scholarly journals Multivariate Inverted Kumaraswamy Distribution: Derivation and Estimation

2020 ◽  
Vol 2020 ◽  
pp. 1-27
Author(s):  
Hanan M. Aly ◽  
Ola A. Abuelamayem
Keyword(s):  
Maximum Likelihood ◽  
Consumer Satisfaction ◽  
Selection Criteria ◽  
Industrial Revolution ◽  
Reliability Engineering ◽  
Unknown Parameters ◽  
Bayesian Approaches ◽  
Lifetime Distributions ◽  
Kumaraswamy Distribution ◽  
Bivariate Exponential

Industrial revolution leads to the manufacturing of multicomponent products; to guarantee the sufficiency of the product and consumer satisfaction, the producer has to study the lifetime of the products. This leads to the use of bivariate and multivariate lifetime distributions in reliability engineering. The most popular and applicable is Marshall–Olkin family of distributions. In this paper, a new bivariate lifetime distribution which is the bivariate inverted Kumaraswamy (BIK) distribution is found and its properties are illustrated. Estimation using both maximum likelihood and Bayesian approaches is accomplished. Using different selection criteria, it is found that BIK provides the best performance compared with other bivariate distributions like bivariate exponential and bivariate inverse Weibull distributions. As a generalization, the multivariate inverted Kumaraswamy (MIK) distribution is derived. Few studies have been conducted on the multivariate Marshall–Olkin lifetime distributions. To the best of our knowledge, none of them handle estimation process. In this paper, we developed an algorithm to show how to estimate the unknown parameters of MIK using both maximum likelihood and Bayesian approaches. This algorithm could be applied in estimating other Marshall–Olkin multivariate lifetime distributions.

scholarly journals New class of Lindley distributions: properties and applications

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Data Sets ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
New Class

AbstractA new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

scholarly journals On the Estimation of Reliability of Weighted Weibull Distribution: A Comparative Study

2016 ◽  
Vol 5 (4) ◽  
pp. 1
Author(s):  
Bander Al-Zahrani
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Real Data ◽  
Reliability Function ◽  
Nonparametric Methods ◽  
Empirical Method ◽  
Density Estimator ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Data Set

The paper gives a description of estimation for the reliability function of weighted Weibull distribution. The maximum likelihood estimators for the unknown parameters are obtained. Nonparametric methods such as empirical method, kernel density estimator and a modified shrinkage estimator are provided. The Markov chain Monte Carlo method is used to compute the Bayes estimators assuming gamma and Jeffrey priors. The performance of the maximum likelihood, nonparametric methods and Bayesian estimators is assessed through a real data set.

scholarly journals Maximum Likelihood Inference for Univariate Delay Differential Equation Models with Multiple Delays

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Ahmed A. Mahmoud ◽  
Sarat C. Dass ◽  
Mohana S. Muthuvalu ◽  
Vijanth S. Asirvadam
Keyword(s):  
Differential Equation ◽  
Maximum Likelihood ◽  
Delay Differential Equation ◽  
Information Matrix ◽  
Likelihood Inference ◽  
Multiple Delays ◽  
Unknown Parameters ◽  
Differential Equation Models ◽  
Delay Differential ◽  
Initial Starting

This article presents statistical inference methodology based on maximum likelihoods for delay differential equation models in the univariate setting. Maximum likelihood inference is obtained for single and multiple unknown delay parameters as well as other parameters of interest that govern the trajectories of the delay differential equation models. The maximum likelihood estimator is obtained based on adaptive grid and Newton-Raphson algorithms. Our methodology estimates correctly the delay parameters as well as other unknown parameters (such as the initial starting values) of the dynamical system based on simulation data. We also develop methodology to compute the information matrix and confidence intervals for all unknown parameters based on the likelihood inferential framework. We present three illustrative examples related to biological systems. The computations have been carried out with help of mathematical software: MATLAB® 8.0 R2014b.

scholarly journals A Note on the Existence of the Location Parameter Estimate of the Three-Parameter Weibull Model Using the Weibull Plot

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Chanseok Park
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Location Parameter ◽  
Weibull Model ◽  
Parameter Estimate ◽  
Reliability Engineering ◽  
Bounded Interval ◽  
Weibull Plot ◽  
Sample Correlation

The Weibull model is one of the widely used distributions in reliability engineering. For the parameter estimation of the Weibull model, there are several existing methods. The method of the maximum likelihood estimation among others is preferred because of its attractive statistical properties. However, for the case of the three-parameter Weibull model, the method of the maximum likelihood estimation has several drawbacks. To avoid the drawbacks, the method using the sample correlation from the Weibull plot is recently suggested. In this paper, we provide the justification for using this new method by showing that the location estimate of the three-parameter Weibull model exists in a bounded interval.

scholarly journals Estimation of Generalized Gompertz Distribution Parameters under Ranked-Set Sampling

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Mohammed Obeidat ◽  
Amjad Al-Nasser ◽  
Amer I. Al-Omari
Keyword(s):  
Monte Carlo ◽  
Real Data ◽  
Small Samples ◽  
Simple Random Sample ◽  
Unknown Parameters ◽  
Bayesian Approaches ◽  
Bayes Estimates ◽  
Gompertz Distribution ◽  
Distribution Parameters ◽  
Credible Intervals

This paper studies estimation of the parameters of the generalized Gompertz distribution based on ranked-set sample (RSS). Maximum likelihood (ML) and Bayesian approaches are considered. Approximate confidence intervals for the unknown parameters are constructed using both the normal approximation to the asymptotic distribution of the ML estimators and bootstrapping methods. Bayes estimates and credible intervals of the unknown parameters are obtained using differential evolution Markov chain Monte Carlo and Lindley’s methods. The proposed methods are compared via Monte Carlo simulations studies and an example employing real data. The performance of both ML and Bayes estimates is improved under RSS compared with simple random sample (SRS) regardless of the sample size. Bayes estimates outperform the ML estimates for small samples, while it is the other way around for moderate and large samples.

An Additive NHPP-Based Reliability Model of Wireless Sensor Networks

2014 ◽  
Vol 602-605 ◽  
pp. 3206-3212
Author(s):  
Bo Zhao ◽  
Jian Feng Yang ◽  
Ming Zhao ◽  
Qi Li ◽  
Yan Liu
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Wireless Sensor ◽  
Reliability Model ◽  
Unknown Parameters ◽  
Failure Data ◽  
Better Than

As the Wireless Sensor Networks (WSNs) are widely implemented in various fields recent years, the quality of WSNs has been increasingly concerned. WSNs can usually be divided into sub-nets, which assumed to work or fail independently. Through the failure data of those sub-nets, the additive NHPP model for reliability evaluation is composed, and then the maximum likelihood estimation is applied to estimate the unknown parameters in the model. Finally, the simulation shows that the additive NHPP model is better than general NHPP model under certain circumstances.

scholarly journals QML Estimators in Linear Regression Models with Functional Coefficient Autoregressive Processes

2010 ◽  
Vol 2010 ◽  
pp. 1-30 ◽  
Author(s):  
Hongchang Hu
Keyword(s):  
Maximum Likelihood ◽  
Linear Regression ◽  
Regression Models ◽  
Asymptotic Properties ◽  
Asymptotic Distributions ◽  
Autoregressive Processes ◽  
Linear Regression Models ◽  
Unknown Parameters ◽  
Quasi Maximum Likelihood ◽  
Functional Coefficient

This paper studies a linear regression model, whose errors are functional coefficient autoregressive processes. Firstly, the quasi-maximum likelihood (QML) estimators of some unknown parameters are given. Secondly, under general conditions, the asymptotic properties (existence, consistency, and asymptotic distributions) of the QML estimators are investigated. These results extend those of Maller (2003), White (1959), Brockwell and Davis (1987), and so on. Lastly, the validity and feasibility of the method are illuminated by a simulation example and a real example.

scholarly journals A Family of Lifetime Distributions

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Vasileios Pappas ◽  
Konstantinos Adamidis ◽  
Sotirios Loukas
Keyword(s):  
Maximum Likelihood ◽  
General Class ◽  
Real Data ◽  
Parameter Family ◽  
Maximum Likelihood Estimates ◽  
Weibull Distributions ◽  
Lifetime Distributions

A four-parameter family of Weibull distributions is introduced, as an example of a more general class created along the lines of Marshall and Olkin, 1997. Various properties of the distribution are explored and its usefulness in modelling real data is demonstrated using maximum likelihood estimates.

scholarly journals Estimation of the Inverse Weibull Distribution Parameters under Type-I Hybrid Censoring

2021 ◽  
Vol 50 (5) ◽  
pp. 38-51
Author(s):  
Mohammad Kazemi ◽  
Mina Azizpoor
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Maximum Likelihood Estimates ◽  
Type I ◽  
Unknown Parameters ◽  
Bayes Estimates ◽  
Hybrid Censoring ◽  
Inverse Weibull Distribution ◽  
Distribution Parameters ◽  
Highest Posterior Density

The hybrid censoring is a mixture of type-I and type-II censoring schemes. This paper presents the statistical inferences of the inverse Weibull distribution parameters when the data are type-I hybrid censored. First, we consider the maximum likelihood estimates of the unknown parameters. It is observed that the maximum likelihood estimates can not be obtained in closed form. We further obtain the Bayes estimates and the corresponding highest posterior density credible intervals of the unknown parameters under the assumption of independent gamma priors using the importance sampling procedure. We also compute the approximate Bayes estimates using Lindley's approximation technique. The performance of the Bayes estimates have been compared with maximum likelihood estimates through the Monte Carlo Markov chain techniques. Finally, a real data set have been analysed for illustration purpose.

scholarly journals New Fusarium species from the Kruger National Park, South Africa

MycoKeys ◽  
2018 ◽  
Vol 34 ◽  
pp. 63-92 ◽  
Author(s):  
Marcelo Sandoval-Denis ◽  
Wijnand J. Swart ◽  
Pedro W. Crous
Keyword(s):  
South Africa ◽  
Maximum Likelihood ◽  
New Taxa ◽  
National Park ◽  
Fusarium Species ◽  
Phylogenetic Inference ◽  
Kruger National Park ◽  
Bayesian Approaches ◽  
Molecular Analyses ◽  
Species Complexes

Three new Fusarium species, F.convolutans, F.fredkrugeri, and F.transvaalense (Ascomycota, Hypocreales, Nectriaceae) are described from soils collected in a catena landscape on a research supersite in the Kruger National Park, South Africa. The new taxa, isolated from the rhizosphere of three African herbaceous plants, Kyphocarpaangustifolia, Melhaniaacuminata, and Sidacordifolia, are described and illustrated by means of morphological and multilocus molecular analyses based on sequences from five DNA loci (CAL, EF-1 α, RPB1, RPB2 and TUB). According to phylogenetic inference based on Maximum-likelihood and Bayesian approaches, the newly discovered species are distributed in the Fusariumbuharicum, F.fujikuroi, and F.sambucinum species complexes.

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