Dispersive ordering of fail-safe systems with heterogeneous exponential components

Let X ₁, . . . , X _n be independent exponential random variables with respective hazard rates λ₁, . . . , λ _n , and Y ₁, . . . , Y _n be independent and identically distributed random variables from an exponential distribution with hazard rate λ. Then, we prove that X _2:n , the second order statistic from X ₁, . . . , X _n , is larger than Y _2:n , the second order statistic from Y ₁, . . . , Y _n , in terms of the dispersive order if and only if

$\lambda\geq \sqrt{\frac{1}{{n\choose 2}}\sum_{1\leq i < j\leq n}\lambda_i\lambda_j}.$

We also show that X _2:n is smaller than Y _2:n in terms of the dispersive order if and only if

$ \lambda\le\frac{\sum^{n}_{i=1} \lambda_i-{\rm max}_{1\leq i\leq n} \lambda_i}{n-1}. $

Moreover, we extend the above two results to the proportional hazard rates model. These two results established here form nice extensions of the corresponding results on hazard rate, likelihood ratio, and MRL orderings established recently by Pǎltǎnea (J Stat Plan Inference 138:1993–1997, 2008), Zhao et al. (J Multivar Anal 100:952–962, 2009), and Zhao and Balakrishnan (J Stat Plan Inference 139:3027–3037, 2009), respectively.

     

An algorithm for panel ANOVA with grouped data

In this paper, we present an algorithm suitable for analysing the variance of panel data when some observations are either given in grouped form or are missed. The analysis is carried out from the perspective of ANOVA panel data models with general errors. The classification intervals of the grouped observations may vary from one to another, thus the missing observations are in fact a particular case of grouping. The proposed Algorithm (1) estimates the parameters of the panel data models; (2) evaluates the covariance matrices of the asymptotic distribution of the time-dependent parameters assuming that the number of time periods, T, is fixed and the number of individuals, N, tends to infinity and similarly, of the individual parameters when T → ∞ and N is fixed; and, finally, (3) uses these asymptotic covariance matrix estimations to analyse the variance of the panel data.     

The influence of variables of attitude on collective entrepreneurship

In the current global corporate climate that surrounds us, firms would do well to encourage the talent and creativity of their employees in order to achieve success. This is achieved, not by giving priority to individual talent, but by optimizing the collective as a whole and the firm’s activity based on team work and joint effort. Heads of organizations might benefit from creating a favorable context for the birth and growth of collective internal cooperation, which is understood to be the collective ability to create and innovate on the part of the team, the firm or the organization. Having contrasted our hypotheses through research on Spanish firms, we have concluded that job satisfaction and commitment to the team are factors that have a direct and positive effect on collective entrepreneurship.     

Recent evidence on the impact of government budget deficits on the ex ante real interest rate yield on Moody’s Baa-rated corporate bonds

This study provides recent empirical evidence on the impact of the federal budget deficit on the ex ante real interest rate yield on Moody’s Baa-rated corporate bonds. The study is couched within an open loanable funds model that includes the ex ante real short term real interest rate, the M1 money supply, net international capital inflows, and the unemployment rate. Using quarterly data for the period 1973.1–2007.4, two-stage least squares estimation reveals that the federal budget deficit, expressed as a percent of GDP, exercised a positive and statistically significant impact on the ex ante real interest rate yield on these corporate issues.