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.  

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

scholarly journals "Evaluation of Some Methods for Estimating the Weibull Distribution Parameters"

2017 ◽  
Vol 4 (2) ◽  
pp. 8-14
Author(s):  
J. A. Labban ◽  
H. H. Depheal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Least Squares ◽  
Mean Square Error ◽  
Random Sample ◽  
Likelihood Estimation ◽  
Mean Square ◽  
Distribution Parameters

"This paper some of different methods to estimate the parameters of the 2-Paramaters Weibull distribution such as (Maximum likelihood Estimation, Moments, Least Squares, Term Omission). Mean square error will be considered to compare methods fits in case to select the best one. There by simulation will be implemented to generate different random sample of the 2-parameters Weibull distribution, those contain (n=10, 50, 100, 200) iteration each 1000 times."

scholarly journals A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1394
Author(s):  
Mustapha Muhammad ◽  
Huda M. Alshanbari ◽  
Ayed R. A. Alanzi ◽  
Lixia Liu ◽  
Waqas Sami ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Confidence Intervals ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Weibull Model ◽  
Mean Square ◽  
Reliability Parameter ◽  
Coverage Probabilities ◽  
The Mean

In this article, we propose the exponentiated sine-generated family of distributions. Some important properties are demonstrated, such as the series representation of the probability density function, quantile function, moments, stress-strength reliability, and Rényi entropy. A particular member, called the exponentiated sine Weibull distribution, is highlighted; we analyze its skewness and kurtosis, moments, quantile function, residual mean and reversed mean residual life functions, order statistics, and extreme value distributions. Maximum likelihood estimation and Bayes estimation under the square error loss function are considered. Simulation studies are used to assess the techniques, and their performance gives satisfactory results as discussed by the mean square error, confidence intervals, and coverage probabilities of the estimates. The stress-strength reliability parameter of the exponentiated sine Weibull model is derived and estimated by the maximum likelihood estimation method. Also, nonparametric bootstrap techniques are used to approximate the confidence interval of the reliability parameter. A simulation is conducted to examine the mean square error, standard deviations, confidence intervals, and coverage probabilities of the reliability parameter. Finally, three real applications of the exponentiated sine Weibull model are provided. One of them considers stress-strength data.

Advanced Topics

2019 ◽  
pp. 57-74
Author(s):  
Carey Witkov ◽  
Keith Zengel
Keyword(s):  
Maximum Likelihood ◽  
Probability Density Function ◽  
Maximum Likelihood Estimation ◽  
Probability Density ◽  
Likelihood Estimation ◽  
Nonlinear Problems ◽  
Probability Density Functions ◽  
Density Functions ◽  
P Values ◽  
Chi Squared

A variety of advanced topics are introduced to offer greater challenge for beginners and to answer thorny questions often asked by early researchers who are just starting to use chi-squared analysis. Topics covered include probability density functions, p-values, the derivation of the chi-squared probability density function and its uses, reduced chi-squared, the Poisson distribution, and advanced techniques for maximum likelihood estimation in cases where uncertainties are not Gaussian or the model is nonlinear. Problems are included (with solutions in an appendix).

New Testifying Method of Unit Weight Mean Square Error of No-Equal Precision Independent Surveying Values

2012 ◽  
Vol 170-173 ◽  
pp. 2904-2907 ◽  
Author(s):  
Yong He Deng
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Mean Square Error ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
New Method ◽  
Unit Weight ◽  
Mean Square ◽  
Maximum Likelihood Estimation Method

For unit weight mean square error of no-equal precision independent surveying values,this paper summed up several old estifying methods, pointed out their scarcities or mistakes, and advanced a sort of new method- maximum likelihood estimation method which is simple and strict.This is useful for theory of unit weight mean square error of no-equal precision independent surveying values to be perfect and for college surveying textbook to be improved and unified.

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.

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