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 Generalizations of Burr Type X Distribution with Applications

2020 ◽  
pp. 1-8
Author(s):  
Noor Akma Ibrahim ◽  
Mundher Abdullah Khaleel
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Density Function ◽  
Likelihood Estimation ◽  
Real Data ◽  
Data Sets ◽  
Lifetime Data ◽  
Simulation Studies ◽  
Cumulative Density Function ◽  
Two Parameters

We propose the generalizations of Burr Type X distribution with two parameters by using the methods of Beta-G, Gamma-G and Weibull-G families of distributions. We discuss maximum likelihood estimation of the model’s parameters. The performances of the parameter’s estimates are assessed via simulation studies under different sets of conditions. In the applications to real data sets, three sets of data are used whereby from the results we can deduce that these models can be used quite effectively in analysing lifetime data. Keywords: cumulative density function; lifetime data; maximum likelihood estimation

scholarly journals Effective estimation algorithm for parameters of multivariate Farlie–Gumbel–Morgenstern copula

2021 ◽  
Author(s):  
Shuhei Ota ◽  
Mitsuhiro Kimura
Keyword(s):  
Parameter Estimation ◽  
Data Analysis ◽  
Computational Complexity ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Asymptotic Normality ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Algorithm ◽  
Simulation Studies

AbstractThis paper focuses on the parameter estimation for the d-variate Farlie–Gumbel–Morgenstern (FGM) copula ($$d\ge 2$$ d ≥ 2 ), which has $$2^d-d-1$$ 2 d - d - 1 dependence parameters to be estimated; therefore, maximum likelihood estimation is not practical for a large d from the viewpoint of computational complexity. Besides, the restriction for the FGM copula’s parameters becomes increasingly complex as d becomes large, which makes parameter estimation difficult. We propose an effective estimation algorithm for the d-variate FGM copula by using the method of inference functions for margins under the restriction of the parameters. We then discuss its asymptotic normality as well as its performance determined through simulation studies. The proposed method is also applied to real data analysis of bearing reliability.

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.

scholarly journals A new generalization of Aradhana distribution: Properties and applications

2020 ◽  
Vol 16 (2) ◽  
pp. 51-66
Author(s):  
A. Hassan ◽  
S. A. Dar ◽  
P. B. Ahmad ◽  
B. A. Para
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Real Data ◽  
Statistical Properties ◽  
Model Parameters ◽  
R Software ◽  
Data Set

AbstractIn this paper, we introduce a new generalization of Aradhana distribution called as Weighted Aradhana Distribution (WID). The statistical properties of this distribution are derived and the model parameters are estimated by maximum likelihood estimation. Simulation study of ML estimates of the parameters is carried out in R software. Finally, an application to real data set is presented to examine the significance of newly introduced model.

scholarly journals New General Transmuted Family of Distributions with Applications

2018 ◽  
pp. 807-829
Author(s):  
Md. Mahabubur Rahman ◽  
Bander Al-Zahrani ◽  
Muhammad Qaiser Shahbaz
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
New Class ◽  
New Family ◽  
Family Of Distributions

In this paper, we have introduced a new family of general transmuted distributions and have studied the cubic transmuted family of distributions in detail. This new class of distributions oers more distributional exibility when bi-modality appear in the data sets. Some special members of the proposed cubic transmuted family of distributions have been discussed. We have investigated, in detail, the proposed cubic transmuted family of distributions for parent exponential distribution. The statistical properties along with the reliability behavior for the cubic transmuted exponential distribution have been studied. We have obtained the expressions for single and joint order statistics when a sample is available from the cubic transmuted exponential distribution. Maximum likelihood estimation of parameters for cubic transmuted exponential distribution has also been discussed. We have also discussed the simulation and real data applications of the proposed distribution.

scholarly journals HALF LOGISTIC MODIFIED EXPONENTIAL DISTRIBUTION: PROPERTIES AND APPLICATIONS

2020 ◽  
pp. 276-287
Author(s):  
Arun Kumar Chaudhary ◽  
Vijay Kumar
Keyword(s):  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Least Square ◽  
Estimation Methods ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Type I ◽  
Data Set ◽  
Von Mises

In this study, we have introduced a three-parameter probabilistic model established from type I half logistic-Generating family called half logistic modified exponential distribution. The mathematical and statistical properties of this distribution are also explored. The behavior of probability density, hazard rate, and quantile functions are investigated. The model parameters are estimated using the three well known estimation methods namely maximum likelihood estimation (MLE), least-square estimation (LSE) and Cramer-Von-Mises estimation (CVME) methods. Further, we have taken a real data set and verified that the presented model is quite useful and more flexible for dealing with a real data set. KEYWORDS— Half-logistic distribution, Estimation, CVME ,LSE, , MLE

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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