Maximum likelihood estimation in the odd generalized exponential-exponential distribution

2018 ◽  
Vol 13 (3) ◽  
pp. 111-123
Author(s):  
Amani Abdullah Al-Salafi ◽  
Samia Abbas Adham
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Exponential Distribution ◽  
Likelihood Estimation

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

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.

scholarly journals Bayesian and Maximum Likelihood Estimation of the Shape Parameter of Exponential Inverse Exponential Distribution: A Comparative Approach

2020 ◽  
pp. 28-43
Author(s):  
Innocent Boyle Eraikhuemen ◽  
Fadimatu Bawuro Mohammed ◽  
Ahmed Askira Sule
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Bayesian Estimation ◽  
Exponential Distribution ◽  
Shape Parameter ◽  
Likelihood Estimation ◽  
Monte Carlo Study ◽  
Comparative Approach ◽  
The Mean ◽  
Inverse Exponential Distribution

This paper aims at making Bayesian analysis on the shape parameter of the exponential inverse exponential distribution using informative and non-informative priors. Bayesian estimation was carried out through a Monte Carlo study under 10,000 replications. To assess the effects of the assumed prior distributions and loss function on the Bayesian estimators, the mean square error has been used as a criterion. Overall, simulation results indicate that Bayesian estimation under QLF outperforms the maximum likelihood estimation and Bayesian estimation under alternative loss functions irrespective of the nature of the prior and the sample size. Also, for large sample sizes, all methods perform equally well.

scholarly journals Bayes Estimators for the Parameter of the Inverted Exponential Distribution Under different Double informative priors

2018 ◽  
Vol 24 (103) ◽  
pp. 18
Author(s):  
جنان عباس ناصر
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Bayes Estimation ◽  
Erlang Distribution ◽  
Mean Square ◽  
Informative Priors ◽  
Chi Squared ◽  
Mean Square Errors

In this paper, we present a comparison of double informative priors which are assumed for the parameter of inverted exponential distribution.To estimate the parameter of inverted exponential distribution by using Bayes estimation ,will be  used two different kind of information in the Bayes estimation; two different priors have been selected for the parameter of inverted exponential distribution. Also assumed Chi-squared - Gamma distribution, Chi-squared - Erlang distribution, and- Gamma- Erlang distribution as double priors. The results are the derivations of these estimators under the squared error loss function with three different double priors. Additionally Maximum likelihood estimation method (MLE) was used  to estimate the parameter of inverted exponential distribution .We used simulation technique, to compare the performance for each estimator, several cases from inverted exponential distribution for data generating, for different samples sizes (small, medium, and large).Simulation results shown that the best method is the bayes  estimation according to the smallest values of mean square errors( MSE) for all samples sizes (n) comparative to the estimated values by using MLE . According to obtained results, we see that when the double prior distribution for  is Gamma- Erlang distribution for some values for the parameters a, b & given the best results according to the smallest values of mean square errors (MSE) comparative to the same values which obtained by using Maximum likelihood estimation (MLE) for the assuming true values for and for all samples sizes.  

Sensitivity and Variability Analysis for Image Denoising Using Maximum Likelihood Estimation of Exponential Distribution

2018 ◽  
Vol 37 (9) ◽  
pp. 3903-3926 ◽  
Author(s):  
Amita Nandal ◽  
Arvind Dhaka ◽  
Hamurabi Gamboa-Rosales ◽  
Ninoslav Marina ◽  
Jorge I. Galvan-Tejada ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Exponential Distribution ◽  
Image Denoising ◽  
Likelihood Estimation ◽  
Variability Analysis

scholarly journals Estimate Stress-Strength Reliability Model Using Rayleigh and Half-Normal Distribution

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Osama Abdulaziz Alamri ◽  
M. M. Abd El-Raouf ◽  
Eman Ahmed Ismail ◽  
Zahra Almaspoor ◽  
Basim S. O. Alsaedi ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Normal Distribution ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Rayleigh Distribution ◽  
Reliability Model ◽  
Method Of Moment ◽  
Life Testing ◽  
Strength Parameters

In the field of life testing, it is very important to study the reliability of any component under testing. One of the most important subjects is the “stress-strength reliability” term which always refers to the quantity P   X > Y in any statistical literature. It resamples a system with random strength (X) that is subjected to a random strength (Y) such that a system fails in case the stress exceeds the strength. In this study, we consider stress-strength reliability where the strength (X) follows Rayleigh-half-normal distribution and stress ( Y 1 , Y 2 , Y 3 , and Y 4 ) follows Rayleigh-half-normal distribution, exponential distribution, Rayleigh distribution, and half-normal distribution, respectively. This effort comprises determining the general formulations of the reliabilities of a system. Also, the maximum likelihood estimation approach and method of moment (MOM) will be utilized to estimate the parameters. Finally, reliability has been attained utilizing various values of stress and strength parameters.

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.

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