Saddlepoint approximations for the sum of independent non‐identically distributed binomial random variables

We discuss saddlepoint approximations to the distribution of the sum of independent non‐identically distributed binomial random variables. We examine the accuracy of the saddlepoint methods for a sum of 10 binomials with different sets of parameter values. The numerical results indicate that the saddlepoint approximations provide very accurate estimates for the probability mass function and the right‐tail probabilities for the cumulative distribution function of the sum.     

A saddlepoint approximation to the distribution of the sum of independent non‐identically beta random variables

The exact distribution of the sum of more than two independent beta random variables has not been known. Even in terms of approximations, only the normal approximation is known for the sum. Motivated by Murakami [Statistica Neerlandica, 2014, doi:10.1111/stan.12032], we derive here a saddlepoint approximation for the distribution of sum. An extensive simulation study shows that it always performs better than the normal approximation.     

A note on the distribution of the product of zero‐mean correlated normal random variables

The problem of finding an explicit formula for the probability density function of two zero‐mean correlated normal random variables dates back to 1936. Perhaps, surprisingly, this problem was not resolved until 2016. This is all the more surprising given that a very simple proof is available, which is the subject of this note; we identify the product of two zero‐mean correlated normal random variables as a variance‐gamma random variable, from which an explicit formula for the probability density function is immediate.     

On random fuzzy variables of second order and their application to linear statistical inference with fuzzy data

This paper summarizes some results on random fuzzy variables with existing expectation and variance, called random fuzzy variables of second order. Using the Frechét-principle and – via support functions – the embedding of convex fuzzy sets into a Banach space of functions it especially presents a unified view on expectation and variance of random fuzzy variables. These notions are applied in developing linear statistical inference with fuzzy data. Detailed investigations are presented concerning best linear unbiased estimation in linear regression models with fuzzy observations. Received: November 1999     

A Cross‐National Study of Fairness in Asia: How Perceptions of a Lack‐of‐Group Bias and Transparency in the Performance Evaluation System Relate to Job Satisfaction

This study explored how managers’ fairness perceptions of performance evaluation systems differ across countries and relate to their job satisfaction. Lack‐of‐group bias and transparency were the constructs used to assess fairness perceptions. The data sample consisted of 903 Asian managers from the subsidiaries of a leading multinational corporation (MNC) strategically expanding its retail markets in Japan, China, Hong Kong, Malaysia, and Thailand. Results showed that the fairness perceptions of lack‐of‐group bias and transparency concerning the common performance evaluation system varied within these Asian countries. Furthermore, those fairness perceptions were significantly related to job satisfaction among Asian managers overall, as well as in each of the five geographical subgroups with the exception of Hong Kong, where the perception of a lack‐of‐group bias was only marginally related to job satisfaction. These findings offer theoretical implications regarding organizational justice, cross‐national management, and performance evaluation, as well as practical implications for leveraging organizational justice perceptions of performance evaluation systems for the effectiveness of MNCs. © 2015 Wiley Periodicals, Inc.