A comparison of different methods of estimation for the Flexible Weibull distribution

Ali, Sajid; Dey, Sanku; Tahir, M. H.; Mansoor, Muhammad

doi:10.31801/cfsuasmas.597680

Cited by 9 publications

(4 citation statements)

References 33 publications

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“…veloped as an alternative method to the maximum likelihood approach using the Kullback-Leibler information measure [25][26][27][28][29]. Suppose the uniform spacing…”

Section: Maximum Product Spacing Mps Technique Was De-mentioning

confidence: 99%

Bounded Odd Inverse Pareto Exponential Distribution: Properties, Estimation, and Regression

Nasiru¹,

Abubakari²,

Angbing³

2021

International Journal of Mathematics and Mathematical Sciences

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In this paper, we introduce a new three-parameter distribution defined on the unit interval. The density function of the distribution exhibits different kinds of shapes such as decreasing, increasing, left skewed, right skewed, and approximately symmetric. The failure rate function shows increasing, bathtub, and modified upside-down bathtub shapes. Six different frequentist estimation procedures were proposed for estimating the parameters of the distribution and their performance assessed via Monte Carlo simulations. Applications of the distribution were illustrated by analyzing two datasets and its fit compared to that of other distributions defined on the unit interval. Finally, we developed a regression model for a response variable that follows the new distribution.

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“…veloped as an alternative method to the maximum likelihood approach using the Kullback-Leibler information measure [25][26][27][28][29]. Suppose the uniform spacing…”

Section: Maximum Product Spacing Mps Technique Was De-mentioning

confidence: 99%

Bounded Odd Inverse Pareto Exponential Distribution: Properties, Estimation, and Regression

Nasiru¹,

Abubakari²,

Angbing³

2021

International Journal of Mathematics and Mathematical Sciences

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“…For example, Kundu and Raqab (2005) for generalized Rayleigh distributions, Teimouri et al (2013) for Weibull distribution, Ali et al (2020b) for twoparameter logistic-exponential distribution, Dey et al (2014Dey et al ( , 2015Dey et al ( , 2016Dey et al ( , 2017b for the two-parameter Rayleigh, weighted exponential, twoparameter Maxwell, exponentiated-Chen, Dagum, transmuted-Rayleigh, two parameter exponentiated-Gumbel, new extension of generalized exponential and NH distributions. Recent literature in this direction may be seen in Alizadeh et al (2020), Eliwa et al (2020), Tahir et al (2018), Ali et al (2020c), Mansoor et al (2020b), Ali et al (2020a), Shafqat et al (2020) and references cited therein. These methods are the method of moment estimation, method of L-moment estimation, method of probability weighted moment estimation, method of least-squares estimation, method of weighted least-square estimation, method of maximum product spacing estimation and method of minimum distance estimation and so on.…”

Section: Introductionmentioning

confidence: 99%

The Poisson Nadarajah-Haghighi Distribution: Different Methods of Estimation

Ali

Dey²,

Tahir

et al. 2021

JRSS

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Estimation of parameters of Poisson Nadarajah-Haghighi (PNH) distribution from the frequentist and Bayesian point of view is discussed in this article. To this end, we briefly described ten different frequentist approaches, namely, the maximum likelihood estimators, percentile based estimators, least squares estimators, weighted least squares estimators, maximum product of spacings estimators, minimum spacing absolute distance estimators, minimum spacing absolute-log distance estimators, Cramér-von Mises estimators, Anderson-Darling estimators and right-tail Anderson-Darling estimators. To assess the performance of different estimators, Monte Carlo simulations are done for small and large samples. The performance of the estimators is compared in terms of their bias, root mean squares error, average absolute difference between the true and estimated distribution functions, and the maximum absolute difference between the true and estimated distribution functions of the estimates using simulated data. For the Bayesian inference of the unknown parameters, we use Metropolis–Hastings (MH) algorithm to calculate the Bayes estimates and the corresponding credible intervals. Results from the simulation study suggests that among the considered classical methods of estimation, weighted least squares and the maximum product spacing estimators uniformly produces the least biases of the estimates with least root mean square errors. However, Bayes estimates perform better than all other estimates. Finally, we discuss a practical data set to show the application of the distribution.

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“…Minimum distance estimators using these statistical distances are called CvM and AD estimators, see e.g. Louzada et al (2016), Bakouch et al (2017), Akgul and Senoglu (2018), Ali et al (2020), Acitas and Arslan (2020). As it can be seen from these papers, numerical methods should be performed to obtain the corresponding parameter estimates since the estimating equations mostly include nonlinear functions of the parameters.…”

Section: Introductionmentioning

confidence: 99%

Modified minimum distance estimators: definition, properties and applications

2021

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Estimating the location and scale parameters of a distribution is one of the most crucial issues in Statistics. Therefore, various estimators are proposed for estimating them, such as maximum likelihood, method of moments and minimum distance (e.g. Cramérvon Mises-CvM and Anderson Darling-AD), etc. However, in most of the cases, estimators of the location parameter μ and scale parameter σ cannot be obtained in closed forms because of the nonlinear function(s) included in the corresponding estimating equations. Therefore, numerical methods are used to obtain the estimates of these parameters. However, they may have some drawbacks such as multiple roots, wrong convergency, and non-convergency of iterations. In this study, we adopt the idea of Tiku (Biometrika 54:155-165, 1967) into the CvM and AD methodologies with the intent of eliminating the aforementioned difficulties and obtaining closed form estimators of the parameters μ and σ . Resulting estimators are called as modified CvM (MCvM) and modified AD (MAD), respectively. Proposed estimators are expressed as functions of sample observations and thus their calculations are straightforward. This property also allows us to avoid computational cost of iteration. A Monte-Carlo simulation study is conducted to compare the efficiencies of the CvM and AD estimators with their modified counterparts, i.e. the MCvM and MAD, for the normal, extreme value and Weibull distributions for an illustration. Real data sets are used to show the implementation of the proposed estimation methodologies.

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A comparison of different methods of estimation for the Flexible Weibull distribution

Cited by 9 publications

References 33 publications

Bounded Odd Inverse Pareto Exponential Distribution: Properties, Estimation, and Regression

Bounded Odd Inverse Pareto Exponential Distribution: Properties, Estimation, and Regression

The Poisson Nadarajah-Haghighi Distribution: Different Methods of Estimation

Modified minimum distance estimators: definition, properties and applications

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