A small sample comparison of maximum likelihood, moments and L-moments methods for the asymmetric exponential power distribution

Delicado, Pedro; Goria, M. N.

doi:10.1016/j.csda.2007.05.021

Cited by 45 publications

(19 citation statements)

References 18 publications

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“…They mention that the LM estimator is efficient in relation to the ML estimator. Similar results are obtained for asymmetric exponential power, generalized Pareto and mixture Weibull distributions, as mentioned in [7], [13], and [16], respectively. We conduct an MC simulation study to verify this efficiency in the cases the BS and EVBS distributions, with results reported in Section 4.…”

Section: Algorithm 2 Approach For Initial Values In Lm Estimation Of supporting

confidence: 73%

“…For example, LM GOF assessment is easy to use and has powerful features for discriminating between distributions. In addition, LM estimators are unbiased, robust and have standard errors (SE) smaller than other estimators [7]. These advantages are particularly important with data which have high variability or skewness, as well as heavy tails, that is, under non-normality.…”

Section: Introductionmentioning

confidence: 99%

“…Estimation of θ then involves the minimization of g(θ). The objective function given in equation (16) was chosen by [7] as the standard least squares (LS) solution surface, which can become quite flat far away from the minimum. For the BS distribution, the objective function given in equation (16) is…”

Section: Parameter Estimation Based On L-momentsmentioning

confidence: 99%

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L-moments of the Birnbaum–Saunders distribution and its extreme value version: estimation, goodness of fit and application to earthquake data

Lillo

Leiva

Nicolis

et al. 2016

Journal of Applied Statistics

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Understanding patterns in the frequency of extreme natural events, such as earthquakes, is important as it helps in the prediction of their future occurrence and hence provides better civil protection. Distributions describing these events are known to be heavy tailed and positive skew making standard distributions unsuitable for such a situation. The Birnbaum-Saunders distribution and its extreme value version have been widely studied and applied due to their attractive properties. We derive L-moment equations for these distributions and propose novel methods for parameter estimation, goodness-of-fit assessment and model selection. A simulation study is conducted to evaluate the performance of the L-moment estimators, which is compared to that of the maximum likelihood estimators, demonstrating the superiority of the proposed methods. To illustrate these methods in a practical application, a data analysis of real-world earthquake magnitudes, obtained from the global centroid moment tensor catalogue during 1962-2015, is carried out. This application identifies the extreme value Birnbaum-Saunders distribution as a better model than classic extreme value distributions for describing seismic events.

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Section: Algorithm 2 Approach For Initial Values In Lm Estimation Of supporting

confidence: 73%

Section: Introductionmentioning

confidence: 99%

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L-moments of the Birnbaum–Saunders distribution and its extreme value version: estimation, goodness of fit and application to earthquake data

Lillo

Leiva

Nicolis

et al. 2016

Journal of Applied Statistics

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show abstract

“…Recently, L-moments and trimmed L-moments have been noticed as appealing alternatives to conventional moments, see [12] and [6]. We believe that the handling of these number sequences would benefit by an umbral approach.…”

Section: Discussionmentioning

confidence: 99%

Symbolic computation of moments of sampling distributions

Nardo

Guarino

Senato

2008

Computational Statistics & Data Analysis

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By means of the notion of umbrae indexed by multisets, a general method to express estimators and their products in terms of power sums is derived. A connection between the notion of multiset and integer partition leads immediately to a way to speed up the procedures. Comparisons of computational times with known procedures show how this approach turns out to be more efficient in eliminating much unnecessary computation.

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“…The EP distribution has been discussed by many authors, for examples, Leemis (1986), Rajarshi & Rajarshi (1988), Hanagal & Dabade (2015), among others. Moreover, exponential power distribution is not only used by survival analysis but is also related with asymmetrical exponential power distributions in statistics as mentioned in Hazan et al (2003) and Delicado & Goria (2008 In recent years, many researchers have discussed statistical inference about the parameter in the EP model from different perspectives. These works include Xie et al (2002), Barriga et al (2010), Lemonte (2013), etc.…”

Section: Introductionmentioning

confidence: 99%

Maximum Likelihood Estimation of Parameters in Exponential Power Distribution with Upper Record Values

Zhi¹

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A small sample comparison of maximum likelihood, moments and L-moments methods for the asymmetric exponential power distribution

Cited by 45 publications

References 18 publications

L-moments of the Birnbaum–Saunders distribution and its extreme value version: estimation, goodness of fit and application to earthquake data

L-moments of the Birnbaum–Saunders distribution and its extreme value version: estimation, goodness of fit and application to earthquake data

Symbolic computation of moments of sampling distributions

Maximum Likelihood Estimation of Parameters in Exponential Power Distribution with Upper Record Values

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