Maximum likelihood estimation of the parameters of student’s <i>t</i> Birnbaum-Saunders distribution: a comparative study

Alam, Farouq Mohammad A.

doi:10.1080/03610918.2019.1659359

Cited by 5 publications

(6 citation statements)

References 20 publications

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“…At the same time, this idea is also widely used to derive the MLE of other distributions. See [15,20,21] for more details about recent works in this topic.…”

Section: Mle Using the Em Algorithmmentioning

confidence: 99%

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A New Generalized t Distribution Based on a Distribution Construction Method

Guan

Cheng

et al. 2021

Mathematics

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In this paper, a new generalized t (new Gt) distribution based on a distribution construction approach is proposed and proved to be suitable for fitting both the data with high kurtosis and heavy tail. The main innovation of this article consists of four parts. First of all, the main characteristics and properties of this new distribution are outined. Secondly, we derive the explicit expression for the moments of order statistics as well as its corresponding variance–covariance matrix. Thirdly, we focus on the parameter estimation of this new Gt distribution and introduce several estimation methods, such as a modified method of moments (MMOM), a maximum likelihood estimation (MLE) using the EM algorithm, a novel iterative algorithm to acquire MLE, and improved probability weighted moments (IPWM). Through simulation studies, it can be concluded that the IPWM estimation performs better than the MLE using the EM algorithm and the MMOM in general. The newly-proposed iterative algorithm has better performance than the EM algorithm when the sample kurtosis is greater than 2.7. For four parameters of the new Gt distribution, a profile maximum likelihood approach using the EM algorithm is developed to deal with the estimation problem and obtain acceptable.

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“…At the same time, this idea is also widely used to derive the MLE of other distributions. See [15,20,21] for more details about recent works in this topic.…”

Section: Mle Using the Em Algorithmmentioning

confidence: 99%

“…Balakrishnan (2019) [20] applied this approach to determine the MLEs for the parameters of Student's t Birnbaum-Saunders distribution. As Balakrishnan points out, this method is an example of an exhaustive search.…”

Section: Parameter Estimation Of Ngtmentioning

confidence: 99%

A New Generalized t Distribution Based on a Distribution Construction Method

Guan

Cheng

et al. 2021

Mathematics

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“…Azevedo et al (2012) studied some mathematical aspects of the hazard rate function of the tBS distribution; namely, they examined the shape of the failure rate function of this distribution alongside the change point and discussed associated estimation. Recently, the parameters of the tBS distribution were estimated using the maximum likelihood theory and the expectation-maximization (EM) algorithm in Balakrishnan and Alam (2019). They reported a few anomalies in their simulation outcomes, such as the unsatisfactory efficiency of both the maximum likelihood estimation and the EM algorithm in the case of the tBS distribution with a unity degree of freedom, i.e., the case of the CBS distribution.…”

Section: Introductionmentioning

confidence: 99%

“…As previously mentioned, some aspects of the CBS distribution are counterintuitive. Hence, estimation methods, such as the modified moments methods can not be used as indicated by Balakrishnan and Alam (2019), while other estimation methods might not thrive in this case. Therefore, the aim of this study is to address this scientific computation challenge by performing numerical comparison between several estimators for the model parameters to identify which of them preform superiorly in terms of estimation efficiency and robustness.…”

Section: Introductionmentioning

confidence: 99%

On Comparing Different Methods of Estimation for the Parameters of a Pathological Distribution with Application to Climate Data

Alam

2022

AJS

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In statistical literature, various probability distributions exist with advantageous properties, while others are considered pathological since their properties are counterintuitive. A well-known pathological probability distribution is the Cauchy distribution, and it has applications in areas related to environmental and financial research. Both the log-Cauchy and half-Cauchy distributions, which have close connections to the Cauchy distribution, are pathological distributions. This paper considers another pathological model called the Cauchy Birnbaum-Saunders distribution. Some of the statistical properties of this distribution are discussed briefly, and its parameters are estimated using eight frequentist estimation methods, including the maximum likelihood, least-squares-based, and minimum distance estimation methods. Monte Carlo simulations are carried out to compare and examine the performance of each estimator numerically. Furthermore, a recent climate data set is analyzed to show the practical applicability of this model.

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“…In practice, one can obtain various estimators for the model parameters. Therefore, several researchers conducted comparative Monte Carlo simulation studies to numerically assess the estimators from different statistical and computation perspectives; see, for example, Gupta and Kundu [14], Alkasasbeh and Raqab [15], Mazucheli et al [16], do Espirito Santo and Mazucheli [17], and Balakrishnan and Alam [18], among other research contributions.…”

Section: Introductionmentioning

confidence: 99%

On Modeling Concrete Compressive Strength Data Using Laplace Birnbaum-Saunders Distribution Assuming Contaminated Information

Alam

Nassar

2021

Crystals

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Compressive strength is a well-known measurement to evaluate the endurance of a given concrete mixture to stress factors, such as compressive loads. A suggested approach to assess compressive strength of concrete is to assume that it follows a probability model from which its reliability is calculated. In reliability analysis, a probability distribution’s reliability function is used to calculate the probability of a specimen surviving to a certain threshold without damage. To approximate the reliability of a subject of interest, one must estimate the corresponding parameters of the probability model. Researchers typically formulate an optimization problem, which is often nonlinear, based on the maximum likelihood theory to obtain estimates for the targeted parameters and then estimate the reliability. Nevertheless, there are additional nonlinear optimization problems in practice from which different estimators for the model parameters are obtained once they are solved numerically. Under normal circumstances, these estimators may perform similarly. However, some might become more robust under irregular situations, such as in the case of data contamination. In this paper, nine frequentist estimators are derived for the parameters of the Laplace Birnbaum-Saunders distribution and then applied to a simulated data set and a real data set. Afterwards, they are compared numerically via Monte Carlo comparative simulation study. The resulting estimates for the reliability based on these estimators are also assessed in the latter study.

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Maximum likelihood estimation of the parameters of student’s t Birnbaum-Saunders distribution: a comparative study

Cited by 5 publications

References 20 publications

A New Generalized t Distribution Based on a Distribution Construction Method

A New Generalized t Distribution Based on a Distribution Construction Method

On Comparing Different Methods of Estimation for the Parameters of a Pathological Distribution with Application to Climate Data

On Modeling Concrete Compressive Strength Data Using Laplace Birnbaum-Saunders Distribution Assuming Contaminated Information

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