Heavy-tailed random samples, as well their sum or average, are encountered in a number of signal processing applications radar, communications, finance, and natural sciences. Modeling such data through the Pareto distribution is particularly attractive due to its simple analytical form, but may lead infinite variance and/or mean, which not physically plausible: fact, samples always bounded prac...

Abstract Pareto distributions are widely used models in economics, finance and actuarial sciences. As a result, number of goodness-of-fit tests have been proposed for these the literature. We provide an overview existing distribution, focussing specifically on type I distribution. To date, only single paper testing has published. However, mentioned much wider scope than is case current as it co...

Employing profits data of Japanese firms in 2003–2005, we kinematically exhibit the static log-normal distribution in the middle scale region. In the derivation, a Non-Gibrat’s law under the detailed balance is adopted together with following two approximations. Firstly, the probability density function of profits growth rate is described as a tent-shaped exponential function. Secondly, the val...

The analytical form of general affine transform families with givenmaximum likelihood estimators for the affine parameters is determined. In this context, the simultaneous maximum likelihood equations of the affine parameters in the generalised Pareto distribution cannot have a common solution. This pathological situation is removed by extending it to a four parameter family, called Pareto type...