Estimation of the bivariate generalized Lomax distribution parameters based on censored samples

2014 ◽  
Vol 9 ◽  
pp. 257-267 ◽  
Author(s):  
A.F. Attia ◽  
S. A. Shaban ◽  
Y. M. Amer
Keyword(s):  
Lomax Distribution ◽  
Censored Samples ◽  
Distribution Parameters

scholarly journals Inference for Inverse Power Lomax Distribution with Progressive First-Failure Censoring

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1099
Author(s):  
Xiaolin Shi ◽  
Yimin Shi
Keyword(s):  
Real Data ◽  
Sampling Procedure ◽  
Maximum Likelihood Estimates ◽  
Inverse Power ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Lomax Distribution ◽  
Censored Samples ◽  
Distribution Parameters ◽  
Credible Intervals

This paper investigates the statistical inference of inverse power Lomax distribution parameters under progressive first-failure censored samples. The maximum likelihood estimates (MLEs) and the asymptotic confidence intervals are derived based on the iterative procedure and asymptotic normality theory of MLEs, respectively. Bayesian estimates of the parameters under squared error loss and generalized entropy loss function are obtained using independent gamma priors. For Bayesian computation, Tierney–Kadane’s approximation method is used. In addition, the highest posterior credible intervals of the parameters are constructed based on the importance sampling procedure. A Monte Carlo simulation study is carried out to compare the behavior of various estimates developed in this paper. Finally, a real data set is analyzed for illustration purposes.

scholarly journals Harris Extended Power Lomax Distribution: Properties, Inference and Applications

2021 ◽  
Vol 10 (4) ◽  
pp. 77
Author(s):  
Adebisi Ade Ogunde ◽  
Victoria Eshomomoh Laoye ◽  
Ogbonnaya Nzie Ezichi ◽  
Kayode Oguntuase Balogun
Keyword(s):  
Time Distribution ◽  
Lorenz Curve ◽  
Life Time ◽  
Lomax Distribution ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
Distribution Parameters ◽  
Rate Functions ◽  
New Distribution ◽  
Extended Power

In this work, we present a five-parameter life time distribution called Harris power Lomax (HPL)  distribution which is obtained by convoluting the Harris-G distribution and the Power Lomax distribution. When compared to the existing distributions, the new distribution exhibits a very flexible probability functions; which may be increasing, decreasing, J, and reversed J shapes been observed for the probability density and hazard rate functions. The structural properties of the new distribution are studied in detail which includes: moments, incomplete moment, Renyl entropy, order statistics, Bonferroni curve, and Lorenz curve etc. The HPL  distribution parameters are estimated by using the method of maximum likelihood. Monte Carlo simulation was carried out to investigate the performance of MLEs. Aircraft wind shield data and Glass fibre data applications demonstrate the applicability of the proposed model.

scholarly journals The E-Bayesian Estimation for Lomax Distribution Based on Generalized Type-I Hybrid Censoring Scheme

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Kaiwei Liu ◽  
Yuxuan Zhang
Keyword(s):  
Bayesian Estimation ◽  
Credible Interval ◽  
Type I ◽  
Hybrid Censoring ◽  
Lomax Distribution ◽  
Censored Samples ◽  
Linex Loss ◽  
Kolmogorov Smirnov ◽  
Bayesian Estimations ◽  
Generalized Type

This article studies the E-Bayesian estimation of the unknown parameter of Lomax distribution based on generalized Type-I hybrid censoring. Under square error loss and LINEX loss functions, we get the E-Bayesian estimation and compare its effectiveness with Bayesian estimation. To measure the error of E-Bayesian estimation, the expectation of mean square error (E-MSE) is introduced. With Markov chain Monte Carlo technology, E-Bayesian estimations are computed. Metropolis–Hastings algorithm is applied within the process. Similarly, the credible interval for the parameter is calculated. Then, we can compare the MSE and E-MSE to evaluate whose result is more effective. For the purpose of illustration in real datasets, cases of generalized Type-I hybrid censored samples are presented. In order to judge whether the sample data can be directly fitted by the Lomax distribution, we adopt the Kolmogorov–Smirnov tests for evaluation. Finally, we can get the conclusion after comparing the results of E-Bayesian and Bayesian estimation.

scholarly journals Estimation of Sine Inverse Exponential Model under Censored Schemes

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
M. Shrahili ◽  
I. Elbatal ◽  
Waleed Almutiry ◽  
Mohammed Elgarhy
Keyword(s):  
Hazard Rate ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Data Fitting ◽  
Exponential Model ◽  
Rate Function ◽  
Numerical Results ◽  
Conditional Moments ◽  
Censored Samples ◽  
Distribution Parameters

In this article, we introduce a new one-parameter model, which is named sine inverted exponential (SIE) distribution. The SIE distribution is a new extension of the inverse exponential (IE) distribution. The SIE distribution aims to provide the SIE model for data-fitting purposes. The SIE distribution is more flexible than the inverted exponential (IE) model, and it has many applications in physics, medicine, engineering, nanophysics, and nanoscience. The density function (PDFu) of SIE distribution can be unimodel shape and right skewed shape. The hazard rate function (HRFu) of SIE distribution can be J-shaped and increasing shaped. We investigated some fundamental statistical properties such as quantile function (QFu), moments (Mo), moment generating function (MGFu), incomplete moments (ICMo), conditional moments (CMo), and the SIE distribution parameters were estimated using the maximum likelihood (ML) method for estimation under censored samples (CS). Finally, the numerical results were investigated to evaluate the flexibility of the new model. The SIE distribution and the IE distribution are compared using two real datasets. The numerical results show the superiority of the SIE distribution.

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 Weighted Power Lomax Distribution and its Length Biased Version: Properties and Estimation Based on Censored Samples

2021 ◽  
pp. 343-356
Author(s):  
Amal Soliman Hassan ◽  
Ehab M. Almetwally ◽  
Mundher Abdullah Khaleel ◽  
Heba Fathy Nagy
Keyword(s):  
Real Life ◽  
Model Parameters ◽  
Weighted Version ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Lifetime Distributions ◽  
Lomax Distribution ◽  
Censored Samples ◽  
Real Life Data ◽  
Asymptotic Confidence Intervals

In this paper, a weighted version of the power Lomax distribution referred to the weighted power Lomax distribution, is introduced. The new distribution comprises the length biased and the area biased of the power Lomax distribution as new models as well as containing an existing model as the length biased Lomax distribution as special model. Essential distributional properties of the weighted power Lomax distribution are studied. Maximum likelihood and maximum product spacing methods are proposed for estimating the population parameters in cases of complete and Type-II censored samples. Asymptotic confidence intervals of the model parameters are obtained. A sample generation algorithm along with a Monte Carlo simulation study is provided to demonstrate the pattern of the estimates for different sample sizes. Finally, a real-life data set is analyzed as an illustration and its length biased distribution is compared with some other lifetime distributions.

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