scholarly journals The Combined-Unified Hybrid Censored Samples from Pareto Distribution: Estimation and Properties

2021 ◽  
Vol 11 (13) ◽  
pp. 6000
Author(s):  
Khalaf S. Sultan ◽  
Walid Emam
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Unknown Parameters ◽  
Hazard Functions ◽  
Hybrid Censoring ◽  
Censored Samples ◽  
Distribution Estimation

In this paper, we use the combined-unified hybrid censoring samples to obtain the maximum likelihood estimates of the unknown parameters, survival, and hazard functions of Pareto distribution. Next, we discuss some efficiency criteria of the maximum likelihood estimators, including; the unbiasedness, consistency, and sufficiency. Additionally, we use MCMC to obtain the Bayesian estimates of the unknown parameters. In addition, we calculate the intervals estimation of the unknown parameters. Finally, we analyze a set of real data in view of the theoretical findings of the paper.

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 The Exponentiated Lindley Geometric Distribution with Applications

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 510
Author(s):  
Bo Peng ◽  
Zhengqiu Xu ◽  
Min Wang
Keyword(s):  
Maximum Likelihood ◽  
Geometric Distribution ◽  
Residual Life ◽  
Information Matrix ◽  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Maximum Likelihood Estimates ◽  
Unknown Parameters

We introduce a new three-parameter lifetime distribution, the exponentiated Lindley geometric distribution, which exhibits increasing, decreasing, unimodal, and bathtub shaped hazard rates. We provide statistical properties of the new distribution, including shape of the probability density function, hazard rate function, quantile function, order statistics, moments, residual life function, mean deviations, Bonferroni and Lorenz curves, and entropies. We use maximum likelihood estimation of the unknown parameters, and an Expectation-Maximization algorithm is also developed to find the maximum likelihood estimates. The Fisher information matrix is provided to construct the asymptotic confidence intervals. Finally, two real-data examples are analyzed for illustrative purposes.

scholarly journals Discriminating between the normal inverse Gaussian and generalized hyperbolic skew-t distributions with a follow-up the stock exchange data

2018 ◽  
Vol 28 (2) ◽  
pp. 185-199
Author(s):  
Hanieh Panahi
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Stock Exchange ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Information Criteria ◽  
Inverse Gaussian ◽  
Unknown Parameters ◽  
Normal Inverse Gaussian ◽  
Exchange Data

The statistical methods for the financial returns play a key role in measuring the goodness-of-fit of a given distribution to real data. As is well known, the normal inverse Gaussian (NIG) and generalized hyperbolic skew-t (GHST) distributions have been found to successfully describe the data of the returns from financial market. In this paper, we mainly consider the discrimination between these distributions. It is observed that the maximum likelihood estimators (MLEs) cannot be obtained in closed form. We propose to use the EM algorithm to compute the maximum likelihood estimators. The approximate confidence intervals of the unknown parameters have been constructed. We then perform a number of goodness-of-fit tests to compare the NIG and GHST distributions for the stock exchange data. Moreover, the Vuong type test, based on the Kullback-Leibler information criteria, has been considered to select the most appropriate candidate model. An important implication of the present study is that the GHST distribution function, in contrast to NIG distribution, may describe more appropriate for the proposed data.

scholarly journals The New Odd Lindley-G Power Series Class of Distributions: Theory, Properties and Applications

2021 ◽  
Vol 16 (3) ◽  
pp. 2819-2941
Author(s):  
Fastel Chipepa ◽  
Broderick Oluyede ◽  
Boikanyo Makubate
Keyword(s):  
Maximum Likelihood ◽  
Power Series ◽  
Structural Properties ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Lorenz Curves ◽  
Proposed Model ◽  
Special Cases ◽  
Family Of Distributions

We propose a new generalized class of distributions called the odd Lindley-G Power Series (OL-GPS) family of distributions and a special class, namely, odd Lindley-Weibull power series (OL-WPS) family of distributions. We also derive the structural properties of the OL-GPS family of distributions including moments, order statistics, Rényi entropy, mean and median deviations, Bonferroni and Lorenz curves, and maximum likelihood estimates. Sub-models of the special cases were also obtained together with their structural properties. A simulation study to examine the consistency of the maximum likelihood estimators for each parameter is presented. Finally, real data examples are presented to illustrate the applicability and usefulness of the proposed model

scholarly journals The lifetime analysis of the Weibull model based on Generalized Type-I progressive hybrid censoring schemes

2022 ◽  
Vol 19 (3) ◽  
pp. 2330-2354
Author(s):  
M. Nagy ◽  
◽  
Adel Fahad Alrasheedi
Keyword(s):  
Real Data ◽  
Weibull Model ◽  
Data Sets ◽  
Type I ◽  
Unknown Parameters ◽  
Hazard Functions ◽  
Hybrid Censoring ◽  
Lifetime Analysis ◽  
Failure Point ◽  
Generalized Type

<abstract><p>In this study, we estimate the unknown parameters, reliability, and hazard functions using a generalized Type-I progressive hybrid censoring sample from a Weibull distribution. Maximum likelihood (ML) and Bayesian estimates are calculated using a choice of prior distributions and loss functions, including squared error, general entropy, and LINEX. Unobserved failure point and interval Bayesian predictions, as well as a future progressive censored sample, are also developed. Finally, we run some simulation tests for the Bayesian approach and numerical example on real data sets using the MCMC algorithm.</p></abstract>

scholarly journals Pareto Distribution under Hybrid Censoring: Some Estimation

2021 ◽  
Vol 19 (1) ◽  
pp. 2-17
Author(s):  
Gyan Prakash
Keyword(s):  
Pareto Distribution ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Data Set ◽  
Hybrid Censoring ◽  
Pareto Model

In the present study, the Pareto model is considered as the model from which observations are to be estimated using a Bayesian approach. Properties of the Bayes estimators for the unknown parameters have studied by using different asymmetric loss functions on hybrid censoring pattern and their risks have compared. The properties of maximum likelihood estimation and approximate confidence length have also been investigated under hybrid censoring. The performances of the procedures are illustrated based on simulated data obtained under the Metropolis-Hastings algorithm and a real data set.

scholarly journals On the Properties of the New Generalized Pareto Distribution and Its Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Najma Salahuddin ◽  
Alamgir Khalil ◽  
Wali Khan Mashwani ◽  
Sharifah Alrajhi ◽  
Sanaa Al-Marzouki ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Mean Squared Error ◽  
Generalized Pareto Distribution ◽  
Real Data ◽  
Parametric Estimation ◽  
Maximum Likelihood Estimates ◽  
Suggested Model ◽  
Practical Applications ◽  
Generalized Pareto

In this paper, a new generalization of the Generalized Pareto distribution is proposed using the generator suggested in [1], named as Khalil Extended Generalized Pareto (KEGP) distribution. Various shapes of the suggested model and important mathematical properties are investigated that includes moments, quantile function, moment-generating function, measures of entropy, and order statistics. Parametric estimation of the model is discussed using the technique of maximum likelihood. A simulation study is performed for the assessment of the maximum likelihood estimates in terms of their bias and mean squared error using simulated sample estimates. The practical applications are illustrated via two real data sets from survival and reliability theory. The suggested model provided better fits than the other considered models.

The exponentiated exponential burr XII distribution: Theory and application to lifetime data

2020 ◽  
pp. 1-14
Author(s):  
Majdah M. Badr
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Significant Heterogeneity ◽  
Lifetime Data ◽  
Fit Statistics ◽  
Mathematical Properties ◽  
New Distribution

Lifetime data collected from reliability tests are among data that often exhibit significant heterogeneity caused by variations in manufacturing which make standard lifetime models inadequate. In this paper we introduce a new lifetime distribution derived from T-X family technique called exponentiated exponential Burr XII (EE-BXII) distribution. We establish various mathematical properties. The maximum likelihood estimates (MLE) for the EE-BXII parameters are derived. We estimate the precision of the maximum likelihood estimators via simulation study. Some numerical illustrations are performed to study the behavior of the obtained estimators. Finally the model is applied to a real dataset. We apply goodness of fit statistics and graphical tools to examine the adequacy of the EE-BXII distribution. The importance of this research lies in deriving a new distribution under the name EE-BXII, which is considered the best distributions in analyzing data of life times at present if compared to many distributions in analysis real data.

A new generalized Lindley-Weibull class of distributions: Theory, properties and applications

2021 ◽  
Vol 71 (1) ◽  
pp. 211-234
Author(s):  
Boikanyo Makubate ◽  
Thatayaone Moakofi ◽  
Broderick Oluyede
Keyword(s):  
Maximum Likelihood ◽  
Power Series ◽  
Order Statistics ◽  
Simulation Study ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Mean Square ◽  
Lorenz Curves ◽  
Special Case

Abstract We propose a new generalized class of distributions called Lindley-Weibull Power Series (LWPS) distributions and their special case called Lindley-Weibull logarithmic (LWL) distributions. Structural properties of the LWPS class of distributions and its sub-model LWL distribution including moments, order statistics, Rényi entropy, mean and median deviations, Bonferroni and Lorenz curves, and maximum likelihood estimates are derived. A simulation study to examine the bias and mean square error of the maximum likelihood estimators for each parameter is presented. Finally, real data examples are presented to illustrate the applicability and usefulness of the proposed class of distributions.

scholarly journals The New Odd Lindley-G Power Series Class of Distributions: Theory, Properties and Applications

2021 ◽  
Vol 16 (3) ◽  
pp. 2825-2949
Author(s):  
Fastel Chipepa ◽  
Broderick Oludeye ◽  
Boikanyo Makubate
Keyword(s):  
Maximum Likelihood ◽  
Power Series ◽  
Structural Properties ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Lorenz Curves ◽  
Proposed Model ◽  
Special Cases ◽  
Family Of Distributions

We propose a new generalized class of distributions called the odd Lindley-G Power Series (OL-GPS) family of distributions and a special class, namely, odd Lindley-Weibull power series (OL-WPS) family of distributions. We also derive the structural properties of the OL-GPS family of distributions including moments, order statistics, Rényi entropy, mean and median deviations, Bonferroni and Lorenz curves, and maximum likelihood estimates. Sub-models of the special cases were also obtained together with their structural properties. A simulation study to examine the consistency of the maximum likelihood estimators for each parameter is presented. Finally, real data examples are presented to illustrate the applicability and usefulness of the proposed model

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