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http://dx.doi.org/10.5351/CSAM.2016.23.4.321

Power t distribution  

Zhao, Jun (Department of Applied Statistics, Konkuk University)
Kim, Hyoung-Moon (Department of Applied Statistics, Konkuk University)
Publication Information
Communications for Statistical Applications and Methods / v.23, no.4, 2016 , pp. 321-334 More about this Journal
Abstract
In this paper, we propose power t distribution based on t distribution. We also study the properties of and inferences for power t model in order to solve the problem of real data showing both skewness and heavy tails. The comparison of skew t and power t distributions is based on density plots, skewness and kurtosis. Note that, at the given degree of freedom, the kurtosis's range of the power t model surpasses that of the skew t model at all times. We draw inferences for two parameters of the power t distribution and four parameters of the location-scale extension of power t distribution via maximum likelihood. The Fisher information matrix derived is nonsingular on the whole parametric space; in addition we obtain the profile log-likelihood functions on two parameters. The response plots for different sample sizes provide strong evidence for the estimators' existence and unicity. An application of the power t distribution suggests that the model can be very useful for real data.
Keywords
skew-t distribution; Fisher information matrix; heavy tail; profile likelihood; skewness; maximum likelihood; four parameter distribution;
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