12 citations · 93 across the 37 of their papers we have counts for
6 papers · 1 filter
Non-existence of measurable solutions of certain functional equations via probabilistic approaches
Kazuki Okamura
This paper deals with functional equations in the form of where is given and and are unknown. We will show that if is a Borel measurable func…
Characterizations of the maximum likelihood estimator of the Cauchy distribution
Kazuki Okamura, Yoshiki Otobe
This paper gives a new approach for the maximum likelihood estimation of the joint of the location and scale of the Cauchy distribution. We regard the joint as a single complex par…
Confidence disc and square for Cauchy distributions
Yuichi Akaoka, Kazuki Okamura, Yoshiki Otobe
We will construct a confidence region of parameters for a sample of size from Cauchy distributed random variables. Although Cauchy distribution has two parameters, a location p…
Bahadur efficiency of the maximum likelihood estimator and one-step estimator for quasi-arithmetic means of the Cauchy distribution
Yuichi Akaoka, Kazuki Okamura, Yoshiki Otobe
Some quasi-arithmetic means of random variables easily give unbiased strongly consistent closed-form estimators of the joint of the location and scale parameters of the Cauchy dist…
Limit theorems for quasi-arithmetic means of random variables with applications to point estimations for the Cauchy distribution
Yuichi Akaoka, Kazuki Okamura, Yoshiki Otobe
We establish some limit theorems for quasi-arithmetic means of random variables. This class of means contains the arithmetic, geometric and harmonic means. Our feature is that the…
On -divergences between Cauchy distributions
Frank Nielsen, Kazuki Okamura
We prove that the -divergences between univariate Cauchy distributions are all symmetric, and can be expressed as strictly increasing scalar functions of the symmetric chi-squar…