Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Power t distribution

  • Zhao, Jun (Department of Applied Statistics, Konkuk University) ;
  • Kim, Hyoung-Moon (Department of Applied Statistics, Konkuk University)
  • Received : 2016.05.24
  • Accepted : 2016.07.15
  • Published : 2016.07.31
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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

Acknowledgement

Supported by : Konkuk University

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