A Lagrangian Non Central Negative Binomial Distribution of the First Kind

A Lagrangian probability distribution of the first kind is proposed. Its probability mass function is expressed in terms of generalized Laguerre polynomials or, equivalently, a generalized hypergeometric function. The distribution may also be formulated as a Charlier series distribution generalized by the generalizing Consul distribution and a non central negative binomial distribution generalized by the generalizing Geeta distribution. This article studies formulation and properties of the distribution such as mixture, dispersion, recursive formulas, conditional distribution and the relationship with queuing theory. Two illustrative examples of application to fitting are given.     

Nonlinear regression modeling via regularized radial basis function networks

The problem of constructing nonlinear regression models is investigated to analyze data with complex structure. We introduce radial basis functions with hyperparameter that adjusts the amount of overlapping basis functions and adopts the information of the input and response variables. By using the radial basis functions, we construct nonlinear regression models with help of the technique of regularization. Crucial issues in the model building process are the choices of a hyperparameter, the number of basis functions and a smoothing parameter. We present information-theoretic criteria for evaluating statistical models under model misspecification both for distributional and structural assumptions. We use real data examples and Monte Carlo simulations to investigate the properties of the proposed nonlinear regression modeling techniques. The simulation results show that our nonlinear modeling performs well in various situations, and clear improvements are obtained for the use of the hyperparameter in the basis functions.     

A modified Conway–Maxwell–Poisson type binomial distribution and its applications

This article proposes a generalized binomial distribution, which is derived from the finite capacity queueing system with state-dependent service and arrival rates. This distribution is also generated from the conditional Conway–Maxwell–Poisson (CMP) distribution given a sum of two CMP variables. In this article, we consider the properties of the probability mass function, indices of dispersion, skewness and kurtosis, and give applications of the proposed distribution. The estimation method and simulation study are also considered.     

Properties of Lagrangian distributions

Abstract

Lagrange’s expansion is the power series expansion of the inverse function of an analytic function, and it leads to general Lagrangian distributions of the first kind as well as of the second kind. We present some theorems in which different sets of two analytic functions provide a Lagrangian distribution. Potential applicability of the theorem to tandem queueing process is studied.     

Convolution of Binomial and Negative Binomial Variables

This paper considers a distribution formed by convolution of binomial and negative binomial variables. The distribution has the flexibility to adapt to the model under, equi, and over dispersion. Some properties of the proposed distribution are discussed, including characterization. Three stochastic processes leading to the distribution are also considered: (1) a three-dimensional random walk; (2) a birth, death, and immigration process; and (3) a thinned stochastic process.     

Historic evolution of public relations in Japan

This study follows the history of public relations in Japan. Meiji restoration in 1867 marked the beginning of modernization of Japan, but as democratization did not accompany modernization, the country was void of autonomous public. The birth of public relations department, though not in the mainland Japan, can be traced back to the 1920s at South Manchurian Railroad in Japan-controlled-Manchuria. After the World War II, the U.S. led Allied Occupation Army urged national and local government to adopt public relations. Shortly afterwards, ad agencies learned from the U.S. the use of public relations, but as marketing gained ground, public relations came to be used as marketing support tool. Criticism of environmental pollution in the 1970s, overseas expansion of businesses in the 1980s, collapse of bubble economy and business crises in the 1990s and onward, each drove public relations in Japan to increase its importance and expand its field.