scholarly journals Marshall–Olkin Alpha Power Weibull Distribution: Different Methods of Estimation Based on Type-I and Type-II Censoring

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Ehab M. Almetwally ◽  
Mohamed A. H. Sabry ◽  
Randa Alharbi ◽  
Dalia Alnagar ◽  
Sh. A. M. Mubarak ◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Methods ◽  
Data Sets ◽  
Type I ◽  
Alpha Power ◽  
Type Ii ◽  
Censored Samples ◽  
Distribution Parameters

This paper introduces the new novel four-parameter Weibull distribution named as the Marshall–Olkin alpha power Weibull (MOAPW) distribution. Some statistical properties of the distribution are examined. Based on Type-I censored and Type-II censored samples, maximum likelihood estimation (MLE), maximum product spacing (MPS), and Bayesian estimation for the MOAPW distribution parameters are discussed. Numerical analysis using real data sets and Monte Carlo simulation are accomplished to compare various estimation methods. This novel model’s supremacy upon some famous distributions is explained using two real data sets and it is shown that the MOAPW model can achieve better fits than other competitive distributions.

scholarly journals Marshall–Olkin Alpha Power Lomax Distribution: Estimation Methods, Applications on Physics and Economics

2021 ◽  
pp. 137-153
Author(s):  
Hisham Mohamed Almongy ◽  
Ehab Mohamed Almetwally ◽  
Amaal Elsayed Mubarak
Keyword(s):  
Monte Carlo Simulation ◽  
Numerical Study ◽  
Likelihood Estimation ◽  
Real Data ◽  
Least Square ◽  
Estimation Methods ◽  
Data Sets ◽  
Alpha Power ◽  
Lomax Distribution ◽  
Distribution Parameters

In this paper, we introduce and study a new extension of Lomax distribution with four-parameter named as the Marshall–Olkin alpha power Lomax (MOAPL) distribution. Some statistical properties of this distribution are discussed. Maximum likelihood estimation (MLE), maximum product spacing (MPS) and least Square (LS) method for the MOAPL distribution parameters are discussed. A numerical study using real data analysis and Monte-Carlo simulation are performed to compare between different methods of estimation. Superiority of the new model over some well-known distributions are illustrated by physics and economics real data sets. The MOAPL model can produce better fits than some well-known distributions as Marshall–Olkin Lomax, alpha power Lomax, Lomax distribution, Marshall–Olkin alpha power exponential, Kumaraswamy-generalized Lomax, exponentiated  Lomax  and power Lomax.

scholarly journals Bivariate Burr X Generator of Distributions: Properties and Estimation Methods with Applications to Complete and Type-II Censored Samples

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 264 ◽  
Author(s):  
M. El-Morshedy ◽  
Ziyad Ali Alhussain ◽  
Doaa Atta ◽  
Ehab M. Almetwally ◽  
M. S. Eliwa
Keyword(s):  
Real Data ◽  
Bivariate Distribution ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Sets ◽  
Type Ii ◽  
Censored Samples ◽  
Type Ii Censored Data ◽  
Modeling Data

Burr proposed twelve different forms of cumulative distribution functions for modeling data. Among those twelve distribution functions is the Burr X distribution. In statistical literature, a flexible family called the Burr X-G (BX-G) family is introduced. In this paper, we propose a bivariate extension of the BX-G family, in the so-called bivariate Burr X-G (BBX-G) family of distributions based on the Marshall–Olkin shock model. Important statistical properties of the BBX-G family are obtained, and a special sub-model of this bivariate family is presented. The maximum likelihood and Bayesian methods are used for estimating the bivariate family parameters based on complete and Type II censored data. A simulation study was carried out to assess the performance of the family parameters. Finally, two real data sets are analyzed to illustrate the importance and the flexibility of the proposed bivariate distribution, and it is found that the proposed model provides better fit than the competitive bivariate distributions.

scholarly journals Statistical inferences for type-II hybrid censoring data from the alpha power exponential distribution

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0244316
Author(s):  
Mukhtar M. Salah ◽  
Essam A. Ahmed ◽  
Ziyad A. Alhussain ◽  
Hanan Haj Ahmed ◽  
M. El-Morshedy ◽  
...  
Keyword(s):  
Exponential Distribution ◽  
Information Matrix ◽  
Expectation Maximization Algorithm ◽  
Location Parameter ◽  
Real Data ◽  
Estimation Methods ◽  
Invariance Property ◽  
Alpha Power ◽  
Type Ii ◽  
Hazard Functions

This paper describes a method for computing estimates for the location parameter μ > 0 and scale parameter λ > 0 with fixed shape parameter α of the alpha power exponential distribution (APED) under type-II hybrid censored (T-IIHC) samples. We compute the maximum likelihood estimations (MLEs) of (μ, λ) by applying the Newton-Raphson method (NRM) and expectation maximization algorithm (EMA). In addition, the estimate hazard functions and reliability are evaluated by applying the invariance property of MLEs. We calculate the Fisher information matrix (FIM) by applying the missing information rule, which is important in finding the asymptotic confidence interval. Finally, the different proposed estimation methods are compared in simulation studies. A simulation example and real data example are analyzed to illustrate our estimation methods.

scholarly journals The Modified Kumaraswamy Weibull Distribution: Properties and Applications in Reliability and Engineering Sciences

2020 ◽  
pp. 433-446
Author(s):  
M. E. Mead ◽  
Ahmed Afify ◽  
Nadeem Shafique Butt
Keyword(s):  
Weibull Distribution ◽  
Information Matrix ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Hazard Rates ◽  
Alpha Power ◽  
Mathematical Properties ◽  
Engineering Sciences ◽  
Maximum Likelihood Estimation Method

We introduce the Kumaraswamy alpha power-G (KAP-G) family which extends the alpha power family (Mahdavi and Kundu, 2017) and some other families. We consider the Weibull as baseline for the KAP family and generate Kumaraswamy alpha power Weibull distribution which has right-skewed, left-skewed, symmetrical, and reversed-J shaped densities, and decreasing, increasing, bathtub, upside-down bathtub, increasing-decreasing–increasing, J shaped and reversed-J shaped hazard rates. The proposed distribution can model non-monotone  and monotone failure rates which are quite common in engineering and reliability studies. Some basic mathematical properties of the new model are derived. The maximum likelihood estimation method is used to evaluate the parameters and the observed information matrix is determined. The performance and flexibility of the proposed family is illustrated via two real data applications.

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 Marshall-Olkin Alpha Power Rayleigh Distribution: Properties, Characterizations, Estimation and Engineering applications

2021 ◽  
pp. 745-760
Author(s):  
Ehab Mohamed Almetwally ◽  
Ahmed Z. Afify ◽  
G. G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Hazard Function ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Estimation Methods ◽  
Data Sets ◽  
Alpha Power ◽  
Monte Carlo Simulation Study ◽  
Bootstrap Estimation ◽  
Proposed Model

In this paper, we introduce a new there-parameter Rayleigh distribution, called the Marshall-Olkin alpha power Rayleigh (MOAPR) distribution. Some statistical properties of the MOAPR distribution are obtained. The proposed model is characterized based on truncated moments and reverse hazard function. The maximum likelihood and bootstrap estimation methods are considered to estimate the MOPAR parameters. A Monte Carlo simulation study is performed to compare the maximum likelihood and bootstrap estimation methods. Superiority of the MOAPR distribution over some well-known distributions is illustrated by means of two real data sets.

scholarly journals The Half-Logistic Generalized Weibull Distribution

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Masood Anwar ◽  
Amna Bibi
Keyword(s):  
Weibull Distribution ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Type I ◽  
Failure Rate Function ◽  
New Model ◽  
Compound Distribution

A new three-parameter generalized distribution, namely, half-logistic generalized Weibull (HLGW) distribution, is proposed. The proposed distribution exhibits increasing, decreasing, bathtub-shaped, unimodal, and decreasing-increasing-decreasing hazard rates. The distribution is a compound distribution of type I half-logistic-G and Dimitrakopoulou distribution. The new model includes half-logistic Weibull distribution, half-logistic exponential distribution, and half-logistic Nadarajah-Haghighi distribution as submodels. Some distributional properties of the new model are investigated which include the density function shapes and the failure rate function, raw moments, moment generating function, order statistics, L-moments, and quantile function. The parameters involved in the model are estimated using the method of maximum likelihood estimation. The asymptotic distribution of the estimators is also investigated via Fisher’s information matrix. The likelihood ratio (LR) test is used to compare the HLGW distribution with its submodels. Some applications of the proposed distribution using real data sets are included to examine the usefulness of the distribution.

scholarly journals Volatility Fitting Performance of QGARCH(1,1) Model with Student-t, GED, and SGED Distributions

2020 ◽  
Vol 11 (2) ◽  
pp. 97-104
Author(s):  
Didit Budi Nugroho ◽  
Bintoro Ady Pamungkas ◽  
Hanna Arini Parhusip
Keyword(s):  
Stock Exchange ◽  
Linear Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Information Criterion ◽  
Estimation Methods ◽  
Data Sets ◽  
Non Linear ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient

The research had two objectives. First, it compared the performance of the Generalized Autoregressive Conditional Heteroscedasticity (1,1) (GARCH) and Quadratic GARCH (1,1) (QGARCH)) models based on the fitting to real data sets. The model assumed that return error follows four different distributions: Normal (Gaussian), Student-t, General Error Distribution (GED), and Skew GED (SGED). Maximum likelihood estimation was usually employed in estimating the GARCH model, but it might not be easily applied to more complicated ones. Second, it provided two ways to evaluate the considered models. The models were estimated using the Generalized Reduced Gradient (GRG) Non-Linear method in Excel’s Solver and the Adaptive Random Walk Metropolis (ARWM) in the Scilab program. The real data in the empirical study were Financial Times Stock Exchange Milano Italia Borsa (FTSEMIB) and Stoxx Europe 600 indices over the daily period from January 2000 to December 2017 to test the conditional variance process and see whether the estimation methods could adapt to the complicated models. The analysis shows that GRG Non-Linear in Excel’s Solver and ARWM methods have close results. It indicates a good estimation ability. Based on the Akaike Information Criterion (AIC), the QGARCH(1,1) model provides a better fitting than the GARCH(1,1) model on each distribution specification. Overall, the QGARCH(1,1) with SGED distribution best fits both data.

scholarly journals Exponentiated Cubic Transmuted Weibull Distribution: Properties and Application

2021 ◽  
pp. 1-11
Author(s):  
Oseghale O. I. ◽  
Akomolafe A. A. ◽  
Gayawan E.
Keyword(s):  
Weibull Distribution ◽  
Real Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Data Sets ◽  
Estimation Technique ◽  
Life Data ◽  
Real Life Data

This work is focused on the four parameters Exponentiated Cubic Transmuted Weibull distribution which mostly found its application in reliability analysis most especially for data that are non-monotone and Bi-modal. Structural properties such as moment, moment generating function, Quantile function, Renyi entropy, and order statistics were investigated. The maximum likelihood estimation technique was used to estimate the parameters of the distribution. Application to two real-life data sets shows the applicability of the distribution in modeling real data.

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