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.     

Strategic planning for telecommunications—a systems approach

This paper outlines the practical application of a systems approach to designing and implementing the Strategic Planning Process in a mid-sized, capital/technology intensive Canadian telecommunications company. The basic General Systems concepts used are briefly mentioned, the design of the Organization Structure and the Information Structure for the Strategic Planning Process are reviewed, the Operational Dynamics of the Strategic Planning Process outlined, outputs and application case described and conclusions reached.     

On Some New α-Modified Binomial and Poisson Distributions and Their Applications

A new class of α-modified binomial distribution has been proposed, and its distributional properties like probability generating function (pgf), moments, and their interrelations have been studied. Two new α-modified Poisson distributions and Poisson distribution have been obtained as limiting distributions. Modified binomial and Poisson distributions introduced by Berg and Jaworski (1988 Berg , S. , Jaworski , J. ( 1988 ). Modified binomial and Poisson distributions with application in random mapping theory . J. Statist. Plann. Infer. 18 : 313 – 322 . [Google Scholar]) have been seen as particular cases. Mixture distributions of α-modified binomial distributions have been derived. A new distributions called α-modified binomial distributions of type j, their moment properties, limiting distributions as α-modified Poisson distribution of type j, their different convolution properties, pgf, parameter estimators have been studied. Two more new distributions namely Doubly α-modified binomial distributions of type (i, j) and α-modified weighted generalized Poisson distributions of type (j ? 1) have also been studied. Various α-modified binomial and Poisson distributions of Berg and Mutafchiev (1990 Berg , S. , Mutafchiev , L. ( 1990 ). Random mapping with an attracting center: Lagrangian distributions and a regression function . J. Appl. Probab. 27 : 622 – 636 . [Google Scholar]) and Berg and Nowicki (1991 Berg , S. , Nowicki , K. ( 1991 ). Statistical inference for a class of modified power series distributions with applications to random mapping theory . J. Statist. Plann. Infer. 28 : 247 – 261 . [Google Scholar]) have been seen as special cases. Application of some of these proposed distributions have been identified.     

Discrete Gamma Distributions: Properties and Parameter Estimations

A two-parameter discrete gamma distribution is derived corresponding to the continuous two parameters gamma distribution using the general approach for discretization of continuous probability distributions. One parameter discrete gamma distribution is obtained as a particular case. A few important distributional and reliability properties of the proposed distribution are examined. Parameter estimation by different methods is discussed. Performance of different estimation methods are compared through simulation. Data fitting is carried out to investigate the suitability of the proposed distribution in modeling discrete failure time data and other count data.     

On some classifiers based on multivariate ranks

Non parametric approaches to classification have gained significant attention in the last two decades. In this paper, we propose a classification methodology based on the multivariate rank functions and show that it is a Bayes rule for spherically symmetric distributions with a location shift. We show that a rank-based classifier is equivalent to optimal Bayes rule under suitable conditions. We also present an affine invariant version of the classifier. To accommodate different covariance structures, we construct a classifier based on the central rank region. Asymptotic properties of these classification methods are studied. We illustrate the performance of our proposed methods in comparison to some other depth-based classifiers using simulated and real data sets.     

On multivariate quantile regression

To detect the dependence on the covariates in the lower and upper tails of the response distribution, regression quantiles are very useful tools in linear model problems with univariate response. We consider here a notion of regression quantiles for problems with multivariate responses. The approach is based on minimizing a loss function equivalent to that in the case of univariate response. To construct an affine equivariant notion of multivariate regression quantiles, we have considered a transformation retransformation procedure based on ‘data-driven coordinate systems’. We indicate some algorithm to compute the proposed estimates and establish asymptotic normality for them. We also, suggest an adaptive procedure to select the optimal data-driven coordinate system. We discuss the performance of our estimates with the help of a finite sample simulation study and to illustrate our methodology, we analyzed an interesting data-set on blood pressures of a group of women and another one on the dependence of sales performances on creative test scores.     

On an adaptive transformation–retransformation estimate of multivariate location

An affine equivariant estimate of multivariate location based on an adaptive transformation and retransformation approach is studied. The work is primarily motivated by earlier work on different versions of the multivariate median and their properties. We explore an issue related to efficiency and equivariance that was originally raised by Bickel and subsequently investigated by Brown and Hettmansperger. Our estimate has better asymptotic performance than the vector of co-ordinatewise medians when the variables are substantially correlated. The finite sample performance of the estimate is investigated by using Monte Carlo simulations. Some examples are presented to demonstrate the effect of the adaptive transformation–retransformation strategy in the construction of multivariate location estimates for real data.