Approximate MLEs for the location and scale parameters of the skew logistic distribution

A. Asgharzadeh (), L. Esmaily () and S. Nadarajah ()

Statistical Papers, 2013, vol. 54, issue 2, 411 pages

Abstract: Azzalini (Scand J Stat 12:171–178, 1985 ) provided a methodology to introduce skewness in a normal distribution. Using the same method of Azzalini ( 1985 ), the skew logistic distribution can be easily obtained by introducing skewness to the logistic distribution. For the skew logistic distribution, the likelihood equations do not provide explicit solutions for the location and scale parameters. We present a simple method of deriving explicit estimators by approximating the likelihood equations appropriately. We examine numerically the bias and variance of these estimators and show that these estimators are as efficient as the maximum likelihood estimators (MLEs). The coverage probabilities of the pivotal quantities (for location and scale parameters) based on asymptotic normality are shown to be unsatisfactory, especially when the effective sample size is small. To improve the coverage probabilities and for constructing confidence intervals, we suggest the use of simulated percentage points. Finally, we present a numerical example to illustrate the methods of inference developed here. Copyright Springer-Verlag 2013

Keywords: Maximum-likelihood estimator; Monte Carlo simulation; Pivotal quantity; Skew logistic distribution (search for similar items in EconPapers)
Date: 2013
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://hdl.handle.net/10.1007/s00362-012-0436-3 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stpapr:v:54:y:2013:i:2:p:391-411

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-012-0436-3

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().