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

2020 ◽  
pp. 149-166 ◽  
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.

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

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.

scholarly journals New Method for Generating New Families of Distributions

Symmetry ◽  
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.

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 Inferences for Weibull parameters under progressively first-failure censored data with binomial random removals

2020 ◽  
Vol 9 (1) ◽  
pp. 47-60
Author(s):  
Samir K. Ashour ◽  
Ahmed A. El-Sheikh ◽  
Ahmed Elshahhat
Keyword(s):  
Monte Carlo ◽  
Censored Data ◽  
Real Data ◽  
Unknown Parameters ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Squared Error Loss Function ◽  
Bayes Estimates ◽  
Monte Carlo Techniques ◽  
Credible Intervals

In this paper, the Bayesian and non-Bayesian estimation of a two-parameter Weibull lifetime model in presence of progressive first-failure censored data with binomial random removals are considered. Based on the s-normal approximation to the asymptotic distribution of maximum likelihood estimators, two-sided approximate confidence intervals for the unknown parameters are constructed. Using gamma conjugate priors, several Bayes estimates and associated credible intervals are obtained relative to the squared error loss function. Proposed estimators cannot be expressed in closed forms and can be evaluated numerically by some suitable iterative procedure. A Bayesian approach is developed using Markov chain Monte Carlo techniques to generate samples from the posterior distributions and in turn computing the Bayes estimates and associated credible intervals. To analyze the performance of the proposed estimators, a Monte Carlo simulation study is conducted. Finally, a real data set is discussed for illustration purposes.

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.

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 On the Estimation Problems for Exponentiated Exponential Distribution under Generalized Progressive Hybrid Censoring

2021 ◽  
Vol 50 (1) ◽  
pp. 24-40
Author(s):  
Aakriti Pandey ◽  
Arun Kaushik ◽  
Sanjay K. Singh ◽  
Umesh Singh
Keyword(s):  
Exponential Distribution ◽  
Real Data ◽  
Expected Number ◽  
Unknown Parameters ◽  
Data Set ◽  
Mean Squared Errors ◽  
Entropy Measures ◽  
Estimation Problems ◽  
Censored Sample ◽  
Termination Time

In this article, we considered the statistical inference for the unknown parameters of exponentiated exponential distribution based on a generalized progressive hybrid censored sample under classical paradigm. We have obtained maximum likelihood estimators of the unknown parameters and confidence intervals utilizing asymptotic theory. Entropy measures, such as Shannon entropy and Awad sub-entropy, have been obtained to measure loss of information owing to censoring. Further, the expected total time of the test and expected number of failures, which are useful during the execution of an experiment, also have been computed. The performance of the estimators have been discussed based on mean squared errors. Moreover, the effect of choice of parameters, termination time T, and m on the ETTT and ETNFs also have been observed. For illustrating the proposed methodology, a real data set is considered.

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 Statistical inference for Kumaraswamy-exponential distribution based on progressive Type-II censored data with binomial removals

2020 ◽  
Vol 53 (2) ◽  
pp. 147-163
Author(s):  
RAKHI MOHAN ◽  
MANOJ CHACKO
Keyword(s):  
Exponential Distribution ◽  
Loss Function ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Type Ii ◽  
Bayes Estimators ◽  
Estimation Of Parameters ◽  
Unknown Parameters ◽  
Data Set ◽  
Better Than

In this paper, estimation of parameters of Kumaraswamy-exponential distribution with shape parameters α and β is considered based on a progressively type-II censored sample with binomial removals. Together with the unknown parameters, the removal probability p is also estimated. Bayes estimators are obtained using different loss functions such as squared error, LINEX loss function and entropy loss function. All Bayesian estimates are compared with the corresponding maximum likelihood estimates numerically in terms of their bias and mean square error values and found that Bayes estimators perform better than MLE’s for β and p and MLEs perform better than Bayes estimators for α. A real data set is also used for illustration.

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