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## On a generalization of the logistic distribution

### Annals of the Institute of Statistical Mathematics (1980-12-01) 32: 161-169 , December 01, 1980

### Summary

Expressions for the moment generating functions, cumulants and coefficients of kurtosis of a generalization of the logistic distribution are derived and used to show that any symmetric version of this distribution can be closely and simply approximated by a Student*t* distribution. Related approximation of the distribution of the logistic sample median is discussed.

## Fractional Factorial Designs: General Case

### A Modern Theory of Factorial Designs (2006-01-01): 85-108 , January 01, 2006

Fractional factorial designs with factors at *s* levels, *s* > 2, are used in practice, especially when the investigator anticipates a curvature effect of a quantitative factor or when a qualitative factor has several levels. Extension of the work in Chapter 3 to such designs with *s* being a prime or prime power is considered here. A general discussion on minimum aberration designs and the method of complementary designs are presented. A catalogue of three-level designs with 27 and 81 runs is given.

## A finite mixture model for image segmentation

### Statistics and Computing (2008-06-01) 18: 137-150 , June 01, 2008

In this paper, we propose a model for image segmentation based on a finite mixture of Gaussian distributions. For each pixel of the image, prior probabilities of class memberships are specified through a Gibbs distribution, where association between labels of adjacent pixels is modeled by a class-specific term allowing for different interaction strengths across classes. We show how model parameters can be estimated in a maximum likelihood framework using Mean Field theory. Experimental performance on perturbed phantom and on real benchmark images shows that the proposed method performs well in a wide variety of empirical situations.

## Approximation of Fractional Brownian Motion by Martingales

### Methodology and Computing in Applied Probability (2014-09-01) 16: 539-560 , September 01, 2014

We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exists a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation problem are given.

## Penultimate limiting forms in extreme value theory

### Annals of the Institute of Statistical Mathematics (1984-12-01) 36: 71-85 , December 01, 1984

### Summary

Let {*X*_{n}}_{n≧1} be a sequence of independent, identically distributed random variables. If the distribution function (d.f.) of*M*_{n}=max (*X*_{1},…,*X*_{n}), suitably normalized with attraction coefficients {α_{n}}_{n≧1}(α_{n}>0) and {*b*_{n}}_{n≧1}, converges to a non-degenerate d.f.*G(x)*, as*n*→∞, it is of interest to study the rate of convergence to that limit law and if the convergence is slow, to find other d.f.'s which better approximate the d.f. of*(M*_{n}−b_{n})/a_{n} than*G(x)*, for moderate*n*. We thus consider differences of the form*F*^{n}(a_{n}x+b_{n})−G(x), where*G(x)* is a type I d.f. of largest values, i.e.,*G(x)*≡Λ(*x*)=exp (-exp(−*x*)), and show that for a broad class of d.f.'s*F* in the domain of attraction of Λ, there is a penultimate form of approximation which is a type II [*Ф*_{α}(x)=exp (−x^{−α}), x>0] or a type III [*Ψ*_{α}(x)= exp (−(−x)^{α}), x<0] d.f. of largest values, much closer to*F*^{n}(a_{n}x+b_{n}) than the ultimate itself.

## Consumer Price Indices ‐ September 2011

### Monthly Digest of Statistics (2011-10-01) 790: 68-89 , October 01, 2011

## Development of a Health Management Support System for Patients with Diabetes Mellitus at Home

### Journal of Medical Systems (2010-06-01) 34: 223-228 , June 01, 2010

Recently, a patient with diabetes mellitus (DM) type 2 has been increasing in Japan. The patient should be managed not only by a specialist but also by himself focusing his attention on the improvement of his lifestyle at home. In the present study, we tried to develop a health management support system by which a diabetic patient in early stage can easily enter his daily life information, i.e. the biological information such as the data of blood sugar levels and blood pressure levels etc., the information of exercise and diet and send the information to the medical institution with a personal digital assistant (PDA). Afterwards, the patient can receive health instruction information by the physician in charge for self-care at his home with a PDA. The daily life information sent from the patient is stored in a server installed at the medical institution and analyzed. The physician can obtain the results of analysis by using a PC and send the instruction information necessary for patient management to the patient at home by using e-mail after diagnosing the patient’s condition by the system. To evaluate usability of the developed patient information input system with a PDA, an experiment was conducted by corporation of 20 volunteers who were possible self management and whose age’s range from 20s to 60s by questionnaire survey. As a result, almost examinees answered that lifestyle information could be easily entered by the sense like a mobile-phone and lots of positive opinions were obtained.

## Working with the New Functions

### Working with the American Community Survey in R (2016-01-01): 15-37 , January 01, 2016

We’ve tried to make this User Guide as detailed as possible, to help you learn about the many advanced features of the new package. As a result, it may look like there is a lot to learn, but in fact the basics are pretty simple: to get ACS data for your own user-defined geographies, all you need to do is:

## Galaxy Correlation Function Constraints on Large-Scale Structure

### Digitised Optical Sky Surveys (1992-01-01) 174: 323-334 , January 01, 1992

We consider whether photometric errors may have induced the apparent large-scale, ≥10*h*^{-1} Mpc (where *h* is the Hubble constant in units of 100 km s^{-1} Mpc^{-1}), power in the angular correlation function ω(θ) estimated from the APM galaxy catalogue. Using the galaxy CCD sequences on 39 of the plates in this catalogue we have made an independent estimate of the random and systematic errors in the APM magnitude scale. In particular we have found that the rms error in the plate zero-points is 0.^{m}084, a factor of ∼2 larger than the estimate found by Maddox et al. (1990b). Further, the distribution of the zero-point residuals over the APM survey area suggests that much of this extra error could arise from large-scale magnitude correlations. Thus, taking these observations into account in the estimate of ω(θ), it is shown that the excess power in the galaxy correlation function may be due to photometric calibration errors and that the standard CDM galaxy formation model may not be in contradiction with the observations.

## Stick-Breaking Representation and Computation for Normalized Generalized Gamma Processes

### Sankhya A (2015-08-01) 77: 300-329 , August 01, 2015

Using fractions of gamma and exponentially titled stable random variables this article develops a stick-breaking representation of a truncated normalized generalized gamma process. Sampling from the posterior of this process requires sampling from gamma titled stable random variables and we develop an algorithm to do so that is readily implemented in the open source software *R*. A Blocked Gibbs sampling algorithm for a Bayesian kernel mixture model is then described and we compare the performance of our algorithm with an algorithm recently proposed in the literature.