A theorem due to L. J. Gleser stating that a gamma distribution with shape parameter no greater than one is a mixed exponential distribution is extended to generalized gamma distributions introduced by E. W. Stacy as a special family of lifetime distributions containing both gamma distributions, exponential power and Weibull distributions. It is shown that the mixing distribution is a scale mix...

We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied to Rényi and Tsallis entropies. The generalized entropy maximization procedure for Rényi entropies results in the exponential stationary distribution asymptot...

the combined effect of non-newtonian rheology and irreversible boundary reaction on dispersion in a herschel-bulkley fluid through a conduit (pipe/channel) is studied by using generalized dispersion model. the study explains the development of dispersive transport following the injection of a tracer in terms of three effective transport coefficients namely exchange, convective and dispersion co...

Abstract. In this paper, we propose to study a generalized form of the exponential power distribution which contains others in the literature as special cases. This unifying exponential power distribution is characterized by a parameter ω and a function h(ω) which regulates the tail behavior of the distribution, thus making it more flexible and suitable for modeling than the usual normal di...

Empirical studies of real world networks revealed that degree distribution often follows a heavytailed distribution, a power law. At that time, there were two kinds of network models: the Erdos-Renyi random graph Gn,p and the Small World graphs of Watts and Strogatz. In both models the degrees were very close to the mean degree and there was little variation. Thus, there was the question of fin...

Empirical studies of real world networks revealed that degree distribution often follows a heavytailed distribution, a power law. At that time, there were two kinds of network models: the Erdos-Renyi random graph Gn,p and the Small World graphs of Watts and Strogatz. In both models the degrees were very close to the mean degree and there was little variation. Thus, there was the question of fin...

In this paper, a four parameters extension of the generalized Lindley distribution is introduced. The new distribution includes the power Lindley, Lindley, generalized (Stacy) gamma, gamma, Weibull, Rayleigh, exponential and half-normal distribution. Several statistical properties of the distribution are explored. Then, a bivariate version of the proposed distribution is derived. Using a simula...

To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus can not be used as a standard distribution. Normally professionals in the area use normal distribution with variable parameters or some other approximate di...

Power law cumulative number-size distributions are widely used to describe the scaling properties of data sets and to establish scale invariance. We derive the relationships between the scaling exponents of non-cumulative and cumulative number-size distributions for linearly binned and logarithmically binned data. Cumulative number-size distributions for data sets of many natural phenomena exhi...