scholarly journals Asymptotically Normal Estimators for the Parameters of the Gamma-Exponential Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 273
Author(s):  
Alexey Kudryavtsev ◽  
Oleg Shestakov
Keyword(s):  
Exponential Distribution ◽  
Probabilistic Models ◽  
Real Data ◽  
Infinite Divisibility ◽  
Applied Theory ◽  
Research Attention ◽  
Asymptotically Normal ◽  
Modified Method ◽  
Asymptotic Confidence Intervals ◽  
Logarithmic Moments

Currently, much research attention has focused on generalizations of known mathematical objects in order to obtain adequate models describing real phenomena. An important role in the applied theory of probability and mathematical statistics is the gamma class of distributions, which has proven to be a convenient and effective tool for modeling many real processes. The gamma class is quite wide and includes distributions that have useful properties such as, for example, infinite divisibility and stability, which makes it possible to use distributions from this class as asymptotic approximations in various limit theorems. One of the most important tasks of applied statistics is to obtain estimates of the parameters of the model distribution from the available real data. In this paper, we consider the gamma-exponential distribution, which is a generalization of the distributions from the gamma class. Estimators for some parameters of this distribution are given, and the asymptotic normality of these estimators is proven. When obtaining the estimates, a modified method of moments was used, based on logarithmic moments calculated on the basis of the Mellin transform for the generalized gamma distribution. On the basis of the results obtained, asymptotic confidence intervals for the estimated parameters are constructed. The results of this work can be used in the study of probabilistic models based on continuous distributions with an unbounded non-negative support.

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 The Flexible Burr X-G Family: Properties, Inference, and Applications in Engineering Science

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 474
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Ibrahim Elbatal ◽  
Hazem Al-Mofleh ◽  
Ahmed M. Gemeay ◽  
Ahmed Z. Afify ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Exponential Distribution ◽  
Real Data ◽  
Exponential Model ◽  
Statistical Properties ◽  
Engineering Science ◽  
Data Sets ◽  
Engineering Sciences ◽  
General Statistical ◽  
Anderson Darling

In this paper, we introduce a new flexible generator of continuous distributions called the transmuted Burr X-G (TBX-G) family to extend and increase the flexibility of the Burr X generator. The general statistical properties of the TBX-G family are calculated. One special sub-model, TBX-exponential distribution, is studied in detail. We discuss eight estimation approaches to estimating the TBX-exponential parameters, and numerical simulations are conducted to compare the suggested approaches based on partial and overall ranks. Based on our study, the Anderson–Darling estimators are recommended to estimate the TBX-exponential parameters. Using two skewed real data sets from the engineering sciences, we illustrate the importance and flexibility of the TBX-exponential model compared with other existing competing distributions.

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 The Weibull Generalized Exponential Distribution with Censored Sample: Estimation and Application on Real Data

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Hisham M. Almongy ◽  
Ehab M. Almetwally ◽  
Randa Alharbi ◽  
Dalia Alnagar ◽  
E. H. Hafez ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Exponential Distribution ◽  
Estimation Method ◽  
Interval Estimation ◽  
Likelihood Estimation ◽  
Real Data ◽  
Mcmc Methods ◽  
Generalized Exponential Distribution ◽  
Censored Sample ◽  
Sample Maximum

This paper is concerned with the estimation of the Weibull generalized exponential distribution (WGED) parameters based on the adaptive Type-II progressive (ATIIP) censored sample. Maximum likelihood estimation (MLE), maximum product spacing (MPS), and Bayesian estimation based on Markov chain Monte Carlo (MCMC) methods have been determined to find the best estimation method. The Monte Carlo simulation is used to compare the three methods of estimation based on the ATIIP-censored sample, and also, we made a bootstrap confidence interval estimation. We will analyze data related to the distribution about single carbon fiber and electrical data as real data cases to show how the schemes work in practice.

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 On Erlang-Truncated Exponential Distribution: Theory and Application

2021 ◽  
pp. 155-168
Author(s):  
Ibrahim Elbatal ◽  
A. Aldukeel
Keyword(s):  
Exponential Distribution ◽  
Real Data ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Mean Deviation ◽  
Model Parameters ◽  
Data Sets ◽  
Survival Times ◽  
New Distribution ◽  
Better Than

In this article, we introduce a new distribution called the McDonald Erlangtruncated exponential distribution. Various structural properties including explicit expressions for the moments, moment generating function, mean deviation of the new distribution are derived. The estimation of the model parameters is performed by maximum likelihood method. The usefulness of the new distribution is illustrated by two real data sets. The new model is much better than other important competitive models in modeling relief times and survival times data sets.

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 Bayesian and Maximum Likelihood Estimation for the Weibull Generalized Exponential Distribution Parameters Using Progressive Censoring Schemes

2018 ◽  
pp. 853-868 ◽  
Author(s):  
Ehab Mohamed Almetwally ◽  
Hisham Mohamed Almongy ◽  
Amaal El sayed Mubarak
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Likelihood Method ◽  
Generalized Exponential Distribution ◽  
Progressive Censoring ◽  
Linex Loss ◽  
Distribution Parameters ◽  
Optimal Censoring

In this paper we consider the estimation of the Weibull Generalized Exponential Distribution (WGED) Parameters with Progressive Censoring Schemes. In order to obtain the optimal censoring scheme for WGED, more than one method of estimation was used to reach a better scheme with the best method of estimation. The maximum likelihood method and the method of Bayesian estimation for (square error and Linex) loss function have been used. Monte carlo simulation is used for comparison between the two methods of estimation under censoring schemes. To show how the schemes work in practice; we analyze a strength data for single carbon fibers as a case of real data.

scholarly journals On the Extended Generalized Inverse Exponential Distribution with Its Applications

2020 ◽  
pp. 14-27
Author(s):  
Sule Ibrahim ◽  
Bello Olalekan Akanji ◽  
Lawal Hammed Olanrewaju
Keyword(s):  
Exponential Distribution ◽  
Hazard Rate ◽  
Generalized Inverse ◽  
Real Data ◽  
Quantile Function ◽  
Exponential Model ◽  
Data Sets ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
Inverse Exponential Distribution

We propose a new distribution called the extended generalized inverse exponential distribution with four positive parameters, which extends the generalized inverse exponential distribution. We derive some mathematical properties of the proposed model including explicit expressions for the quantile function, moments, generating function, survival, hazard rate, reversed hazard rate and odd functions. The method of maximum likelihood is used to estimate the parameters of the distribution. We illustrate its potentiality with applications to two real data sets which show that the extended generalized inverse exponential model provides a better fit than other models considered.

Sign in / Sign up

Export Citation Format

Share Document