arXiv subjects

Takayuki Shiohama

Publications and source records attributed to Takayuki Shiohama.

3 recordsLinked to original sources

arXiv2024

A mixture transition distribution modeling for higher-order circular Markov processes

The stationary higher-order Markov process for circular data is considered. We employ the mixture transition distribution (MTD) model to express the transition density of the process on the circle. The underlying circular transition distribution is based on Wehrly and Johnson's bivariate joint circular models. The structures of the circular autocorrelation function together with the circular partial autocorrelation function are found to be similar to those of the autocorrelation and partial autocorrelation functions of the real-valued autoregressive process when the underlying binding density has zero sine moments. The validity of the model is assessed by applying it to some Monte Carlo simulations and real directional data.

stat.ME↗

arXiv2024

An extension of sine-skewed circular distributions

Sine-skewed circular distributions are identifiable and have easily-computable trigonometric moments and a simple random number generation algorithm, whereas they are known to have relatively low levels of asymmetry. This study proposes a new family of circular distributions that can be skewed more significantly than that of existing models. It is shown that a subfamily of the proposed distributions is identifiable with respect to parameters and all distributions in the subfamily have explicit trigonometric moments and a simple random number generation algorithm. The maximum likelihood estimation for model parameters is considered and its finite sample performances are investigated by numerical simulations. Some real data applications are illustrated for practical purposes.

stat.ME↗

arXiv2022

Identifiability of asymmetric circular and cylindrical distributions

Identifiability of statistical models is a fundamental and essential condition that is required to prove the consistency of maximum likelihood estimators. The identifiability of the skew families of distributions on the circle and cylinder for estimating model parameters has not been fully investigated in the literature. In this paper, a new method combining the trigonometric moments and the simultaneous Diophantine approximation is proposed to prove the identifiability of asymmetric circular and cylindrical distributions. Using this method, we prove the identifiability of general sine-skewed circular distributions, including the sine-skewed von Mises and sine-skewed wrapped Cauchy distributions, and that of a Möbius transformed cardioid distribution, which can be regarded as asymmetric distributions on the unit circle. In addition, we prove the identifiability of two cylindrical distributions wherein both marginal distributions of a circular random variable are the sine-skewed wrapped Cauchy distribution, and conditional distributions of a random variable on the non-negative real line given the circular random variable are a Weibull distribution and a generalized Pareto-type distribution, respectively.

math.ST↗