A COMPARISON OF ESTIMATION METHODS FOR ONE PARAMETER INVERSE GOMPERTZ DISTRIBUTION

In this paper, we compare the methods of estimation for one parameter lifetime distribution, which is a special case of inverse Gompertz distribution. We discuss five different estimation methods such as maximum likelihood method, least-squares method, weighted least-squares method, the method of Anderson-Darling, and the method of Crámer–von Mises. It is evaluated the performances of these estimators via Monte Carlo simulations according to the bias and mean-squared error. Furthermore, two real data applications are performed.

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Bayesian and Classical Estimation for the One Parameter Double Lindley Model

Pakistan Journal of Statistics and Operation Research ◽

10.18187/pjsor.v16i3.2966 ◽

2020 ◽

pp. 409-420 ◽

Cited By ~ 3

Author(s):

Mohamed Ibrahim ◽

Wahhab Mohammed ◽

Haitham M. Yousof

Keyword(s):

Least Squares ◽

Least Squares Method ◽

Weighted Least Squares ◽

Estimation Method ◽

Ordinary Least Squares ◽

Likelihood Method ◽

Unknown Parameters ◽

Weighted Least Squares Method ◽

Von Mises ◽

New Distribution

The main motivation of this paper is to show how the different frequentist estimators of the new distribution perform for different sample sizes and different parameter values and to raise a guideline in choosing the best estimation method for the new model. The unknown parameters of the new distribution are estimated using the maximum likelihood method, ordinary least squares method, weighted least squares method, Cramer-Von-Mises method and Bayesian method. The obtained estimators are compared using Markov Chain Monte Carlo simulations and we observed that Bayesian estimators are more efficient compared to other the estimators.

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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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The Extended Inverse Weibull Distribution: Properties and Applications

Complexity ◽

10.1155/2020/3297693 ◽

2020 ◽

Vol 2020 ◽

pp. 1-11

Author(s):

Said Alkarni ◽

Ahmed Z. Afify ◽

I. Elbatal ◽

M. Elgarhy

Keyword(s):

Least Squares ◽

Weighted Least Squares ◽

Real Data ◽

Weibull Model ◽

Estimation Methods ◽

Type I ◽

Data Application ◽

Inverse Weibull Distribution ◽

Simulation Results ◽

Von Mises

This paper proposes the new three-parameter type I half-logistic inverse Weibull (TIHLIW) distribution which generalizes the inverse Weibull model. The density function of the TIHLIW can be expressed as a linear combination of the inverse Weibull densities. Some mathematical quantities of the proposed TIHLIW model are derived. Four estimation methods, namely, the maximum likelihood, least squares, weighted least squares, and Cramér–von Mises methods, are utilized to estimate the TIHLIW parameters. Simulation results are presented to assess the performance of the proposed estimation methods. The importance of the TIHLIW model is studied via a real data application.

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Exponentiated Generalized Inverted Gompertz Distribution: Properties and Estimation Methods with Applications to Symmetric and Asymmetric Data

Symmetry ◽

10.3390/sym13101868 ◽

2021 ◽

Vol 13 (10) ◽

pp. 1868

Author(s):

Mahmoud El-Morshedy ◽

Adel A. El-Faheem ◽

Afrah Al-Bossly ◽

Mohamed El-Dawoody

Keyword(s):

Least Squares ◽

Weighted Least Squares ◽

Quantile Function ◽

Reliability Function ◽

Moment Generating Function ◽

Rate Function ◽

Estimation Methods ◽

Gompertz Distribution ◽

Asymmetric Data ◽

Von Mises

In this article, a new four-parameter lifetime model called the exponentiated generalized inverted Gompertz distribution is studied and proposed. The newly proposed distribution is able to model the lifetimes with upside-down bathtub-shaped hazard rates and is suitable for describing the negative and positive skewness. A detailed description of some various properties of this model, including the reliability function, hazard rate function, quantile function, and median, mode, moments, moment generating function, entropies, kurtosis, and skewness, mean waiting lifetime, and others are presented. The parameters of the studied model are appreciated using four various estimation methods, the maximum likelihood, least squares, weighted least squares, and Cramér-von Mises methods. A simulation study is carried out to examine the performance of the new model estimators based on the four estimation methods using the mean squared errors (MSEs) and the bias estimates. The flexibility of the proposed model is clarified by studying four different engineering applications to symmetric and asymmetric data, and it is found that this model is more flexible and works quite well for modeling these data.

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Weighted generalized Quasi Lindley distribution: Different methods of estimation, applications for Covid-19 and engineering data

AIMS Mathematics ◽

10.3934/math.2021688 ◽

2021 ◽

Vol 6 (11) ◽

pp. 11850-11878

Author(s):

SidAhmed Benchiha ◽

◽

Amer Ibrahim Al-Omari ◽

Naif Alotaibi ◽

Mansour Shrahili ◽

...

Keyword(s):

Least Squares ◽

Mean Squared Error ◽

Weighted Least Squares ◽

Stochastic Ordering ◽

Real Data ◽

Ordinary Least Squares ◽

Lifetime Distribution ◽

Model Parameters ◽

Lindley Distribution ◽

Von Mises

<abstract><p>Recently, a new lifetime distribution known as a generalized Quasi Lindley distribution (GQLD) is suggested. In this paper, we modified the GQLD and suggested a two parameters lifetime distribution called as a weighted generalized Quasi Lindley distribution (WGQLD). The main mathematical properties of the WGQLD including the moments, coefficient of variation, coefficient of skewness, coefficient of kurtosis, stochastic ordering, median deviation, harmonic mean, and reliability functions are derived. The model parameters are estimated by using the ordinary least squares, weighted least squares, maximum likelihood, maximum product of spacing's, Anderson-Darling and Cramer-von-Mises methods. The performances of the proposed estimators are compared based on numerical calculations for various values of the distribution parameters and sample sizes in terms of the mean squared error (MSE) and estimated values (Es). To demonstrate the applicability of the new model, four applications of various real data sets consist of the infected cases in Covid-19 in Algeria and Saudi Arabia, carbon fibers and rain fall are analyzed for illustration. It turns out that the WGQLD is empirically better than the other competing distributions considered in this study.</p></abstract>

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Statistical Inferences on Odd Fréchet Power Function Distribution

Journal of Reliability and Statistical Studies ◽

10.13052/jrss0974-8024.1417 ◽

2021 ◽

Author(s):

Muhammad Ahsan ul Haq ◽

Mohammed Albassam ◽

Muhammad Aslam ◽

Sharqa Hashmi

Keyword(s):

Least Squares ◽

Weighted Least Squares ◽

Real Data ◽

Estimation Methods ◽

Data Sets ◽

Statistical Inferences ◽

Proposed Model ◽

Power Function Distribution ◽

Anderson Darling ◽

Von Mises

This article introduces a new unit distribution namely odd Fréchet power (OFrPF) distribution. Numerous properties of the proposed model including reliability analysis, moments, and Rényi Entropy for the proposed distribution. The parameters of the OFrPF distribution are obtained using different approaches such as maximum likelihood, least squares, weighted least squares, percentile, Cramer-von Mises, Anderson-Darling. Furthermore, a simulation was performed to study the performance of the suggested model. We also perform a simulation study to analyze the performances of estimation methods derived. The applications are used to show the practicality of OFrPF distribution using two real data sets. OFrPF distribution performed better than other competitive models.

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Comparisons of six different estimation methods for log-Kumaraswamy distribution

Thermal Science ◽

10.2298/tsci190411344t ◽

2019 ◽

Vol 23 (Suppl. 6) ◽

pp. 1839-1847

Author(s):

Caner Tanis ◽

Bugra Saracoglu

Keyword(s):

Monte Carlo ◽

Least Squares ◽

Weighted Least Squares ◽

Real Data ◽

Estimation Methods ◽

Unknown Parameters ◽

Monte Carlo Simulation Study ◽

Kumaraswamy Distribution ◽

Bayesian Least Squares ◽

Von Mises

In this paper, it is considered the problem of estimation of unknown parameters of log-Kumaraswamy distribution via Monte-Carlo simulations. Firstly, it is described six different estimation methods such as maximum likelihood, approximate bayesian, least-squares, weighted least-squares, percentile, and Cramer-von-Mises. Then, it is performed a Monte-Carlo simulation study to evaluate the performances of these methods according to the biases and mean-squared errors of the estimators. Furthermore, two real data applications based on carbon fibers and the gauge lengths are presented to compare the fits of log-Kumaraswamy and other fitted statistical distributions.

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