Efficient estimation of Pareto model using modified maximum likelihood estimators

Estimation based on probability-weighted moments is a well-established method and an excellent alternative to the classic method of moments or the maximum likelihood method, especially for small sample sizes. In this research, we developed a new class of estimators for the parameters of the Pareto type I distribution. A generalization of the probability-weighted moments approach is the foundation for this new class of estimators. It has the advantage of being valid in the entire parameter space of the Pareto distribution. We established the asymptotic normality of the new estimators and applied them to simulated and real datasets in order to illustrate their finite sample behavior. The results of comparisons with the most used estimation methods were also analyzed.

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“…Combining the asymptotic results for T 0 and T n , the limit distribution in (27) follows straightforwardly.…”

Section: Distributional Behavior Of the Lgpwm Estimatorsmentioning

confidence: 89%

“…Singh and Guo [22], Caeiro and Gomes [23,24] and Munir et al [25] considered probability-weighted moment estimators. Bhatti et al [26,27] proposed modified maximum likelihood estimators and Chen et al [28] dealt with the estimation of the Pareto parameters with a modification of ranked set sampling.…”

Section: Introductionmentioning

confidence: 99%

A New Class of Generalized Probability-Weighted Moment Estimators for the Pareto Distribution

Caeiro

Mateus

2023

Mathematics

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“…These modifications outperformed the existing traditional procedures for different probability distributions like 3-parameter Weibull, lognormal, Rayleigh, Exponential and Pareto. [28][29][30][31][32][33] Modified estimation strategy was also used and recommended for the estimation of two-parameter Power Function distribution by Zaka and Akhtar. 34 Keeping in view the relevance of the Power Function distribution for real-life modeling, the importance of percentile estimation method and superiority of modified estimators for different probability models, the current paper is focused on proposing some new modified percentile estimators (based on descriptive measures) for the Power Function distribution.…”

Section: Introductionmentioning

confidence: 99%

“…In literature devoted to parameter estimation of probability distributions, starting from Cohen and Whitten, 26,27 different modified estimators have been suggested and compared with the existing ones. These modifications outperformed the existing traditional procedures for different probability distributions like 3‐parameter Weibull, lognormal, Rayleigh, Exponential and Pareto 28–33 . Modified estimation strategy was also used and recommended for the estimation of two‐parameter Power Function distribution by Zaka and Akhtar 34 …”

Section: Introductionmentioning

confidence: 99%

Some modified estimators for efficient estimation of power function model

Bhatti

Irfan

Azeem

et al. 2023

Quality & Reliability Eng

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The Power Function distribution is one of the most suitable distributions for failure times modeling, especially of electric components and devices. The article proposes some new modified estimators for parameter estimation of the Power Function distribution. The proposed modified estimators are based on the mean and geometric mean of the distribution. The performance of these estimators is compared with existing traditional and modified estimators by means of Monte Carlo simulation and two real‐life examples. Total mean square error, total relative deviation, root mean square error and mean absolute error are used as performance criteria. The performance of the estimators is also compared on two real‐life data sets repressing the device failures times. From both, Monte Carlo simulation and real‐life applications, the results indicated that the proposed modified estimators perform better than the competing estimators and hence their use is recommended for parameter estimation of the Power Function probability model. The findings will help to get more precise parameter estimates for the distribution which is very much applied in different fields particularly in modelling failure times of electronic devices and components.

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“…Dalpatadu and Singh 29 proposed estimators based on minimization of a distance function. Modified percentile and maximum likelihood estimators were studied in Bhatti et al 30,31 . The estimation of a parametric function of the scale and shape parameters was studied in Barranco‐Chamorro and Jiménez‐Gamero 5 .…”

Section: Introductionmentioning

confidence: 99%

A new class of estimators for the shape parameter of a Pareto model

Mateus

Caeiro

2020

Comp and Math Methods

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The Pareto model, first used in socioeconomic problems, has successfully been applied in many other areas such as astronomy, biology, bibliometrics, demography, insurance, or risk management. Although there are several variants of this distribution, the current study focuses on the classic Pareto distribution, also known as the Pareto type I distribution. We propose a new class of estimators for the Pareto shape parameter, obtained through a modification of the probability weighted moment method, called the log generalized probability weighted moments method. In addition to the asymptotic distribution, Monte Carlo simulations were performed to analyze the finite sample behavior of the proposed new estimators. A comparison with the most used estimators, such as the moment, the maximum likelihood, the least squares, and the probability weighted moments estimators was also performed. In addition, the estimators were used to construct asymptotic confidence intervals. To illustrate an application of the different estimation methods to a real data set from a clinical trial complete the article. Results indicate an overall good performance of the new proposed class.

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Efficient estimation of Pareto model using modified maximum likelihood estimators

Abstract: In this article, we have proposed some modifications in the maximum likelihood estimation for estimating the parameters of the Pareto distribution and evaluated performance of these modified estimators in comparison to the existing maximum

Cited by 3 publications

References 20 publications

A New Class of Generalized Probability-Weighted Moment Estimators for the Pareto Distribution

A New Class of Generalized Probability-Weighted Moment Estimators for the Pareto Distribution

Some modified estimators for efficient estimation of power function model

A new class of estimators for the shape parameter of a Pareto model

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