estimated using maximum likelihood estimation, and simulation studies are performed to examine the finite sample properties of the parameters. An application of the model is demonstrated using a real data set. Finally, a bivariate extension of the model is proposed.

Maximum Likelihood Estimation Modeling of Welded Joints Based on Metal Magnetic Memory Parameters

2016 ◽  
Vol 853 ◽  
pp. 458-462
Author(s):  
Hai Yan Xing ◽  
Hua Ge ◽  
Guan Ga Dai ◽  
Zheng Shuai Yu ◽  
Xiao Jun Sun
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Normal State ◽  
Kernel Density ◽  
Likelihood Estimation ◽  
Magnetic Memory ◽  
Metal Magnetic Memory ◽  
Damage State ◽  
Modified Maximum Likelihood ◽  
Density Values

In order to quantitatively identify critical hidden damage for weld joints by using the metal magnetic memory technology (MMM), the modified maximum likelihood estimation MMM model is first proposed. The experimental materials are Q235B welded plate specimens. Fatigue tension experiments were operated to find the MMM feature laws of critical hidden damage by comparing with synchronous X-ray detection results. Four MMM characteristic parameters, that is, ΔHp(y) , Kymax , mmax and S(K), are extracted corresponding to the normal state and the hidden damage state, respectively. The probability density values of ΔHp(y) , Kymax , mmax and S(K)are calculated by the optimized bandwidth kernel density estimation. The quantitative maximum likelihood estimation MMM model is established based on optimized bandwidth kernel density. The verification result shows the maximum likelihood value of hidden damage state is twice as much as that of the normal state, which is consistent with the practical results. This provides a new method for quantitative MMM identification of weld critical hidden damages.

scholarly journals Comparing Bayes estimation with Maximum Likelihood Estimation of Generalized Inverted Exponential Distribution in Case of Fuzzy Data

2017 ◽  
Vol 23 (101) ◽  
Author(s):  
Qutaiba Naief Nayef Al-Kazaz ◽  
Hawraa J. Kadhim Al-Saadi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Bayes Estimation ◽  
Fuzzy Data ◽  
Centroid Method

في هذا البحث تم تقدير معلمتي الشكل والقياس لمعكوس التوزيع الاسي المعمم والذي يعد من التوزيعات المهمة في دراسة اوقات الفشل ولكن بعد ازالة الضبابية التي تتصف بها بياناته إذ ان بياناته عبارة عن اعداد ضبابية ثلاثية ولتحويلها إلى اعداد اعتيادية تم استخدام (centroid method). وبما أن التوزيع المدروس ذو معلمتين فكان من الصعوبة الفصل بين المعلمتين وتقديرهما بشكل مباشر ففي طريقة الإمكان الاعظم تم الاستعانة بطريقة نيوتن رافسون التكرارية. اما المقدرات البيزية فقد تم الحصول عليها بفرض توزيع كاما كتوزيع اولي لمعلمتيه ومن ثم استعمال دالة الخسارة التربيعية وبالاعتماد على خوارزمية  Metropolis-Hasting . وتم توليد عينات مختلفة  تمثل المجتمع المدروس باستخدام اسلوب المحاكاة. وبعد تقدير معلمتي التوزيع ومقارنة نتائج طريقتي التقدير وفق مقياس متوسط مربعات الخطأ. تم التوصل الى أن افضل طريقة كانت طريقة الامكان الاعظم تليها الطريقة البيزية

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