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

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.

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

Complexity ◽

10.1155/2021/5533799 ◽

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.

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Estimation Methods of Alpha Power Exponential Distribution with Applications to Engineering and Medical Data

Pakistan Journal of Statistics and Operation Research ◽

10.18187/pjsor.v16i1.3129 ◽

2020 ◽

pp. 149-166 ◽

Cited By ~ 6

Author(s):

Mazen Nassar ◽

Ahmed Z. Afify ◽

Mohammed Shakhatreh

Keyword(s):

Monte Carlo ◽

Monte Carlo Simulations ◽

Exponential Distribution ◽

Real Data ◽

Medical Data ◽

Estimation Methods ◽

Alpha Power ◽

Unknown Parameters ◽

Data Set ◽

Distribution Parameters

This paper addresses the estimation of the unknown parameters of the alphapower exponential distribution (Mahdavi and Kundu, 2017) using nine frequentist estimation methods. We discuss the nite sample properties of the parameterestimates of the alpha power exponential distribution via Monte Carlo simulations. The potentiality of the distribution is analyzed by means of two real datasets from the elds of engineering and medicine. Finally, we use the maximumlikelihood method to derive the estimates of the distribution parameters undercompeting risks data and analyze one real data set.

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On Progressive Type-II Censored Samples from Alpha Power Exponential Distribution

Journal of Mathematics ◽

10.1155/2020/2584184 ◽

2020 ◽

Vol 2020 ◽

pp. 1-8

Author(s):

Mukhtar M. Salah

Keyword(s):

Exponential Distribution ◽

Interval Estimation ◽

Location Parameter ◽

Alpha Power ◽

Type Ii ◽

Unknown Parameters ◽

Progressive Type ◽

Type Ii Censored Data ◽

Best Linear Unbiased Estimators ◽

Two Parameter

In this paper the two-parameter α -power exponential distribution is studied. We study the two-parameter α -power exponential μ , λ distribution with the location parameter μ > 0 and scale parameter λ > 0 under progressive Type-II censored data with fixed shape parameter α . We estimate the maximum likelihood estimators of these unknown parameters numerically since it cannot be solved analytically. We use the approximate best linear unbiased estimators μ ∗ and λ ∗ , as an initial guesses to obtain the MLEs μ ^ and λ ^ . We estimate the interval estimation of these unknowns’ parameters. Monte Carlo simulations are performed and data examples have been provided for illustration and comparison.

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Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.1.39 ◽

2020 ◽

pp. 507-522

Author(s):

Parisa Torkaman

Keyword(s):

Least Squares ◽

Exponential Distribution ◽

Mean Squared Error ◽

Weighted Least Squares ◽

Real Data ◽

Minimum Variance ◽

Cumulative Distribution ◽

Estimation Methods ◽

Data Set ◽

Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

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New Method for Generating New Families of Distributions

Symmetry ◽

10.3390/sym13040726 ◽

2021 ◽

Vol 13 (4) ◽

pp. 726

Author(s):

Lamya A. Baharith ◽

Wedad H. Aljuhani

Keyword(s):

Exponential Distribution ◽

Real Data ◽

Rate Function ◽

New Method ◽

Likelihood Method ◽

Alpha Power ◽

Unknown Parameters ◽

Failure Rate Function ◽

New Approach ◽

Numerical Studies

This article presents a new method for generating distributions. This method combines two techniques—the transformed—transformer and alpha power transformation approaches—allowing for tremendous flexibility in the resulting distributions. The new approach is applied to introduce the alpha power Weibull—exponential distribution. The density of this distribution can take asymmetric and near-symmetric shapes. Various asymmetric shapes, such as decreasing, increasing, L-shaped, near-symmetrical, and right-skewed shapes, are observed for the related failure rate function, making it more tractable for many modeling applications. Some significant mathematical features of the suggested distribution are determined. Estimates of the unknown parameters of the proposed distribution are obtained using the maximum likelihood method. Furthermore, some numerical studies were carried out, in order to evaluate the estimation performance. Three practical datasets are considered to analyze the usefulness and flexibility of the introduced distribution. The proposed alpha power Weibull–exponential distribution can outperform other well-known distributions, showing its great adaptability in the context of real data analysis.

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The Censored Beta-Skew Alpha-Power Distribution

Symmetry ◽

10.3390/sym13071114 ◽

2021 ◽

Vol 13 (7) ◽

pp. 1114

Author(s):

Guillermo Martínez-Flórez ◽

Roger Tovar-Falón ◽

María Martínez-Guerra

Keyword(s):

Power Distribution ◽

Information Matrix ◽

Real Data ◽

Likelihood Method ◽

Data Sets ◽

Alpha Power ◽

Score Functions ◽

New Family ◽

Two Parameters ◽

Family Of Distributions

This paper introduces a new family of distributions for modelling censored multimodal data. The model extends the widely known tobit model by introducing two parameters that control the shape and the asymmetry of the distribution. Basic properties of this new family of distributions are studied in detail and a model for censored positive data is also studied. The problem of estimating parameters is addressed by considering the maximum likelihood method. The score functions and the elements of the observed information matrix are given. Finally, three applications to real data sets are reported to illustrate the developed methodology.

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Mixture of Inverse Weibull and Lognormal Distributions: Properties, Estimation, and Illustration

Mathematical Problems in Engineering ◽

10.1155/2015/526786 ◽

2015 ◽

Vol 2015 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

K. S. Sultan ◽

A. S. Al-Moisheer

Keyword(s):

Information Matrix ◽

Real Data ◽

Likelihood Method ◽

Model Parameters ◽

Component Mixture ◽

Data Set ◽

Hazard Functions ◽

Lognormal Distributions ◽

Proposed Model ◽

Estimation Of Model Parameters

We discuss the two-component mixture of the inverse Weibull and lognormal distributions (MIWLND) as a lifetime model. First, we discuss the properties of the proposed model including the reliability and hazard functions. Next, we discuss the estimation of model parameters by using the maximum likelihood method (MLEs). We also derive expressions for the elements of the Fisher information matrix. Next, we demonstrate the usefulness of the proposed model by fitting it to a real data set. Finally, we draw some concluding remarks.

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Estimation of Multicomponent Reliability Based on Progressively Type II Censored Data from Unit Weibull Distribution

WSEAS TRANSACTIONS ON MATHEMATICS ◽

10.37394/23206.2021.20.30 ◽

2021 ◽

Vol 20 ◽

pp. 288-299

Author(s):

Refah Mohammed Alotaibi ◽

Yogesh Mani Tripathi ◽

Sanku Dey ◽

Hoda Ragab Rezk

Keyword(s):

Information Matrix ◽

Credible Interval ◽

Estimation Methods ◽

Type Ii ◽

Parametric Function ◽

Data Set ◽

Common Parameter ◽

Bayesian Procedures ◽

Mh Algorithm ◽

Type Ii Censored Data

In this paper, inference upon stress-strength reliability is considered for unit-Weibull distributions with a common parameter under the assumption that data are observed using progressive type II censoring. We obtain di_erent estimators of system reliability using classical and Bayesian procedures. Asymptotic interval is constructed based on Fisher information matrix. Besides, boot-p and boot-t intervals are also obtained. We evaluate Bayes estimates using Lindley's technique and Metropolis-Hastings (MH) algorithm. The Bayes credible interval is evaluated using MH method. An unbiased estimator of this parametric function is also obtained under know common parameter case. Numerical simulations are performed to compare estimation methods. Finally, a data set is studied for illustration purposes.

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