• Article  

      An application of a density transform and the local limit theorem 

      Cacoullos, Theophilos; Papadatos, Nickos; Papathanasiou, Vassilis (2002)
      Consider an absolutely continuous random variable X with finite variance σ2. It is known that there exists another random variable X* (which can be viewed as a transformation of X) with a unimodal density, satisfying the ...
    • Article  

      Self-inverse and exchangeable random variables 

      Cacoullos, Theophilos; Papadatos, Nickos (2013)
      A random variable Z will be called self-inverse if it has the same distribution as its reciprocal Z -1. It is shown that if Z is defined as a ratio, X / Y, of two rv's X and Y (with P[X=0]=P[Y=0]=0), then Z is self-inverse ...
    • Article  

      Variance inequalities for covariance kernels and applications to central limit theorems 

      Cacoullos, Theophilos; Papadatos, Nickos; Papathanasiou, Vassilis (1997)
      A simple estimate for the error in the CLT, valid for a wide class of absolutely continuous r.v.'s, is derived without Fourier techniques. This is achieved by using a simple convolution inequality for the variance of ...