Power t distribution

• Published in: Communications for statistical applications and methods Vol. 23; no. 4; pp. 321 - 334
• Main Authors: Zhao, Jun, Kim, Hyoung-Moon
• Format: Journal Article
• Language: English; Korean
• Published: 한국통계학회 31.07.2016
• Subjects: Fisher information matrix; four parameter distribution; heavy tail; maximum likelihood; profile likelihood; skew-t distribution; skewness; skew-t distribution; heavy tail; profile likelihood; maximum likelihood; skewness; four parameter distribution; Fisher information matrix
• ISSN: 2287-7843
• DOI: 10.5351/CSAM.2016.23.4.321

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.